JPRS ID: 10210 TRANSLATION SYNCHRONIZATION OF PCISION TIME AND FREQUENY STANDARDS BY GLEB NIKOLAYEVICH PALIY AND YELENA VITOL'DOVNA ARTEM'YEVA

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JPRS L/ 10210
23 December 1981
T rc~nslat~on
- SY~1CHRaNIZATION OF PRECISION T!-ME
AND FREQUENCY STANDARD~
~y
Gleb Nikol~yevich Paliy ar~d Yelena V~~ol'dovna Ar.tem'yeda
. F~~$ FOR~EIGN BROADCAST INFORM~4TION SERVICE
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tUR OFFIC'lAl. t :SF ANI,'1'
JPRS L/10210
23 December 19~1
~ SYNCHRONIZATION OF PRECISION TI~1E AND ~RE9UENCY STANDARDS
~~2oscow SINKHRQNIZATSIYA VY30KOTOCFIN`IRH MER VREMENI I CHASTOTY in
Rt~ssian 1976 (sign~d to press 21 Jun 76) pp 2-39, 60-153, 164-168
[Annotation, introduction, chaptErs 1-3, 5-?, references and table of
= conte~zts from book "Synchronizatiun of Precision Time and ~'requency
Standards"~ by'G1eb Nikolayevic~ Paliy and Yelena Vitol'dovna
Artem'yeva, Izddtel'stvo standarto~>, 5,000 copies, ].68 ~ages]
CONTENTS
Annotation 1
- Introducti~n J.
Qtapter 1. Precisj.on Frequency and Time ~tandar3s 4
?.l. Metro~ogical (haracteristics 4
I.2. StrL:cture of High-Preci~sion Standards 9
(hapter 2. Types of Synchronization of Precision ?~requency and Time
- Standards..........a 19
,~n
2.1. Induced Synchronization '
2.2. Semi-Autonomous Syn^hronization ~3
2.3. Autonomous Synchronization 25
Ghapter 3. Methods of Determining ~'requency Difference of Synchronized
and Synchronizing Standards 26
3.1. Method Based on Rea;~lts of Detarmini.r~g rhe Effe~tive
Frequency of the Standard To Be Synchroni~d 26
' 3.2. Method Based on Measurements of Change in P'hase Differenae
~ of Waveforms of S}mchronizing and Synchronized Standarde...... 30
Ghapter 5. Signal Txansmission Methods Using VLF Radio Channels........... 30
5.1. ~'ransmitting Facilitiea 30
- 5.2, Methods of Tim~ Signal Transmission 32
~ . - a- [I- USSR-MFOUO]
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rvt~ vrrt~.te~t, u.~r, ~ura,t

~
; 5.3. Elements of the Theory o~ VL~ Propagat~qn in the Spherical
Earth-Ionoaphere Waveguide 37
' 5.4. D3ily Variations o.~ rhase and Amplitude o~ Signal at
Reception Point 42
5.5. Method of Calculating Phas~ and Amplitude of a Signal.......... 43 ;
5.6. Error of Calculating Propagation, Time 47
Chapter 6. Methods of Synchronizing Spatially Segarated F'~equency
and Time Standards in the UHF and Microwave Bands ~,9
6.1. Using Reflections From Meteos Trials 50
6.2. Use of Tel~vision Channels 53
6.3. Using Artificial Sate~lites 67
6.4. Using the Orbita Reception-Point System for Global
- Synchronization of Time Scales i2
6.5. Synchronization Error due ~o Inconstaixcy of, Radio Wave
Propagation 76
- Chapter 7. Reco~endations on Synchronizing Time and Hrequency
Standards 77
7.1. Sy~nchronization Facilities 77
i.2. Syn~hronization Methods 81
7.3. Synchr~nizing Frequency Standards 82
7.4. Synchronization ot Time Standards 90
7.5. I~ethods of Processing Reaults of Measurements Made by the
Phase Method 99
7.6. Con$tructing Trape~oids of Changes in p From Results
of ~e Differential Measu~ement Method ....................e... 105
References 106
- b -
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Annotation
[TextJ The book describes the principal methods and means of synchronizing high-
stability frequency and time standards with ma~ar emphasis on new wide-band systems
that have enabled synchronizatj.on of standards separated by different distances
with error c~f 1 us or less. A erief description is given of the corresponding
measurement facflitie~, their basic metrological characteristics are indicatzd,
_ and an examination is made of possible regimes of synchronization of frequency
and time S~~?ards. Methods are described for synchronizing frequency and time
standards situated in direct proximity to one another, methods of transmitting
and calculatin~ travel time of the time and frequency signals in the short-wave
ard VLF bands, methods and means of synchronization in the VHF and microwave bands.
Rkcommendations are m~3e on determining the irradiance of the transmission path,
and on measuring signal delay in receiving and recording equipment, methods of
proczssing m~a~~urement results and deternzining the principal metrological character-
istics of ineasurement facilities. Some inforiaation is given on national time ser-
~ vices� az~d on the ne~a UTC [universal coordinated time] system.
The book is intended far scientific ~orkers o~ the appropriate profile, engineering
- and technical per~onnel of various time and frequency services, and may also.be
of use to undergraduate and graduate students of 3.~stitutions of higher education.
Tables 12, f igures 46, re~ferences 51.
Introduction
The unit of time, the second, is one of the principal physical quantities in all
systems of units, including SI. The unit of frequerc~y, the hertz, is a derivative
unit that corresponds tc, *_he fr~quency of a periodic process such that one cycle
of this process occurs in one second.
Until the mid twentieth century, local time was determined with respect to the
position of a given point of the earth relativ~ to the sun and stars, it being
~ 1
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originally assumed that rotation of the planet takes ~lace unifornily. The period
of rotation of the earth relative to its axis was taken as a natural time standard,
- the mean solar day, and the second was defined as 1/86400 of a mean solar day. As
- measurement technology developed and the requirements for accuracy of ineasuremente
increased, the def inition of the second underwent considerable changes. Even pendu-
lum clocks showed a sys~ematic slowing down of the diurnal rotation of the earth.
To i.^~prove accuracy of reproduction of the unit of time, it was redefined in 1960 ~
with reference to the motion of the earth around the sun based on the astronomical
definition of universaZ ephemeris time. The second was calculated as 1/3155925.9747
of the tropieal year (time between two vernal equinoxes) for Januar~� 0 of the year
1900 at 12 hours ephemeris tir~e.. This improved the accuracy of time reproduction
by nearly two orders of magnitude.
However, the realization of such accuracy require~3 acczunulation pf results of astro-
- nomical observations over a pexiod of one or two years. Besides, it was established
' by quartz clocks that even with consideration of the regular slowing down of d:~urnal
rotation of the earth the duration of a day was still inconstant, i. e. the very
period of revolution of the earth around the sun is sub~ect to irregular fluctua-
tions. The creation of quantum-mechanical sources of electromagnetic waveforms
(these sources are based on the capacity of atoms and molecules to emit and absorb
energy with transition from one energy s~ate to another) enabled introduction of
the concept of the physical c,r atomic se:cond in 1967. This was c?~fin~d as tila
interval of time required for 919263177f) oscillations corresp�~.d.itig to thP r~;~ .onant
_ frequency of the energy transition between levels of the hypzrfir~e structurE~ of
the ground state of an atom of cesi~-133 in the absence of perturbations by ex-
ternal fields.
~ The development of masers enabled refinement of the ninnerical values of the unifor,n
rotation of the earth. It was established that the secular dQCeleration of the
- xotation of the earth due to tidal friction over a century leads L-o.a change in
~ the duration of the day by 0.(3016 s. Seasonal nonunifoYmities ir~ r~tation of the
earth over half a year cause cha~ges in the duration of a dsy by ~.-1 ms (with re~pECt
= to frequency this amounts to ~1�10'8).
1~ut even with acceptance of the atomi~ second, the astr~non~ical system of time
measurement hss not been displaced. The two scales mutually crncplement one aaother.
The time scale based on the atomic second reproduces an abstract uniform time.
" It is not associat~.d with the go;;ition of the earth relative to the sun or other
heavenly bodies, and reproduces a unit of time intervals with temporal zero position
that is arbitrary, just as the phase of any waveforms is arbitrary. The scale
- of ephemeris time reproduces elapse3 time with respect to the position of the earth
in cosmic space, fixes its position, and changes along with a change in the rate
of motion of the eaYth. The scale of e.phemeris time reproduces both ar~ interval
and an instant of time. Th~ scale of atomic time reproduces a time intzrval and
stores the instant transferre3 to it by the ephemeris second.
Units of time and frequency are reproduced by time and fre~uency standards. The
purpose of the ~requency standard is to reproduce waveforms wi~h a given value
of frequency and predetei~lined metrological characteristics. The purpose of. the
time standard is to r~~roduce a time scale, i. e. a sequence of time interva"ls
- with set temporal position of the beginning of the interval (instant of time).
2
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The assurance of unity of ineasurements of time and frequency is not merely th~
- reproduction of :xnits of these quantities with minimum e~rrors relative to s:he State
~ tiuie and frequency standard [Gosudar3tvennyy etalon vremeni i chastoty; GEVCh];
- assurance of unity of ineasurements is inseparabl;~ tied up with the availabili~y
of correspondingly accurat~ means ~f synchroaization and methods of transmitting
time and frequency signals. To ensur~e unity of time measurements it is necessary
not only to synchronize time intervals, but also to correlate the signals of the
time scale with the GEVCh scale. The signals from the reference standard tliat
are used to bring the t3sae scales into r_oincidence do not arrive instantaneously,
but over a certain time, and consequently a correction for this time must be intro-
, duced into tlie time scale being synchronized.
The synchronization method is dictated by tlae method cf determ.ining the difference
of frequencies or phases of the signals of the synchronizing and synchronized stan-
dards in combination with different signal transmission channels. This combination
depends on the require~ precision, the errors of the standards, and thej.r relative
location. Analysis of these and many other technical factors in applicatioil to
specific conditions enables determination of the most effective methods and means.
The main facilities for synchronizing frequEncy and ti.me sta~dards are radio sta-
� tions operating in various bands. They transmit information on instants and inter-~
valc of time:
by pulse signals, each having a ch3racteristic point that coin~lcies with the instant
of onset of some event that determines the beginning of readout of the time standard
to be synchranized (pulse systems);
by continuous harmonic oscillations, or waveforms with frequencies that perioclically
alter phase relations (phase systems);
by pulse signals in which the phase of one of the periods of the carrier frequency
is combined ~aith the epoch of the time standard to be synchronized (puls~a-ph~se
~;ystems) .
As a rule, frequency standards are synchronized with respect to the high-precision
carrier frequencies of these radio stations.
It becomes possible to use precise time and standard frequency sign,als transmitted
- via radio stations to make an exact check on measurement facilitierjr~u~t only~~~,iith
respect to frequency and time, but also witta respect to voltage, power and so on.
At the same time, this method does not completely me~t the dema.nds of a large.
- range of use rs w i Ch regard to accuracy and reliability. The er.ror of synchroniz-
ing frequency and time standards by these signals is due to ma�ny factors, primarily
ins~ability of the characteristics of transmitting and receiving equipment and
the inconstancy of conditions of radio wave propagation. Th~~se components will
have various weights fc~ different wave bands.
In the very-Zow frequency band, the radio wave propagatioz~ channel can transmit
instants of time signals with a small error of the order of 10 us, ~ut the time-
inconst2. 11
Fig. 7. Simplified block diagram of Chl-43 rubidium frequency
standard:
1--exciter of spectral lamp; 2--lamp thermostat; 3--spectral
lamp; 4--thermal filter; 5--optical filter; 6--thermostat; 7--
absorption cell; 8--resonator; 9--photodiode; 10--amplifier;
11--phase detector; 12--low-frequency oscillator; 13--multiplier;
14--quartz oscillator; 15, 16--divid~r; 17--frequency synthesizer
The frequency of quartz oscillator 12 is broughr by multiplier l,0 and synthesizer
17 to the transition frequency, is modulated by the voltage of low-frequency oscil-
lator 12, and is coupled by a loop in~o cavity resonator 8. The absorption of
light by rubidiwm vapor in cell 7 depends on deviation of the frequex~cy of the
~ microwave signal from the transition frequency. And since the microwave signal
is frequency-modulated, the light beam passing through the cell from light source
3 is also modulated by this frequency. The ligY~t beam acts on photodiode 9, and
an error signal is produced at the output of this photodiode with the frequency
of the modulating signal cophased with the modulation frequency if the microwave
field frequency�is less than that of the transition, and 180� out of phase if the
microwave field has a frequency higher than that o� the transition. The signal
- from the output of the photodiode passes through amplifier 10 and is summed in
phase detector 11 with the signal of the modulating oscillator, forming a constant
voltage at the output proportional the the frequency difference af the microwave
- field and the quantum transition; the polarity determines the sign of.thi.s differer~ce.
The voltage regulates the frequency of the quartz oscillator with respect to the
quantum transition frequency.
The mean square hourly variation of the frequency of the Chl-43 is ~�10-11.
18
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CHAPTER 2:. TYPES OF SYNCHRONIZATION OI~' P'RECISION F'REQI~ENCY AND TIME $TAI~'DARDS
Synchr4nization is what we call ad~ust~?ent ~of the period of synchronized oscil-
lations to the period of synchronizing signaZs. Synchronization of a frequenCy
standard r.~eans ad3ustment of the frequency f~ of the osciYlatious that it reproduces
- to the value f3 associated with the frequency of the synchronizing standard assigned
an integral value n that may be multidigital. Consequently, in synchronization
it is necessary to satisfy the equality
nf~--f9 = 0 or j~-fs = p.-- (2.1)
For practical purposes, these equalities are not equal to zero, and their value
_ is the synchronization err~r
ni~- t9 or t~ - t. _~i� (2.2>
The frequency errors of both the synchronize~d and synchronizing standards,are in-
constant in time. If it is assumed that at ~he point ~f collation they are resnec-
tivel.y described by the relations
7o.e = 70.~~ -F- Yn.c ( t lo) ~
. ao.c ~ (2 . 3)
! le l-!~
and ~
70.. = 70.9 -f- v~.s ~ t- to) � ao... (2 . 4)
_ r t, ~-eo
then the relative synchronization error is
~'n~ _ ( 7~.c - 7~~:~)r ~ 70., - 7o.~)r~ -F- (~o.~ - yo..) (t to)~ ~ Qo.~ -I- ao.9. ~2.5)
Synchronization of time standards meanE coincidence or mutual tie-in of the time
scales that they reproduce (a sequence of time-coincident signals), i. e. satis-
faction of the~equality
T, r~ = o. . 6>
r ~
If it is assumed that the time standards are based on frequency standards described ~
by expressions (2.3) and (2.4), then the temporal positions of the time scales
that they reproduce will be described by the expressions
Tc-~-7n.c~~-tp~-f' 2 ~o.e~l-to)2 (2.7~
_ and 1
ry I g-T Yo.~ l t- f0~ 2 ~O.Y l0~=� '~'L ~~8~
f fo .
The error of synchronization or error of tie-in of such time standards is
1 2
'{~e=~Tc - Ts~t = ~ Te - Ts)~e ~,7o.c - To.~~ ~ t lo~ -f- 2 ~ ~o.c - ~o.e) ~ t ~o~~, ~ . 9)
The process of synchronization of time standarda includes synchronizatiori of the
oscillators (frequency standards) and ad~ustment of the phase of the synchronized
signals.
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The synchronizatiun syste~: contains: 1) a mixer that simms the wa~�eforms and pro-
' duces a synchro-information signal functional.ly relzted to the frequency difference
of the summed waveforms or to the phase difference; 7_) a controlling element or
cdntirolling circuit for regula.ting the frequency and phase of the standard to be
~ synchronized by the mixer out~~ut (synchro-information signal); 3) channels for
signal transmission from the synchronizing and synchronized standards to the mixer
~ (Fig. 8). Depending on the synchronization conditions, the elements of the ~,~stem
can be made with a variety of hardware.
1 f Z 3 4 S fc
6
Fig. 8. Block diagram of the synchronization system:
1--synchronizing standard; 2, 4--transmission channels; 3--
mixer; 5--synchronized standard; 6--controlling element
Let us consider three methods of synchronization: 1) induced synchronization where
the synchro-information acts contir~uously on the standard to be synchronized; 2)
semi-autonomous, where the s~~nchro-information acts periodically on the standard
= to be synchronized; 3) autonomous, where there is no synchro-information.
The first method is used if the error of the standard being synchronized is greater
than the error introduced by the signal transmission channels, which is negligibly
small compared with the error of the synchronizing standard. Such conditions are
encountered nearly exclusively in the circuits of oscillators that are frequency-
stabilized. .
The second method is used in stabilizing standards that have commensurate errors
but are territorially separated. In this case, special channels are used for signal
transmission, and the influence af the channel parameters on the transmitted signals
cannot be disregarded. That is why the synchro-information is used to correct
~ the standard beinfi synchronized over definite time intervals rather than continu-
ously.
The third method can be used if the errors of the synchronized and synchronizing
standards are of the same order of magnitude, and neither standard is associated
with the other by synchro-information during operation.
2.1. Induced Synchronization ~
Induced frequency synchronization is based on a closed automatic control system,
where compensation of the deviation of .the controlled quantity from a set value
- takes place with respect to the difference between these values as dete~ined by
the method of comparison [Ref. 11J. ,
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An automati~ freouency control (AFC) syatem is used in casea where the error intro-
~ duced by the transmission char.nels can Le disregarded. This is feasible if the
synchronizing and synchx~nized standards are situated in direct proximity to one
- an~ther (i. e. Lhey make up a single unit), or if the time of automatic synchroni-
, zation is such that the error introduced by the transmission channel is negligible,
or finally, if the given error can be automatically compensated.
In the caae considered here, tt~.e synchronization circuit is made up of the mixer
proper, and the controlling element. A block diagram of such a system is shown
in Fig. 9.
, '
1 f9 2 3 f~
4 , .
Fig. 9. Block diagram of AFC:
1--synchionizing standard; 2-~-mixer; 3--synchronized standard;
~ 4--controlling eiement
The output (synchronized) frequency f~ has a predetermined functional~~elation
to the input :(conventional standard) frequency f3 at an invariable o- constant
value of the latter. The frequency to be synchronized is sent through the feed-
back circuit to the mixer together with the standard frequenc~?. A control signal ~
is produced at the mixer output with amplitude determined by the mismatch--the .
difference between frequencies f~ and f3.
The change in phase of the oscilla~ions is unambiguously related to~the change
in frequency of these oscillations ~w. Therefore the change iri both frequency
and phase can be used to produce a control signal at the output of the mismatch
sensor. That is, automatic frequency control is possible with two kinds of mis-
match sensors: a phase detector with tun,ing to a definite phase, and a frequency
detector-discriminator with tuning to a definite frequency. In accordance with
this, two AFC groups are formed: phase AFC and frequency t~E'C.
The result of action of either scheme is the same: the frequQncy of the standard
to be synchronized is re~ulated with respect to the source of synchronizing wave-
forms. But the phase and frequency AFC systems ttiemselves are different both with
respect to the circuit design and with respect to their regulating action. The
phase AFC system is in a state o� stable eqsilibrium only when the controlling
factor is constant, whtle the voltsge at the output of the phase detector remains
constant only when the phases of the voltages being compared are invariable, which
necessitates equality of frequencies. In the frequency AFC system in the stea.dy
state, the controlling factor can be constant only ~hen the frequency difference
is constant. Consequently in the frequency AFC system there is always a difference
between the frequencies of the synchronized and synchronizing waveforms.,
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_ In the frequency control process, this dffference must be adjusted to the discri~ui-
nator tuning frequeucy .
f~? = to- js~ ~2.10)
~ i
where fo is the value of the frequency to which the standard is Co be syr~chronized.
'
Thz voltage appearing across the mixer load has the difference frequency of the
standard, f~ or f3. This voltage acts on the discriminator, which is located at
- the output of the mixer. A controllir.g voltage is formed at the discriminator
output. When f~ =fo, this voltage is equal to zero and the frequency AFC system
does not operate.
The process of frequency establishment when the frequency AFC system is cor::.acted
to the oscillator being stabilized beginQ 1t the t~.-ne when the difference is equal
to some beginning mismtach f~ - fo= ~fbeg~ Under the action of the voltage coming
fro~*~ the discriminator.output, the controlling element changes the frequency of
the oscillator being synchronized toward the side opposite (in sign) to the initial
mismatch, resulting in reduction of the difference.
The phase difference of two waveforms can remain constant in time only in the case
where tl~e frequencies of these two waveforms are the same. If the frequencies
of the wavef.arn,a are unequal, but differ by a constant value, the phase difference
is
_ ~r = (u~~ -u,~) t -I- y''o = Awt'-~- ~o, (2.11)
.
where ~o is the initial phase difference, w~ and c~3 are the frequencies of the syn-
chronized and synchronizing oscillators respectively.
J If the f,requency difference is not constant in time, the instantaneous phase dif-
ierence is �
~ = fe~dt., ~2. i2>
and hence
Au, ~ d`~ , ( 2 .13)
The constancy of tl~~e phase difference guarantees equality of the frequencies of
two waveforms; this is the design basis of the phase AFC system.
The structural difference of block diagrams of frequency and phase AFC systems
dictates the different physical procesaes that taka place in these systems.
In phase AFC systems a variable-frequency voltage appears at the output of the
phase deCector that is transmitted to the controlling element of the oscillator
to be synchronized.
The beginning mismatch ~mbeg of the oscillator being synchronized should not exceed
- t~ie stopband for c~fficient operation of the system. In this case a constant phase
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- difference is set up in the system, i. e. equality of frequencies m~ and w3 is
assured. Hence the stopband also determines the locking-in band, the maximum mis-
match of the oscillator to be synchronized at which phase AFC will accomplish syn-
chronization.
Phase shifts in the automatic control channel cause delay of the controlling signal.
The voltage across the output of the phase detector is determined by the phase
difference of the signals being compared. Therefore when the frequencies of these
signals are equal, the voltage across the output of the phase detector is constant.
On the other hand, if the frequenci~s are not eq,ual, the change in phase difference
is determined by expression (2.12), and the voltage across the output of'the phase
detector is a fe~nction of time.
' It is not only the useful driving waveforms that act on an actual AFC system, but
also interference. Interference causes changes in the frequency of the sy^chronized
oscillator relative to the avera_ge value of the frequency in the steady state,
- atid this change is equal to the mean square error.
Additional elements must be introduced into the circuit in order for the AFC system
to track the useful signal with the greatest possible accuracy and not react to
interference.
Masers are systems with phase AFC. The converted signal from the quartz oscillator
- is added to the signal from the maser in the mixer. The difference-frequency signal
- that arises at the output of the mixer acts an the phase detector simultaneously
with the converted signal of the quartz oscillator; an error signal is produced
that is used to adjust the quartz oscillator frequency to the maser frequency.
In frequency standards with quantum discriminator, the quartz oscillator is synchro-
nized by a frequency AFC system.
2.2. Semi-Autonomous Synchronization
When the oscillators are spatially separated, and the siRnals are transmitted from
- the synchronizing oscillator by different ~:hannels (cable lines, radio channels
of all waves bands, television channels, satellites, meteoric channels and so on),
since no methods for automatic elimination or compensation of errors have as yet
been found on the present stage of investigation of destablizing factors introduced
due to the inconstancy of parameters of such channels, automatic induced synchro-
- nization of precision frequency measures is impossible. Therefore seni-autonomous
- synchronization is used, necessarily with the participation of a human operator
who analvzes the results of comparison of the synchronizing and synchronized fre-
quency standards and introduces needed corrections.
In the general case, the block diagram of synchronization of spatially separated
fr.equency and time standards takes the form shown in Fig. 10. The two standaYds
1 and 2 are connected by a channel. The mixer-receivers are devices that pick
- up the signals simultaneously from the two standards and produce a signal in which
one of the parameters is related in a definite way to the difference of the fre-
- quencies or phases of the received signals. Such devices may be standard radio
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- und ~elevision receivera, standard oscilloscopes, and also special receivers--
- phase comparators and frequency comparators.
~
~
2 f9 ,
3 4 S . ~
i
~
� ~y r
Fig. 10. Block diagrata of synchronization of spatially separated
frequency standards:
1--standard to be synchronized; 2--synchronizing standard; 3--
converter; 4--comparator; 5--display
Cable lines are used in synchronization by a time and frequency calibrated reference
for laboratory standards intended for radio trans~ission of exact time and reference
_ frequency signals, and in synchronization of precision standards situated at small
distances from each other within the confines of a aingle institution, or a single
time and frequency service.
A cable line is equivalent to a two-terminal pair network with distributed param-
eters R, L, C and ge
- Inconstancy of these parameters causes a change in frequency of the transmitted
signals and their transmission time.
In practice, signals can be transmitted over cable lines to distances of 10-100 km
with frequency variation of (1-2)�10-9 and variation of tranamission time of
(1-2)�10-4 s.
Radio communication ch~~nnels are used in synchronizing time and frequency standards
separated by distances of from 50--100 to 10,000-15,000 lan or more. Depending on
the distance between the standards and the required synchronization accuracy, dif-
ferent radio wave bands and correspondingly different methods of transmission are
- used.
' Signals from the synchronizing stand~rd aresent over one of:the transmission chan-
nels and arrive at the comparator-receiver, where the difference of frequencies
or phases of the signals of the synchronizing and synchronized~standards is de-
termined. If the synchronizing signals are transmitted over cable lines, th~y .
_ go directly to the comparator after a~plification. On the other hand, if transmis-
sion is by radio communication channels, the signals go to the reception device,
with circuit determined by the radio band of the received signals, and from there
to the comparator.
In semi-autenomous synchronization, signals from the synchronizing standard are
periodically received at the point of location of the standard being synchronized.
The time between receptions (discreteness time) is established depending on the
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required synchronization accuracy:, the ratio between the metrological characteristics
- of the two standards, and the signal transmissior~ error.
~he metrological characteristics of the standard to be synchronized must be calcu-
_ lated on the basis of certain measured effective frequencies. Therefore the time
between signal receptions must not exceed the time during which the~metrological
characteristics of the standard are determined. The error of the effective fre-
quency is made up of the error of frequency com~arison and the error introduced ~
by the transmission channel. Systematic errors introduced by the transmission
channel are eliminated by making appropriate corrections, and random errors are
added in with the comparison erxors.
For example with error Sog of determination of the effective frequency, and error
� SoZ introduced by the transmission channel, the totaJ. error is
So = ~~So~ -I- 5~~. ~2.14)
If the effective frequency is determined by the differential method, the necessary
measu:-ement time with consideration of SoZ is calculated by formula
~
= 7~, . (2.15)
So~ -So~
If the effective frequency is determined as a result of discrete measurements,
the necessary number of ineasurements n is established from the relation
n(n - 1)- _ I Z (f~ --fa)a (2.16)
:
fa" So' -So~
- or , assinning n~ 1,
. n
v~ ~~t "~niZ
. ~c ~ (2.17)
~
~n S~! ~
The overall error should be 3-10 times smaller than the permissible synchronization
error.
When metrological characteristics are already known, measurements can be done after
still greater time intervals. In this case the measurements can be con~idered
control measurements, and the method of semi-autonomous synchronization becomes
a method of autonomous synchronization.
2.3. Autonomous Synchron3zation
If the synchronizing and synchronized standards have identical metrological char-
~ acteristics and their laws of time variation are also identical, then a single
- determination of the phase difference of the generated signals is sufficient in
principle to synchronize such standards.
Most closely approaching such conditions in practice is the QFS, although this
device also has small but systematic frequency variations. At the present stage,
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the instability of the QFS is much less than the error of determination of param- I
eters of signal transmission channels and their incon~tancy. Ther~fore a method ~
of autonomous synchronization is used to synchronize frequency standards based ~
on ~he QFS: the standards are not connected by transmission channels, and the
- frequencies of the waveforms that they generate remain invariable over a permi.ssible
range. For control purposes, the frequency must be periodically compared with
that of the synchronizing sCandard (the period is determined by the reliability
of retention of the metrological characteristics of the standard to be synchronized).
Synchronization of time standards based on the QFS also necessitates periodic con-
trol measurements of the temporal position of the signals. Besides, the measurements
must be made after each cutoff of the standard, even briefly.
i With consideration of the fact that the standard being synchronized must copy all
changes in the characteristics of the synchronizing standard, both standards must
be periodically combined in some way during autonomous synchronization as well.
It is most effective to use portable time and frequency standards for this regis-
tration. Such a frequency standard based on the QFS--atomichron or rubidium clock--
is synchronized to the sync.hronizing standard, and then transported by air to the
point of location of the standard to be synchronized, where this synchronization
is carried out [Ref. 12J.
CHAPTER 3: METHODS OF DETERMINING FREQUENCY DIFFERENCE OF SYNCHRONIZED AND SYNCHItO- ,
NIZING STANDARDS
3.1. Method Based on Results of Determining the Effective Frequency of the Standard
to be Sy~.chronized
The effective frequency fA can be determined by the method of direct evaluation
using a frequency meter, or by a differential meth~d by comparing the frequenices
of the synchronized and synchronizing standards (GOST 13628-68 "High-Stability
Oscillators. Methods and Means of Checking the Frequency of Electric Signals").
The former method is the simplest; a counting-type frequency meter is used for
measurement with an external source, which may be the synchronizing standard.
- In this case the error of determination of the frequency of the synchronized stan-
dard is only the error of discreteness of ttie frequency meter,
- ti - t~ . ~3.1)
U~ 19ZN
~ If a frequency meter without external source is used for measurement, the error
due to discreteness is combined with the error of the reference oscillator of the
frequency meter
S~~ - -i- ~ . (3.2)
(9~~~
The accuracy of determining fA of the synchronized standard is increased by doing
_ n repeated measurements in time Ty, during which variation of ineasurement conditions
can tie disregarded. The error in this case is reduced by a factor of
When the differential method is used, it is necessary that the summation of the
- waveforms of the synchronized and synchronizing standards produce beats; the beat
frequency is then measured and used to determine the frequency difference of the
~ two standards.
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It is known that when scalar oscillations v1= V1 cos 2~rf lt and v2 = V2 cos 2~rtf2t are
added, the resultant waveform is
z~ = V cos (2~j11- (3. 3)
wher~
V- V, `ir 1-~- 2/c cos 2~ (f~ - f:) t-~ h'; (3. 4)
~p = sfrCtg !'sln 2R ( fi - f~) t . (3.5)
1-{- h coc 2a (~l t,
_ Va
h =
V,
These formulas are valid for any fl and f2, but if fl- f2~f1, the resultant wa~~form
is ~erceived as alternations of waveforms of the same frequency with amplitude
varying periodicaTly on the difference frequency. Such signals are conventionally
= called beats. Beats may also be produced by combining waveforms with frequencies
that are appreciably different. For example the sum of two mutually p~rpendicular
vector waveforms
_ , , .i
'r'i ~ cus 2r, f 1! and v2 = V~ CUS `lT/'zl,
whose frequencies are f 1= Zf o+ ~1, f2 = kf o+ ~2 , where Z and k are integers, ~nd
pl< fl, ~2< f2, are described by the equation '
cus (/z arccos I ~rccas l=cos 2~ ~~e, - ce~r. (3 . 6)
~ vi t~s /
.
For each instant of time t, this equation describes some figure on plane vlv2.
_ If k~1= Z~2, the figure is invariant. If k~l~ Z02, the figure is deformed with
period
I 1
7' _ . (3.7)
kn, . _ rn: kl~ - ~l~
If F= T=(kf 1- Zf 2) af 1 or f 2, the resultant waveforms are perceived as beats.
Beats of two electric signals are produced by mixers, which may be an electric
circuit that alters the spectrian of si$nals acting on it, ~.nd isolates the component
of the difference frequency from this spectrum, or a cathc?de-ray tube that does
not change the spectrum of the suimned waveforms, but enables obseroation of beats.
Tf the frequencies of the synchronized and synchronizing standards lie in a range
of 100 Hz-1 MHz, the difference frequency can be measured with an electronic oscil-
loscope (from Lissa~ou figures or from a circular scan; in the latter case an elec-
tronic oscilloscope with radial scale on the screen is used).
By this means, frequency differences of less than 2-3 Hz can be determined by mea-
suring the time of part of a period or of an integral number of periods of the
difference-frequency waveforms.
Measurements by Lissajou figures are possible at a ratio of nominal values of the
frequencies of the synchronized and synchronizing standards up to 1:10;,measurement
- time cannot be less than the period of the beats.
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The rate of periodic change in the Lissa~ou f igure is proportional to the~ frequency
difference being measured. The beginning of the period is taken as the instant
_ when the Lissa~ou fiRure becomes a single line. The timer is energized at this
instant. The timer is disconnected when the Lissa~o~z figure again becomes a line
oriented in the same way as the initial line. The time indicated by the timer
determines the beat period. ~ ~
It is n4t possible to determine the sign of frequency deviation of the synchronized ~
standard directly from measurements. It is determined either by changing the fre- ~
quency of the synchronized standard in a known direction, or by using an auxiliary
oscillator. '
Measurements with respect to a circular scan are possible at a ratio of the nominal
frequencies of the synchronized and synchronizing standards up to 1:100; measurement
_ time may be less than the period of the beats.
When voltages are applied to the circular beam scan and to the brightness modulator
with corresponding regulation of their levels and the brightness of the electron
beam, one (when the nominal values of f~.H=f3.H) or m bright points (when
fc.H/f3.x - m) are formed on the screen that move in a circle with a velocity pro-
portional to the beat frequency. The instant of readout is taken as the t3.me when
a point crosses any marker of a scale on the screen. At this instant a~imer is
enzrgized, and it is switched off when the point crosses the same marker of the
- scale if the time of a whole period of beats is being measured, or any other marker
of the scale if the time of a part of the beat period is being measured.
The sign of frequency deviation of the synchronized standard is determined directly
during the measurement from the direction of motion of the points around the circle.
The beat frequency is calculated from the formula
(3.8)
T~~
where n is the part of a period er whole numbe~c of periods of the beats in time TK. .
When f~,fl= f3.x and f~~y = I-f3,H, the frequency error of the synchronized standard
is equal to the beat frequency.
7,� = F. ( 3 . 9)
When kf~.f{= f3.H, the error is determined from the formula
T~=~-k.
F (3.10)
~f the synchronized and synchronizing frequencies lie in a range of 100 kHz-30 MHz,
the difference frequency can be measured by a heterodyne method, using a nonlinear
frequency mixer (see Fig. lU).
_ Measurements by the heterodyne method are possible at a ratio of nominal frequencies
up to 1:200; measurement time cannot be less than the period of oscillations of the
difference frequency.
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This method enables isolation and measurement of the difference frequency both
c?irectly between the fundamental frequencies of the synchronized and synchronizing
standards, and between the frequencies of their harmonics.
A special mixer or all-wave radio receiver is used for the measurements; in the
case of harmonics, distorters of the waveshape of their oscillations are used.
When signals on close frequencies are sent simultaneously to the input of the mixer,
a voltage modulated by the difference frequency appears at its output. Depending
on the magnitude of the difference frequency, it is measured eith~r by counting
- the number of. periods of beats over a time determined by a timer, or by a counting-
type frequency meter.
The error of the synchronized frequency is calculated by the formula
k('� _-I(~ _ F ~ (3.11)
k k
where k, Z are the numbers of the utilized harmonics of the synchronized and syn-
chronizing frequencies respectively.
. The error of the differential method of ineasurement is due chiefly to the error
of ineasurement of the difference frequency. In direct measurement of the beat
- frequency F, the error is determined by the error of the frequency meter ~F/F.
In indirect measurement, the error is due to imprecision of time measurement (~T1)
and imprecision of registration of the number of beats (~n); for the calculations we
use the law of summation of the mF~n errors:
S F ~(~i 1'_~, (~~~,s, (3.12)
~ ~ I ~ 1
In practice, it is difficult to separate errors ~T1 and en, and therefore the over-
~11 error of time measurement is estimated
L1T = ~ ' Otla ~taa~
where ~T2 = F, and the error is calculated by the fortnula
.S~ = F or Sa = F( � . (3.13)
Z , 1C.II Z
Values of ~T lie in a range of 0.3-0.5 s for different beat frequencies (0.3-5 Hz).
If the frequency di.~ference is less than 0.01 Hz, the comparator may be a phase
discriminator with registration of periods of the difference frequency on a chart
recorder. The electric circuit of this method can provide a linear rise in amplitude
of the difference frequency Qver the entire period with an abrupt drop at the end
of the period (Fig. 11). Therefore, to determine the frequency error of the stan-
dard that is being synchronized, the time of the periods is read out from the output
of the chart recorder, and the difference frequency is calculated. On Fig. 11,
T1 = T2 = T3 = T4 = T; N= 4; Tn = NT = 4�21600 = 86400 s. If f~ = 100 kHz, the �relative
error of the synchronized standard is Yo.c-4�6�10'l0.
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t~~ t., t: t,~ t~
~~.._Tt �_~i-- - _ _ ~,i_. _ _ 7!... '
!l1Q _ 1 p16 L /ij 1 : _ 2
Hours of the day
Fig. il. Change in amplitude of difference frequency at phase
discriminator output ~
3.2. Method Based on Measurements of Change in Phase Difference of Waveforms of
Synchronizing and Synchronized Standards
In the phase method af determining the error of the standard being synchronized,
exact time signals produced by the synchronizing standard are used. An oscillo-
scope or counting-type frequency meter is used to observe the phase difference
of oscillations of the synchronized and s,ynchronizing standards.
Determination of the error of the synchronized frequency from exact time signals ~
consists in fixing instants T1 and T2 of signals of ~exact time relative to signals
~ of the standard to be synchronized after time interval t. To do this, an imsge of
the signal is produced on the oscilloscope screen by scanning it with the signal
of the standard being synchronized, and using a phase shifter to achieve registra-
tion between the beginning of the signal of the synchronizing standard and the
beginning of the scan, noting the respective positions 171 and I72 of the phase
~F shifter.
The relative error o'c the standard being synchronized is calculated by the formula
r, - � r~ i~~ (3.14)
7~~.~~ ~ _ -.T.~,
T
The error of establishment of time int~rval T and the error of registration of
s~gnal times cause errors in determination of the effective frequency of the stan-
dard being synchroni2ed in accordance with formula (3.13).
CHAPTER 5*: SIGNAL TRANSMISSION METHODS USING VLF RADIO CHANNELS
5.1. Transmitting Facilities '
By convention, myriametric radio waves are those with wavelengths of 10-30 km,
which corresponds to radio signal frequencies of 10-30 kHz. These limits are not
rigorous, as radio waves in a frequency band of 6-60 kHz propagate.by a similar
- mechanism. .
*Chapter 5 was written by Candidate of Technical Sciences M. V. Bolotnikov.
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It is known from tlie roures of propagation of radi~ waves that when a signal propa-
~ gates in non-ideal media or close to their boundaries, attenuation decreases with
increasing wavelength. BecausE af this, VLF radio channels are used to synchronize
frequency and time standards separated by distances of more than 10,000 km. ~
' However, in transmission of long-wave signals of the order of kilometers or more,
considerable difficulties arise. The monograph by S. I. Nadenenko [Ref. 20] points
out that the radiation impedance of a transmitting antenna that characterizes its
efficiency decreases rapidly with decreasing ratio of antenna height Za to the .
wavelength of the emitted signal
>
E~ = 160aa (5.2)
i1 ~ ~
Formula (5.1) is more conveniently represented as
R~ 160r.$
f a ,
c~
where the speed of light c= 3�108 m/s.
The hei~ht of antenna towers of the largest VLF stations is no more than 500 m,
i. e. no more than 5% of the wavelength. To.ensure efficient radiation, such anten-
nas are "capacitance top-loaded" [Ref. 20]. Here the capacitance is a system of
horizontal wires stretched between the central tower and somewhat shorter peripheral
towers. The total capacitance C of a~.ultiple-tower VLF antenna with developed
system of horizontal wires may reach 0.1 uF. The combination of inductance of
" the wires with the capacitance of the horizontal web forms a parallel oscillatory
tank with distributed parameters. During transmission, this tank is tuned to reso-
nance with the exciter signal by special large-scale tuning coils. The wave im-
_ pedance p of the antenna under these conditions is determined by its total capaci-
tance C,
p 2~fG ' (5.2)
and the Q of the a~ltenna tank
p _ ~z _ 2,14 � 161a
. ~ ll:: - 320a~/a=(~C !a=~~C
is inversely proportional to the cube of the frequency of the transtnitted signal.
The F~assband of the antenna is
!1 3'lUa' j'l; - 4,62 � 10-'qj~l~9C, (5.3)
c
Takin~ 7,= S00 m, for a frequency of f ~ 20 kHz we get II= 200 Hz. and for f= 10 kHz
it is 12.5 Hz.
The main purpose of- VLF radio stations is long-range radio communications. Time
signals are transmitted by these radio stations during specially selected broad-
casting sessions or in a combined schedule. Because of the very high cost of VLF
transmitters, and especially antennas, a rather limited number of VLF stations
of comparatively low power have been built specifically for synchronization.
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5.2. Methods of Time Signal Transmission
~
~ao principal methods are used for transmitting exact time signals in the VLF range:
pulse modulation and sequential transmission of coherent carrier frequencies. ;
_ In time signal transmission by the former method (in mode A-I) synchronization
accuracy is influenced by~the narrow-band nature of the antenna systems and by
the quite considerable level of natural interference. As shown by calculations
(see Section 5.1), the risetime T of the signal radiated from the antenna on a
frequency of 20 kHz will be 3-5 ms, and on a frequency of 10 kHz T= 50-100 ms.
Natural interference ~n the VLF band is mainly due to lightning discharges and
= is markedly pulsed. The average level of interference at the latitude of Moscow
is of the order of 0.5-1 mV/m in the 1 kHz band. As will be shown below, the
field strength of VLF radio signals from moat transmitters in this band at a dis-
tance of 3,000-6,000 lan is 0.5-1.5 mV/m. For a receiver pass band of 1 k.Hz, the
signal-to-noise ratio at its output is 1-3, and the accuracy of registration of
the instant of pulse arrival at the reception antenna can be estimated by the for-
mula [Ref. 20]
Q~ c t;~~ a l ms. (5.4)
4
By observing the received signal on the screen of an c~scilloscope with afterglow,
an experienced operator can determine the position of the received pulse relative
to the local time scale with error of the order of 200-300 us. Errors that arise
due to inexact knowledge and delay instability in th~ receiver can be eliminated
with fair accuracy if this delay is measured by usin~; a special simulator of re-
ceived signals before the synchronization sequence sttarts. ~
- In virtue of simplicity of the reception equipment, the pulse method of synchroni-
zation in the VLF band is being extensively used in complexes and systems where
the permissible synchronization error is 0.5 ms or more.
The method of sequential transmission of coherant carrier frequencies improves
_ synchronization accuracy by more than an order of magnitude, but involves con-
siderable complications of transmitting and reception equipment. The method was
originally developed and implemented in application to problems of the Omega VLF
radionavigation system for the U. S. Navy [Ref. 22]. To explain the working prin-
ciple, let us consider a hypothetical system that sequentially transmits coherent
monochromatic signals with frequency of 12.5, 12.6, 13 and 15 kHz. In the shaper
- of the transmitter, these signals are phased in such a way that they simultaneously
pass through zero 100 times per second, and once per second this coincides synchro-
- nously with the second pulse of the master clock at the station. Let there be
some time storage device at the reception point with scale that lags behind that
of the master clock by To, and let an analogous time grid be formed from its signals
as well. The time of signal propagation from the transmitter to the receiver on
all frequencies will be taken as identical and equal to TP.
The phase difference of the rece~.v~d and local signals with frequency fi at the
reception point is
J o T'~ .
f~ ~T o ~ i- - n~ r n~, .
i
~
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where Ti is the period of signal with frequency fi, ns entier (T/Ti) is the whole
- number o+~ periods of Ti contained in time interval T= To + tP. Let us note that
here and below for purposes of greater compactness in writing them out, the values
of the phases and phase differences are expressed in fractions of the period a~
" the corresponding signal.
The difference of phase shifts for two different frequencies is
~~~~i = - - ~ft ~ f~) T - ~ nr - n/)
or T . _
~l~ j~ T'J - nl~~ .
where Tii is the period of the effective difference frequency Fi~, and ni3 = ni- n~
is the wfiole number of such periods in interval T= Tp+ TP.
Thus knowledge of the phase shift ~Yi on some carrier frequency fi or of the dif-
ference of such shifts Y'ij enables determination of the corresponding shift of
time scales with an uncertainty that is a multiple of Ti or T~,3. With a reduction
in frequency difference, the band of unambiguous readout o� the measured in*erval
increases, but there is a simultaneous increase in the error of ineasurement of
this interval
_ ^ _ ` ~ Q2 1
�il ~ �~e~ + w~ Fl f'
- To resolve the uncertainty, it is necessary to determine the number of geriods
ni. Let us assume that the measured shift of the local scale and the received
signals T= To+TP is less than the period of the least of the difference frequencies
T21. Then from th~a corresponding difference of the phase readouts Y'21 we can un-
ambiguously fir_~ che measured shift T= Y'21T21. Hence the number of perio3s of
- the next difference frequency T31 in the measured interval is
~i - enficr ~~"T" (5.5)
.
. T~,
In this case, the measured interval
= ( na? ~~~a~ ) 7~a~
can be determined with accuracy corresponding tu the higher difference frequency
F31. Performance ~~f these calculations is in no way limited by the fact that
physically the difCerence frequencies Fii are not formed in the receiver, and the
phase readouts 'Pi~ are ca~culated from tfie results of ineasurements made on the
corresponding carrier~frequencies fi and f~. In the general case .
nr~.~.i,i = 2ntier~~r"T" ZS.6)
T~+~~~ .
Calcul~.tions by for.mula (5.6) are done until transition to readout on carri.er fre-
quency fl. Ultimarely
T J' n1nTf1-I- (i�~ `~i) f~~. ~5.7)
l~~1
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where p is the numl~er of sequentially transmitted carrier frequencies, ml is the

J number of periods uf the carrier frequene; as calculated for the maximum difference ,
_ frequency FP1, m31 is the quantity previously denoted in formula (3.5) as n31:
Formul~ (5.6) has a serious =1aw: if readout on a greater difference fxequency :
Fi+l,l is close to unity, it is quite possible as a consequence of unavoidable ;
measurement errors that the whole number mi+l,l will be incorrectly determined.
More stable with respect to errors of this kind is the relation
~~t1~.~,~ ~ A/I ~~~n Tri ~uJ.~~~~ ~ (5.8)
LT~~�~.~ -1
- where N is the operation of determining the nearest whole number. Regardless of
the specific values of Y'i~ and ~'i+l,l~ ~
- l, -'~~l'7'n _ . ?~r1+i~~ (5. 9)
- ~�~+i~~
will be a~ahole number in the absence of ineasurement errors. In practice, this
- quantity differs from a whole number increasingly with increasing error of inea-
surement of the phases of the carrier frequencies.
Ambiguity is correctly resolved if the error of determination of I'(denoted by
dr) for the given measurement series satisfies the inequality dr < 0.5. PhysicalZy,
this means that the error of readout on frequency Fi91 assumed in the time expres-
sion must not exceed the period of the nest higher difference frequency Fi+l,l�
From formula (5.9) we get the following relation between dr and the errors of phase
measurement of the carrier frequencies �
~~�-=-;.-1+~
~(~~,-~~,)--(~Y,+,-~~~)= x(a~,-~~,)--(a~,+~-a~,).
Taking the errors of phase measurement on sequentially transmitted carrier frequen-
cies as mutually independent and equal in mean-square value, we get
_ ~c j/2 o V I - ~ ~ ~ (5.10)
n
where a~, ar are the mean square errors of ineasurement of phases and of determining
I' respectively. Assuming that these errors are distributed according to normal
- law, we can determine the probability of correct resolution of ambiguity for one
transition between readings on ad~acent difference frequencies by the formula
p ~ Q~ r~Q~l, (5.11)
1 ~1
Tt-I~~
where ~(K) is the probability integral. The ratio x-- which to a great extent
Tt-F-t,~
determines the probability of correct resoluti.on of embiguity, is called the coef-
ricient of transition, or the scale ratio. ,
34
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0
Let us consider a practical examp~e. Let the measured phase ahifts be ~1= 0.65,
- ~Z = 0.56, ~3~ 0.11~ ~ya 0.99. Data processing is done in the following order.
; 1. Phase shifts on effective difference frequencies are determined by the formula
'~t~ _ ~t - ( -I- 1).
Here the phase of the loweY-frequency signal is subtracted from that of the higher-
- frequency signal. If the phase difference is negative, unity is added,
~l~s~ = 0,56- 0,65 0,09 1) - 0,91;
. ~u� = 0,11- 0,65 - -~p~~ ( -f- 1) � 0,46;
~~1 = 0,99 - 0 65 = 0 34� _ _ r;
~ .
~ , ~ ;
~~si = ~Pi = 4.~.
2. The whole numbers of periods of the difference frequencies contained in the
- measured displacement of time scales are determined
nrs, - N (0,91 = ~ ~ - 0, 467 = N ( 4,09) = 4;
~
m~l = N~0,96 = 4~ - 0,34~ - N(1,96)~=- 2; �
n:a,--nc,-N(0,34=-4~-0,651=N(1,05)=1~
~ ~
- where the numb~rs 10,000, 2,000, 400, 80 are the periods of the difference frequen-
' cies and the first carrier frequency expressed in microseconds. For our example
K=S.
3. The time interval to be measured is calculated
= � 200U ~ ~ - 2 . ~{00 (1 !),65 ) � 80 8932 us .
, The error of thc~ reception equipment when using the multiscale synchronization
method (usually digital phase meters) is made up of the error caused by nc,ises
and the discr~teness error. The first of these can be calculated from the relation
I
�w = - ~
2ny,~~
where q~ is the si~nal-to-noise ratio with respect to field strength in the band
of the phase meter [see formula (5.3)]. The effective pas~band of the digital
- phase meter is 3etermined in turn by the duration fn of signal transmission on
the given carrier frequency
1
tl,~, : = 2~r� '
Let tn = 300 s. Then even at a signal-to-noise ratio of 0.05 in a 1 kHz band,
9~D - yiKn~ /j/ `lz (UO()[~~ ~ �
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[subscript 1xI'u-= 1 kHz] in the phase meter passband which corresponds to error
due to noises that is equal to 0.003 period, or expressed in timp--U.024 us.
A much greater error is associated uith determining the exact time of propagation
on the carrier frequencies. This error can be conventionally divided inta two
components: random Qp and systematic dp. The random error is understood to be ~
that due to chaotic changes in the phase of the arriving signal under fixed con-
" ditions on the path from the transmitter to the receiver. As implied by data of
years of observations, such changes, and consequently Qp, fluctuate frr~m 1.5 (day-
time, summer), to 4 us (nighttime, winter) [Ref. 23J. The systematic error in
determination of phase velocity on rransmitted frequencies ts fundamental, and
under unfavorable conditions may reach 30-50 us nn paths up to 6Q00 km long.
If d is the same on all frequencies, it has no effect on the probability of correct
- reso~ution of ambiguity. In this case the v~ appearing in formula (5.10) can be
defined as ~
_ ~ V \ ~i )a c~~ ~ ~5.12)
where d is the discreteness of phase readout by a digttal phase meter.
- Using formulas (5.11) and (5.12) we evaluate the probability of correct resolution
of ambiguity for one transition in the hypothetical system we are consider3ng.
Setting d= 0.01, op = 2 us (0.0250 per~od on frequency of 12.5 kHz), we get
Q= 0,035; P- ~D r'o 4~ (2,84 O,SI~).
r . (0,175)
So correspondingly for Qp = 4 us we get P~? 0,. 3.
From a formal standpoint, the result should nave been raised to a power equal to
the number of transiti~ns (four in our case)o However, on low difference frequen-
cies the correlation of ineasurement errors is so strong that the corresponding
transitions are always made unambiguously. The loss oi` this unambiguous proper~y
can ocr.ur only with transition from the greatest differe~nce frequency to the carrier
frequency. Such an occurrence gives rise to a measureme:it error equa~. to the period
of the carrier freo,uency (in our case 80 us).
The existence of two fundamentally different methods of time signal transmission
in the VLF band necess3tates two approaches to the problem of calculating the time
_ of propagation of transmitted signals. To determine corrections for delay in the
propagation channel with the purpose of refining phase readings, it is necessary
to know the phase velocity vP, which enables us to find the total phase shift of
the signal [hat has covered a distance Z from receiver to transmitter,
[
?x~, ~plp ~cj~~ = v
~ (5.13)
f
Formula (5.13) is also frequentty written as
~P - ~ lti~� .
, Zp 2rz
36
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where Itt "'t = 2a f! is the so-ca?lerl propagation constant, or wave number.
vp L'p ~t .
For free space, this symbol will be used without a subscript.
To determine the pulse signal delay, its group velocity vg should be known, i. e.
Che velocity of displacement of energy from the transmitting to the receiving an-
tenna. In this case, T~,
v~,
If the phase velocity of the signal is independent of its frequency, the group
velocity is exactly equal to the phase velocity. If such a dependence does hold
between them, then there is a difference that is the stronger the greater the rate
- of change in vP as frequency changes
, ~
v,~(J') - v~ (f ) ~~v~i f) f (5 �:14).,
_ . _
~ or as signal wavelength changes in free apace
vT. ,ca
i~,~ v,, ~
~
~ �
From the relations given in Section 5.3 it follows that 0~ ~ v~ < 3�10-3, in virtue
r.
of which the group velocity of pulsed VLF signals can be taken as equal to the
speed of light in the case of an error in signal registration.
Thus we must have an opportunity to determine vP to solve the problem of determining
propagation time in the VLF band.
5.3. Fl~mants of the Theory of VLF Propagation in the Spherical Earth-Ionosphere
Waveguide
VLF radio waves propagate in the concentric earth and ionosphere that are walls,
as it were, of a spherical waveguide. A strict mathematical description of the
_ signal with the ionosphere with actual consideration of its properties does not
' permit us to find an analytical solution for signal parameters even when the char-
acteristics of the prop agation channel are known. Unfortunately, information that
is currently available relative to the region of the ic~nc+sphere of significance
for the propagation of VLF waves, ionization layers at an altitude of 50-100 lan,
does not enable a suff iciently exact description of the physical processes that
take place therein. _
_ The lower ionisphere, closed off as it is from the principal sources of ionization
by upper layers, i5 less sub~ect to the influence of a change in ionizing factors,
ar.d consequently is more stable than the upper ionosphere. The altitude dependence
of electron concentration Ne for typical daytime conditions is shown in Fig. 20a,
~ and for nighttime conditions--in Fig. 20b [Ref. 24]. The field of the VLF radio
_ signal for the actual profile of the ionosphere can be calculated only by numerical
methods, using a computer.
The waveguide nature of VLF radio signal propagation causes simultaneous excitation
of several wave modes near the antenna that differ with respect to the altitude i
37
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;
- s
~
\ 4 . . ~ r . ~
~ ~ ~
~ ~ ~ ~
i~~+ ~ O
~ I ~ ~
~ i ~ ~1~? I
~ ' ;
~ � ~ ~ I
~ ~ ~ i ~ 111 . ~
- z ~ a~
~ z
"~n ;s mn ~rs %,hM ~
a b
Fig. 20. Altitude dependence of electron concentration in the
lower ionosphere for typical daytime (a) and nighttime (b) con-
- ditions
~depen~ence of the corresponding components of field intensity. The lower the mode
_ number n, the less the fluctuations observed in this dependence. Each mode is
- characterized by a modulus an and a phase ~an of the coefficient of excitation,
a phase velocity vn and an attenuation Sn. The dependence of the field strength
~
vector ~n on distance to the transmitter is
~
1:,~~1) Ln~~) H V-a~l�s A e-~2�~~~~,~ , (5.15)
n
I� sin H
where
~'o ~1) _ 300 f P (5 .16)
is� the field strength that would have been set up by a transmitter of power P
under an infinitely conductive unbounded plane [in formula (5.16) Eo is expressed
in~mV/m, P in kW and Z in lan], 0 is the ratio of the distance Z from the transmitter
in proportion to the radius of the earth Rg, h is the effective altitude of the
ionosphere,
~rt = f~�c-P~:~; ~?n -0,~2J-~-~~n f l. (5.17)
U~
are respectively the relative amplitude and phase of the given mode. The amplitude
A and phase ~ of the resultant field are determined from the relations
~
A= I:o~~) H jKi ~~~iA~CU32~t~Pn)9 -~-~}~An s(n 2a~,~)R~ (5.1$) .
~ sln H " "
~:An ~ill 2a~p~~
~irc.t~;" - , (5.19)
ZAR cos 2rt~p~ �
_ ' 38 .
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Thus to determine the phase and amplitude of the field at the reception point it
is necessary to detern?ine the parameters of the most intense modes and to perform
vector suinmation oE the fields that they produce in accordance witih formulas (5.18)
and (5.19). In view of the considerable difficulty of general solution of such
a problem, idealized models of the channel with different degrees of complexity
are used for approximate evaluation of the parameters of the modes.
A model with idealLy reflective earth and ionosphere enables estimation of the
phase velocities of the modes only. In this case, the strict solution for -
f< 16 kHz corresponds most nearly to the relation
' t~n -cI�1 ~2n 32h)~~R -ir2~a 1~ (~.20)
l 3 1
h being the only parameter of the model. ~
In practice, instead of the absolute value of the phase velocity vn, we often use
its difference from the speed of light expressed relatively. In this case
a T'~r ~ 1 - ~~p._~~s~a -h._.~, (5.21)
n� C 3?hz ~k3
From formulas (5.20), (5.21) we see that at comparatively lower altitudes of the
ionosphere the phase velocities of some modes may be greater than the speed of
light. This does not in any way contradict the faaaous assumption of relatively
theory since the value of vn only describes the apatial distribution of the phase
of the field at a certain instant, and is not the velocity of propagatiok of any
physical object. Any signal that is a change in phase or amplitude of the field
near an antenna will lead to a reception point with group velocity that is always
less than the speed of light.
A model with a sharply bounded ionospherethat accounts for nonideality of reflection
from the walls of the ~quivalent waveguide perroits evaluation of all four parameters
of each mode, but in the general case requires numerical solution of the problem
on a computer. The parameters of the model are: altitude h of the ionosphere,
conductivity of tl~e earth ag, and conductivity of the ionosphere oi. Instead of
Qi, the literature conventionally uses the so-called characteristic frequency of
~ the ionosphere
- a~ .
- iu~ _
EV
where Eo - 36~r~ 10-9 F/m is the dielectric constant of free space.
Since losses are small in practice in the earth and ionosphere, we can get approxi-
mate formulas for estimating mode parameters. In doing this, it is p~rmissible
to use the representation
_ an n.n, -I.. /~a(a~) -f- L~a(~~?,), (5.22)
~n - ~~�:i~ (i(u~i~. (5.23~
39
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i. e. the influence of earth and ionosphere on the characteristics of mode propaga- ~
tion shows up independently in the first approxitnation. We give the corresponding
formulas without derivation ~
S
' da (a,i) _ - 0,25 ~ ; (5 .24)
li ~
. ;
_ (;(a~) ~ 0,046 h a . (5.25) ~
r v
Let us note that the values of Da(vg) and S(crg) are the same for a11 modes of the ~
radio signal. ~ ~
na(~u,) - -U,70 � 10-a(2n-- 1)z~ ~ ; (5.26)
~ ~ Y~~
. ~~~u~)=-_O,U192~2n~~ I)~~ (j/1.- ~ 1 ~5.27)
~ I L 1'
where ~ ` :1'?li~
g l~ I 1+(`ln - i)aR:s~~ l~ 1 F,283~ �
,
In formulas (5.25), (5.27), the altitude of the ionosphere and signal wavelength
are expressed in km, conductivity in mS/m, signal frequency in kHz, and attenuation
in dB/lan. To evaluate the modulus and phase of the coefficients of excitatiori
we can use the relations
401~; r h~
n~ ('lli- l~z /?g~~ ' ~5.28~
a h~
~p'~n R~e= (2n - i ' (5.29)
Analysis of these formulas shows that the attenuations of modes increase rapidly
with increasing mode numbers. Because of this, at sufficiently great distances
from the transmitter the phase and amplitude of the field are determir~ed by the
one or two most intense modes. This circumstance, which appreciably simplifies
the summation of modes according to formulas (5.18), (5.19), is used in presen-
tation of the method of calculating the VLF transmission path (see Section 5.4).
A three-parameter ~nodel {h, ~3, wr} with proper aelection of parameters enables
calculation of the phase velocities af modes and the total phase delay of a signal
with relative error of no more than (3-5)�10-4 for paths Z>. 2000 lan. Since it
is practically impossible to measure h, Qg and ~r independently, their values are
estimated from measured parameters of the field at the reception point. At the
present time it is usually assumed that h= 70 lan for day and 90 km for night, and
~~r = 2�105. The conductivity of the earth in S/m, depending on the type of underly-
ing surface, is:
sea. . . . . . . . . . . 8
prairie, wet ground. . . 5�10-3
prairie, dry ground. . . 1�10-3-2�10-4 ,
fresh water. . . . . . . 1�10-3
40
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!'OR flF ~'If.'!AL U~ QNLY`
mountains. . . . . . . . 1�10-4-3�10'S
permafrost . . . . . . . 3-5�10'S
~ permanent ice. . . . . . less than 1�10;5 ~
TABLE 1
Phase velocities of f irst three modes without consideration.of losses
in the walls of the equivalent spherical waveguide
For day (h 7p �km~ - For�'night ~Eh ~~90 km)
~ a~ � 1N ' St.' ~Z i.
~
10 I IS I :0 i 23 I 30 I 10 I 15 I 20 I 25 I 30
� l 2,62 -l,35 -2,tiE -3,63 -4~07 -1,25 -3,96 --5,01 -5,5(i -5,9
2,A9 - u,94 2,31 2,95 3,25
2 48,5 1~~,09 8,66 3,61 0,92 26,2 8,28 1,95 --~,55
3 140,6 60,10 31,70 IS,II 10,92 81,7 32,7 15,8 7.95 3.37
TABLE 2
Corrections to values of phase veloc~ty with consideration of
nonideality of reflection from the ionosphere
For day F~r night
� n~�~o~ at. f, � kSz ~ '
io I is I ~ I ss I ~o ~o I ~s I 2o I ~s I ~
1 0,35 ~.15 I 0,14 0,12 ~ 0,~7 O~AO 0,22 I 0,120 0~08 0,07
2 1,41 0~37 0,30 0,15 Ci,10 0~70 0,20 0,16 0,14 0,08
3 3,4G 0,81 I 0,62 0,32 G1,16 1,45 0~38 0~30 0,18 0~10
TABLE 3
I
Attenuations of modes due to interaction with ionosphere ~
For day Fa~...night
~ ~a. d8~/km ~at ~ kHz .
~,o~,~i~~~~~~~o~,6I~l~~
- 1 3~42 2,54 2,25 2,11 2,Oti 2,A1 2~29 2,24 2,02 l~9g
2 1`1,79 G.32 4,34 3.37 2~89 6,6.5 4~09 2~93 2,64 2~39
- 3 :i1.53 13,89 8,57 5.8T 4.56 ~:4~21 5.51 5.29 3.87 3.22
Knowing the parameters of the propagation channel, we can readily calculate the
components of Aa(a3) and s(~3) from formulas (5.24), (5.25). Tables 1-4 summarize
the values of ano,,~a(mr) and S(wr), which are more difficult to calcul~te. .It
was pointed out above that formula (5.21) givea fairly accurxte values of ano for
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TABLE 4 `
Coefficient of excitation of the first mode* and its phase
. , aB w raction o
f, cycle ~
daytime Inighttim daytfine Inighttime
10 --�2,0!'? --0,43 0,005 O,OI
- I~i -�4,79 -9,91 0,011 O,J24
2U -R,Ifi �--17,41 Q,019 U,042
25 --13,37 --27,2 0 032 O,OtiS
30 -20,1,4 --90~9 O,MB U.Qi)9
*For modes with other numbers An and �~n can
be calculated from the formulas
A~ _ p~~~
~n = (2n.- I)a' 4= ~2n-1)z '
f< 16 kHz. For the frequency range of 20-25 kHz, the values of a,no are understated
by (0.6-0.7)�10-3. ~
5. 4. Daily Variations of Phase and Amplitude of Signal at Reception Point
The principal conclusions and relations of Section 5.3 have been derived on the
basis of the assumption that either daytime or nighttime conditions obtain on the
entire path from the transmitting to the reception point.` Such routes are called
equiluminant. They correspond to values of phase and amplitude that are nearly
invariant in time. In reality, the path between transmitter and receiver crosses
- the line between ni~;ht and day (terminator) twice daily. Exceptions are paths
with one end lying in the polar region, which dictates anomalous conditions of
illuminance (absence of total day or total night, continual day or continual night).
The period of crossing the line between day and night is called the transition
period, and transmission paths at this time are non-equiluminant. During the transi-
tion period, the phase and amplitude of the f ield change rather rapidly, passing ,
fr~m the daytime to the nighttime value and vice versa. At s~sfficiently great
distances from the transmitter, where the interference of terms of the mode series
- has no effect, these variations are trapezoidal. P. Ye. Krasnushkin, who was the
- first to observe the curve of diurnal phase variation and to give it an interpre-
tation based on the mode appxoach [Ref. 2~], called it the phase trapezoid.
In daylight the phase velocity as a rule is gre~~ter than at night, while the signal
phase at the reception point is greater in the ~lighttime than during the day. The
peak-to-eak diurnal fluctuations of the phase--the amplitude of the phase trapezoid
--at a distance can be defined as
' ~t c (a~~~ -a~~~~~~)_ ~ ~va~~ - v~~~~~~), (5. 30)
[subscripts Ax, Ho~ denote "day" and "night" respectively] where v~H, vHO~ are ~
the phase velacities of leading modes for daytime and nighttime conditions.
42
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~ IrR Al~'F7(1 Al . t ~ ~flN~t ~t
Let distance Z be great enough that the first mode is the leading mode both during
the day and at night. Then on the basis of �ormula (5.21) we get
huov -haN h~w~i^ hnu
-
aA~~ - a~~~~~ = . ~ , (5. 31)
32 h= h 2R;~
where h is the mean altitude of che ionosphere, equal to 80 1~. Substituting *~umeri-
cal values of parameters in formula (5.31), we get
anu - aiinv 0,244 � 10-5~a 1,5? � 10-3. .
Most points on the territory of the USSR get reliable reception of signals from ~
a VLF radio station in Great Britain situated about 100 lan to the north of London,
and operating with call letters GBR on a carrier frequency of 15 kHz. Since this
frequency corresponds to ~ wavelength of 18.75 km, with consideration of formula
(5.31) we get ~T = 8.1Z us (distance Z is expressed in thousands of km). The dis-
tance from station GBR to Moscow is about 2550 km, which should correspond to an
,amplitude of the phase trapezoid of the order of 21 us. The resultant value agrees
- well with experimental data of the authors for this route. Analogously, for the
GBR-Irkutsk route we get OT = 8.1 5.220 = 42.3 us; iu Ref. 26, diurnal phase varia- .
tions of the order of 37-45 us were determined for thls longer route.
In cases where different modes predominate during the day and at night, the data
of tables 1 and 2 should be used for calculating the diurnal phase variation.
5.5. Method of Calculating Phase and Amplitude of a Signal (Correlation of Mode
and Ray Approaches and Their Limits of Applicability)
The method of calculating the field of a VLF radio signal must include the following
. principal stages:
1) determination of mode parameters;
2) determination of ratios of levels of the terms of the mode series at the recep-
tion point;
3) selection of the~leading mode or making a decision on the necessity of adding
several terms of the mode series;
4) calculating the phase and amplitude of the signal with respect to the leading
mode or by using a relation that accounts for several modes.
Ixi calculating the phase it is usually considered that the phase velocities of
the most significant modes as a rule differ from the speed of light in free space
by no more than (5-7)�10-3. This enables us to express the total phase delay or
its corresponding apparent time of propagation as
= f (1 a~ ==~TO ~Anii~ ~ ~ 1 -F- a) _ '~o -I-'P~on~ (5.32)
[subscript Ron = additional] To, �o are calculated with respect to the speed of
light, and the corrections to these values are called the additional phase advance
and additional propagation time respectively. Based on the feasibility of repre-
sentation of expressions (5.32), it is advisable to calculate the phase in three
stages:
43
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F'talt U! !'iC'tAL tk~ ~1N1S1P
calculation of the time of propagation t~~ the reception point "at the speed of ~
- light"; i
- ~
determination of the additional propagation time with re~nect tc~ the leading mode `
or by summation of several modes; . ~
4
calculation of the total phase of the field. 1
~
We will give a detailed exposition of the method based on an example of calculation ~
- of a specific transmission path. ~
- Initial data: transmitter is the GBR radio station; r.ec~~ption point in the vicinity
of Moscow; radiation power of the transmitter 60 kW; sign,al frequency 16 kHz; the
route passes almost entirely aver dry land, plains without mountains or permafrost;
path length 2610 km; reception time 15h00m Moscow time in June.
Parameters of the equivalent waveguide: Lhe nomogram of Fig. 36 shows us that '
tt~e entire transmission path is completely illuminated durin;~ the reception period,
and therefore h= 70 km. In accordanc~ with the data on pp 40-41, Q3 = 5 mS/m for
the given type of terrain. Based on recommendations in the literature, we take ;
the characteristic frequency of the ionoaphere as wr s 2�lOs s-l.
Let us determine the parameters of modes.
1. Auxiliary parameters associated with signal frequency:
T= 1000 = 62. 5 us, J~ = 3 f~ = 18. 75 km, W= 6.283f = 1.05 � 105 s-1. ,
2. Phase velocities of the first three modes without consideration of logses
(vn = c(1+ an)). Since the signal frequency f lies between the two tabulated values
fT~ fT+S~ We use linear interpolation:
~ u,,,~ '~~,~~~~�)-f- f-jr ~'~~~o~f~�-I- 5)--a,,,,(~7.~~. (5.33) ,
(i) = 5
For the first mode we get
1
a~p (1G) I. 1,35 2,8G 1,,35) I� lU-3 I,G5 � 10-3,
for the second a2o =-17.01�10-3, and for the third a3o= -54.54�10-3.
3. Attenuations of modes: '
components of attenutation that are due to the finite conductivity of the earth,
,
ii� ca3) ~,~n~,-~:s l%" Q~ =~,~7 �~o~-~ aBl~?;
the component of attenuation due to nonideality of reflection from the ionosphere
is found by interpolating the data of Table 3 using a formula analogous to (5.33).
~ After interpolation we get
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~1(wr) = 2.54�10'3 dB/1~, S2(w~) = 6.32�10'3 dB/km,
g 3(wr) � 13 . 89 � 10- dB/1aa.
4. Coefficients of excitation of modes;
Al - - 5,45 . 10-~' ~i = - 5,45 � 10-3 ~ --5~35 dB;
in accordance with Table 4
n2 = -0.6 as; n3 = -0:2 as:
5. Reiative levels of modes at the reception point:
in accordance with formulas (5.23) and (5.16) for the first mode
~t = (1,~7 2,54) � 10-~ = 4,41 � 10-3 dB/km;
.41=- 5~35 - 4,01 � 10-y � 2e10 = - 5,35 - 10,47=-15,82 dB; �
for the second
~Z = (1, 47 6,32 ) . 10-3 = 7~79 � 10-3 dB /km;
. ~
A2 0,6 - 7,79 � 10-3 � 2G10 20~83 dB;
for the thir.d
= (1,~7 13,89) . 10-3 = 15,36 � 10-3 dB/lcm;
A, U,2 - 15,36 � 10-3 . 2610 37,29 gg; ~
6. Error of calculating the phase of the field with consideration of only the
first (leading) mode:
o 10--~n,-A~~izn~ ~ . 10-S~o~~so= ~ =0,087 cycle.
~ ~ ln G,2R 1.8 � G.28
F
7. Corrections to the phase velocity for the leading mode. In accordance with
fonnula (5.24)
o, 2~ 0 35 ~ 10's
c�:a> - 5
. i~ - ' '
Interpolation of data of Table 2 gives ~a(wr) _-0.15�10-3.
8. Fina.l value of the phase velocity of the leading~mode:
a~ - 7~� -I 1~a~ -I ~1a~ (a~~) ^ - ( l,Gri 0,35 -}-0,15) . lU _ 2,15 � 10-3.
- 9. Phase of the coefficient of excitation of the leading mode:
according to formula (5.29), ~~1= 3�= 0.01 cycle, which corresponds to 0.6 us�
10. Additional propagation time ~
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- -
`-2. I 5. 1 U-a � 2610
la~~~~ = T (Q,125 -F-'f.~,~ -h al ~ _ (0,01 ~,125) . 62,5 = 28,8 us.
- t
k
11. Total apparent time of propagation j
4
- - - - . . _ __.__T ;
'~pE _~nou-f- tnon -f- ~~3~ 1-~- ~~7 � 10-3) = 28~8 8705~1 = 8733~9118.. . ~
1
~
12. Complete phase of the field
_ ~P/T = 8733,g/62,5 = 139,74 cycles . ~
13. Correction for phase delay of signal during propagation
~L,, _ ~,,y - entier ( ~p~,E) = 139,74 139 - 0,74. . ~
The resultant number is the sought correction for signal propagati.on in the earth-
ionosphere waveguide.
14. Signal amplitude is determined by using the results already found. First
the constant factor is found tYiat depends on transmitter power P, wavelength a and
altitude of the ionosphere h ;
~3 _ 3c1~ I~ Na .
R3
For our case
.
= 300 ~~so � ts,?5 - 1,81 mV/m.
~o ss7s
Then the factor that depends only on the distance from the transmitter is determined
u ( l ) _ ~ _ = 1,63.
.in ~ slo ~'-10
~ ~ R;~ &378
The field strength of the signal at the reception point is
F~(~) = B~~ (l) � 10^isn
In accordance witl~ point 5, A a-15.82 dB. Finally
li 1,(i;i � I,R1 � 1(1~-~~;s~ = 2,95~6,20 = 0,475 mV/m.
This er.ample demonstrates an important advantage of the mode approach at suffi-
ciently ~reat distances from the transmitter: it has the capability of accounting
for one mode alone, and thus makes it comparatively aimple to calculate the ampli-
tude and phase of the field aL� the reception antenna. At short distances, where
it is necessary to account for several terms of the mode series, this advantage
disappears. The difficulty of the mode approach is inversely proportional to the
length of the transr~eission path, which is opposite to the situation for'the ray
method considered in Chapter 4.
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Let us recall that the ray method at distances of the order of 500-1000 lan permits
consideration of only one or two rays that have arrived at the reception point
with different numbers of reflections [Ref, 27]. Oa shor:. routes the ray approach
can be successfully used instead of the mode approach or on an equal basis with'
it. As the distance from the transmitter increases, there is a sharp increase ~
in the number of rays with approximately equal amplitudes that are incident on
the reception antenna. Besides, at a considerable distance from the transmitter,
the fundamental limitations of the ray method also begin to make themselves feit.
When it is used in implicit form, it is asstmmed that the signal travles in an fini-
tesimally thin ray, and after colliding with the walls of the equivalent wa.veguide
it changes direction of propagation in accordance with the law of mirror reflection.
However, in reality, even in free space, the signal travels to the reception point
_ as if through some channel that narrows at the ~ransmitting and receiving antennas
and widens ou.t on the middle distances between them.
The maximtnn width of the channel dm~X may be taken as equal to the diameter of ~
the so-called first Fresnel zone [Ref. 28],
AI
dmnx = 2 �
The width of the channel can be disregarded, and it can be considered a ra~ only
in the case where it is less than the height of the equivalent waveguide
d~ua: = I~ 2t h. (5. 34)
From expression (5.24) we get a formula for the radius of the zone of applicability
of the ray approach: .
4?t' (5.35)
A
Calculation~ by formula (5.35) show that in the VLF range, the ray approach can
be used in pure form only at distances up to about 500 1~ in daytime and 1000 lan~
at night [Ref. 27 (this paper gives a detailed description of the ray method as
applied to the VLF band)]. ~
With transition to higher-frequency bands the radius of the zone of applicability
of the ray approach increases. Made damping practically ceases to grow as mode
number ~.acreases, and there is an increase in the number of propagating modes.
- In comparison all this negates the noted principal advantage of the mode approach.
Thus the mode and ray approaches mutually complement one another, enabling compara-
tively simple engineering calculation of transmission paths over a wide range of
frequencies and distanees from the transmitting antenna.
5.6. Error af Cal.culating Propagation Time ~
The error of calculating the phase and group velocities of VLF radio r~ignals is
dictated mainly by two factors: inadequacy of the model of the propaga~ion channel,
and inexactitude of knowledge of its parameters.
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The structure of tlie error due to inadequacy of determining the difference of the
phase velocity of the mode from the speed of light is given rather well by a series ~
of the form , ~
Q = a~A -F- Aa~, . (5 . 36) ~
~ ~
I
where an,~ corresponds to the simplest model--a plane waveguide with ideal reflec-
tion from the walls; ~as is the correction sequentially introduced in accounting
" for the actual properties of the propagation channel. Series (~.36) slowly converges
- to the value corresponding to the actual behavior of the fiEld of a VLF radio signal. ~
The ninnber of terms is large (in principle it is infinite);� however, each specific
model has a corresponding sum of a f inite number of terms of the series. The sum
_ of the dropped terms, or the approximate value of the first of these is the error ~
due to inadequacy of the model. Thus ~al is the error due to nonequivalence of
the plan3r ideal waveguide to a spherical waveguide; ~a2 is the error of the spheri- ,
cal wsveguide with ideal reflection as compared with a model that accounts for
losses in the earth and ionosphere, and so on. The next step in refinement of
the mode'. is transition from a stepwise approximation of the ionosphere to consider- ~
ation of the actual behavior of the altitude dependence of the concentration of
charged particles and the frequency of collisions (correction ~a3). '
;
An important factor is consideration of the horizontal component of the earth's
magnetic field HZ. This disrupts azimuthal symmetry of the model, so that the
corresponding correction ~ay will depend on the direction of the path. .Attempts
have also been made to account for deep layers of the earth, terrain relief, vege-
tation on the transmission path and sa on.
~ The rough values of the corrections due to non-equivalence (inadequacy) for f= 20
kilohertz are: ~al =-5�10-3, Da2 =-0.3�10'3, Da3 =�0.25�10'3, ~a4=.�0.5�10'3.
It must be borne in mind that the actual parameters of the channel are in one-
to-one correspondence only with the parameters of a nonexistent ideal model that
accounts for all terms of series (5.36). The parameters of all existing models
are effective, and have a certain dependence on signal frequency. As a rule, these ~
parameters are nat determined by direct measurement, but are rather chosen in accor-
dance with the principle of b~:~st conformity of the field amplitude and phase calcu- ;
lated with their use to the vaiues observed in reality. Such an approach is called
the "inverse problem method" [Ref. 25]. This is the way in particular that we
have found the daytime and nighttime altitudes of the ionosphere frequently quoted
in this chapter (70 and 90 km) for the model with stepwise approximation of the
- behavior of electron concentration--the model with a sharply bounded ionosphere.
The more perfect the model, the wider will be the range of frequencies, and the
more accurate will be the correspondence of predicted results to experimental data
of investigation of the signal field on different transmission paths. However,
refinement of the model requires more and more information on the parameters of ~
the actual path ~f propagation--in particular on the ionosphere. The possibility
of getting information on the lower ionosphere without analyzing the results of
amplitude and phase measurements in the VLF band is quite limited, and l~oils down ,
to point probing with geophysical rockets at a few scattered points [Ref. 24].
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Because of this, a reasonable comp,:omise is needed between complexity and accuracy
of the model. If the error of calculation of phase velocities of the modzs is
to be of the ~rder of (0.5-1)�10-3, it would be advisable to stop at the three-
~ parameter model {h, a~, wr} discusserl in this chapter with sharply bounded iono-
sphere. When parameters have been appropriately chosen, the model enables calcu-
lation of time of propagation with error of the order of 1-3 us on a 1000 km trans-
mission path in daytime conditions. At nighttime and in the transition period,
model {h, a3, wr} and others that have been studied are less exact than under day-
time conditions (for example, the error of the model th3t we have selected may
reach 5-6 us over 1000 km). Nonethelss, the good agreement between the calculations
of Section 5.4 and experimentally measured amplitudes of the phase trapezoid is
evidence that the ~iven rough value is the upper limit of the computational error.
The additional error of calculation due to inexact knowledge of the parameters
of the model can be estimated by standard methods of error theory, which we leave
to the reader. Most appreciable in practice is the error due to inexact knowledge
of the altitutde of the ionosphere Ahn(~h). The formula for.calculating this ad-
ditional error takes the form
a= n~~ en
oa, ~eh~= ~s~1= R~' cs.3~)
Formula (5.31) 3mplies that in the middle part of the VLF band, ~al(~h)/~h is of
the order of i..l�10-3 1~-1.
Since such error components as ihstrument error, and the error due .`.o statist.ical
fluctuations of the phase at the reception point amount to a few m~:crosecon4s and
are weakly dependent on distance [Ref. 29], the cited error (1-3 us g~'r 1000 km)
is what determines the realistically attainable accuracy of synchronization with
the use of VLF radio channels. For typical transmission paths (Z = 3000-6000 km)
the error of synchronization in the VLF band may reach 10-15 us.
All the given values of synchronization error apply to the case of determination
of the position of the time scale of the reception point relative to the scale
of the transmitting point. The error of mutual tie-in of the scales of two recep-
_ tion points for which the mutual distance Zmut is much less than the distance to
the transmitter is much lower because of the compensation of common systeII?atic
components. For a rough estimate of this effect we can use the semi-empirical
formula
amut~arec= Zm~~ ~ (5.38)
- where d~ut is the error of mutual synchronization of the scales of the reception
points; drec is the error of synclironization of each of the recept~.on points with
respect to signals of the transmitting station. Thus for a typical case (1.mut/Z=
0.25), we get d~ut~brec = 0.5.
CHAPTER 6: METHODS OF SYNCHItONIZING SPATIALLY SEPARATED FREQUENCY AND TIME STAN-
DARDS IN THE UHF AND MICROWAVE BANDS
Regular transmissions of televiaion broadcasta and communications in these bands
rely on radio relay lines, intercity cable lines and artificial satellites.
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Propagation of radio waves in these bands is within the limits of direct visibility ~
for surface radio relay channels (wirhin a range of 50-150 lan), and practically
- unlimited when three artificial satellites are used. In long-range transmissions
over surface channels in these bands, intermediate relay broadcast stations are ~
used that extend the lines between two points on the surface of the earth. ~
These existing channels of television broadcasting and communications are used
likewise for synchronizing and transmitting time and frequency units to users. ;
Radio communications regulatiAns have set aside three frequency bands for these i
systems: 8-th (30-:300 MHz), 9-th (300-3000 MHz) and 10-th (3000-30000 MHz). ~
Radio wave propagation in these bands is influenced by atmosphe~ic inhomogeneities,
turbulence, inconstancy of the parameters of atmospheric waveguides and also the
sporadic ES layer. As will be shown below, when using radio relay lines the in-
fluence of these parameters produces an error of 0.1 u s or less. When using atri-
ficial satellites, the effect of the ionosphere will show up in Faraday rotation ~
of the plane of polarization. In the 9-th band, the coefficient of refraction
will also depend on humidity, temperature and pressure, which differ in different
regions, and at diffe~rent times and seasons.
6.1. U;aing Reflections From Meteor Trails '
For purposes of synchronization by reflection from meteor trails,.frequencies of
40-100 MHz are used in the 8-th band. Meteor trails that can reflect radio waves
are formed at an altitude of 50-100 km due to the fact that the,earth's atmosphere
is continually penetrated by tens of billions of solid particles with mass of
' 0.~1-0.001 mg from outer space moving at a velocity~of 12-70 km/s relative to the
earth. As they penetrate the earth's atmosphere, the meteoric particles are heated
by repeated collisions with molecules of air. Atoms are removed from the surface
of the particles and undergo collisions with molecules of air, resulting in heating ~
of the ambient medium and ionization of atoms. Ae a consequence of ionization
where a meteor has psssed, a trail is formed that contains~free electrons that
over a time of 0.01-1.5 s can reflect radio waves of the 8-th band.
It can be assumed in a first approximation that the number of particles penetrating
the atmosphere in a unit of time is related to their mass; n= k/m, where m is the
mass of a particle; n is the number of particles with mass greater than m; k is
a coefficient that depends on time of day, season of the year and other factors.
The average number of trails ntr crossing 1 m2/s is calculated by the formula
ntr = 160/Ne, where Ne is the number of electrons per meter ~lOl4_1016~,
The meteor trail has a number of specific properties that must be taken into consider-
ation when using it to synchronize time and frequency standards:
the meteor trail has a limited lifetime (a few second or less);
The occurrence of ineteor trails is random over the course of a day, and their dis-
tribution is determined by solar activity;
the energy flux of radio waves reflected from a meteor trail is sharply directional.
- During its lifetime, the trail takes a sinuous c~nfiguration due to wind action, and
- ~ 50
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the ref lected beam in ~some cases of coherent sr.attering of radio waves by an under-
- compacted trail (electron density q�1012 el.ectrons per cm of trail length) is
dispersed.
In the case of such a mechanism of scattering, the following may be po~sible causes
of phase instability:
diffraction effects associated both with the process of trail formation due to
the f inite velocit~ of ineteors, and with the process of trail destr~ction under
- the action of diffusion;
_ displacement of the ref lecting region under the action of winds in the atmosphere..
Ionized meteor trails ref lect signals almost specularly, the reflected signal being
characterized by an init ial surge of amplitude, and rapid decay in accordance with
an exponential function. This Cype of signal makes up about 44~ of the total number
of reflections. Upon reflection from overcompacted trails, the f alling part of
the amplitude of the ref lected signal shows peaks and valleys due to the action
of high-altitude stratospheric winds. Besides this, the reflections from over-
compacted trails (q > 1012 electrons per cm of trail length) laf,t for long times--
up to several seconds--and during this time the turbulent wind twists and breaks
the ionized column, resulting in multibeam prop agation.
The number of ineteoric reflections during signal transmissions depends on the extent
of the path, the time of day and the season of the year (Fig. 21) [Ref. 30].
- ntr _ _ _
20 - - -
~
Z
12 - -
4 _
60 !00 140 1B0 220 260 300 J40 9B0 420 460 nM
_ Q
ntr
4p - - - - -
.~0 _ - - - -
zo - - - -
~a -
f? 16 ?0 ~ 24 04 OB t, hours
Fig. 21.. Population of ineteoric reflections as a function of '
altitude (a) and time of day (b) [Ref . 30]
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The number o~ sinKle sessions of synchroni~tation by ntr varies depending on the j
time of day (Fig. Zlb) and the orientation of antenna systems (Fig. 21~). The .
data of Fig. 21 apply to deflection of the antenna 22� toward the north. When ,
the antenna is turned 22� toward the south, there is a noticeable increase in ntr
in the period from 12h to 18h. The observed diurnal variations of ntr confirm
the advisability of reorienting antennas with a change from nighttime to daytime
measurements.
On Fig. 21a, curve 1 shows the calculation, and curve 2 shows the experimental
behavior of the number of ineteoric reflections as a function of range (altituue)
for the main lobe of the antenna radiation pattern.
Studies of Ref. 31-33 showed that the channel of ineteoric communication has a rela-
tively broad passband (0.2-0.8 MHz), high security of transmission, and is not
overly subject to the influence of ionospheric perturbations thanks to the direc-
tional properti~~s of antennas and the simplicity of sending and receiving equipment.
These advantages allow this system to be successfully used for synchronizing time
and frequency standards at a distance of up to 1200-1400 lan. ~
The point of occurrence of a meteor trail is random and not subject to prediction,
and therefore the path and time of signal transmission is determined only experimen-
tally by using simultaneous opposed transmissions and receptions of signals (methods
of two-, three- and four-beam transmissions). During a synchronization session,
the transmitters are practically in a state of radiation, and the reception devices
fix the occurrence of a meteor trail on the transmissioh path with uniYateral and
bilateral passage of time signals.
The first experimental transmissions were done on a frequency of 73 MHz with a
transmitter having 80 kW pulse power and directional antennas: four seven-element
cophased arrays of the wave channel type. The transmitted time signals were pulses ~
= from a master timer *aith pulse recurrence rate of 100 Hz and duration of 10 us.
Variation in altitude of reflection fram the meteor trail was 86-105 km. The field
strength at the reception point was of the order of 10 uV/m. ~
In this research, clock synchronization was by a methcd of simultaneous transmission
and r~gistration of time signals (two-beam method). A disadvantage of the method
:.s the necessity of exchanging results of registration over an additional communi- ,
- cation channel.
Subsequently, duplex synchronizat~on methods with unilateral or bilateral rebroad-
casting were used for such systems in synchronization of time standards. Fig. 22
shows a system for synchronizing the time scale of point 5 by using reflection
from meteor trails. Time signals from a clock at point A are transmitted after
reflection from the meteor trail to point 5 and returned to point A together with
- time signals tranmitted from point B. Simultaneously with emission of the time
signal from point A, a reversible counter is triggered there that operates in the
addition modE (forward count). The time signal from point E switches the counter
at point A to the subtraction mode, and the time signal transmitted from point A,
after it has been rebroadcast from point E, stops the pulse count of the counter.
Half the difference of the count gives the discrepancy of the time scalgs reproduced
at points A and B.
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FY~R c1F t~ trl!?1. t~5~: c?Nt.Y ~
. /
' / \ .
~ \
r ~
/ . ~ .
~ 2 3 2 ~
A 5
9 4 4 9
B 6 S 5 6 B
7 Q f0
. ~ stBYt ~ , ~
. ~
~ ~ i ~ T"~ reverae To "~top .
i
. ~ i~ ~ I i ~ / I
~ ~ ~ 7 ~ I
f~ ~j ~ ~ � ~
---~----i�~. . d ~ � Cotlrit d T "COi1rit
. _ I _ - - -------f---------~
~ ~e
p'
Fig. 22. System for synchronizing time scales using reflection
from meteor trails:
a--block diagram of reception and transmission equipment; b--
diagrams of signal transmission; 1--receiver; 2--antenna commu-
tator; 3--UHF transmitter; 4--modulator; 5--submodulator; 6---
matching device; 7--synchronizing standard; 8--reversible counting-
type frequency meter (in the mode of time interval measurement);
9--interference-killing and commutation equipment; 10--time stan-
dard to be synchronized
Thus clock synchronization is done automatically wi~hout, additional exchange of
information between points. In addition, such a method er;ables verification of
the correctness of the setting of the synchronizing clock at the point being syn-
chronized, which in this case may be unattended.
With identical.equipment at both points, the method gives high precision of clock
_ synchronization.
Experimental~work on Moscow-Gor'kiy and Moscow-Khar'kov transmission paths [Ref. 34]
- has shawn that clocks can be synchronized with an error of less than 1 us when
- meteor trails are used. ~
6.2. Use of Television Channels
Intercity cable and radio relay lines are_characterized by a broad passt~and, a
signal-to-noise ratio of 50 dB, high stability of the parameters of equipment and
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transmission channel (which in turn enaures high constancy of the time of passage
of exact time signals over long distances), and by the capability of direct measure-
- ment of the time of signal transmission.
Thanks to the wide passband, the risetime of the transmitted pulses at the reception
point is of the order of 0.2 us or less.
Bandwidth is determined by the ratio of the message spectrwn ~F and the signal
spectrum W. The latter in turn is determined by the selected type of modulation
and signal duration T. For narrow-band systems ~
~F = W and OFT = WT = 1, '
J
while for wide-band systems
- W�~F and WT = 100-1000. '
Frame and line synchronization signals and signals of other types are transmitted ~
together with the picture signals to stabilize the image on television screens.
As they are introduced into the makeup of the television signals, the3~ can be used
to transmit information on the instants of exact time signals in a variety of tele-
vision systems differing chiefly in the order and rate of analysis and synthesis
of image elements.
The following image-scanning techniques are known: linear (sequential), inter-
laced, diagonal and spiral.
r ~
2
~ 3
3 S
4 6
~ ~
t-1 ~
Z-~ ' i
Z a
z ,
' ~ Q+0,5
a a
Fig. 23. Image scanning
In sequential scanning (Fig. 23a), the elements are analyzed by continuous tracing
of the transmitted image in sequence along each Iine. The number of lines in a
frame may be constant, in which case
- f, � : Z~ . (6.1)
iN
where z is the number of lines of the scan.
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In the case of interlaced scanning (Fig. 23b) there is no such relation between ,
scanning frequencies, and
f: = m (a -i- b), (6. 2)
fK
where m is the scanning multiFlicity, and a is an integer; b is any number.
In a television broadcast system it is assumed that m= 2, b= 0.5, a= 312, i. e.
in each image field there are 312.5 lines, and as a result during frame scanning
the lines of both fields of one frame are automatically shifted.
Interlaced scanning is used in the Soviet Union. Fig. 24 shows signals of the
- first and seconci fi~lds of a television image.
~ z ~
_ 2sN=a / j
?1SN ?SN ?,SH H ~II
Q
611~67J
624~62S~I ~62 ~ J ~ 4 ~ S ~ i6 s, ~22 ~ t3 ~ ~ ~
2-nd field~�-~I-st fi~eld I .
~ I
I 25H"Q f 1
2,SH ?,SN 2,5N 1
~ L
- n n n n n,~~ n n n n ti n n n n~(~
309 J/0 3/1 3/2 9/24 nd J6 3>7 d1B J19 ,~JS 3J6
1-st f ield' 0 f-~`f 1eld ~7
~B ~
..9 I~ ~6~ us _ ~
T
u z,~ ~ 10
~ ~V'~~
Fig. 24. Complete television signal at the beginning of each .
first (a) and second (b) f ield: ~
I--white level; Il--black level; III--bl.anking level; IV--synchro-
nizing pulse level; 1--line signal; 2--time signal; 3--line blank-
_ ing pulse; 4--frame blanking puls~; 5--line synchronizing pulse;
6--leveling pulse; 7--frame ~ynchronizing pulse; 8--pulse shaped
from cutoff of frame synchropulse; 9--local cloc:c seconds pulse;
10--beginning of line; 11--beg3nning of field; a--duration of
line quenching pulse 12 � 0.3 us; numerals indicate frame line
n~nabers
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The duration of tl~e entire frame quenching pulse is 25H= 25�64 �s (where H is the ~
duration of a line). In interlaced scanning, the frames of the television image ~
alternate at a repetition rate of 25 frames per second. The line scanning frequency i
is fZ = 15625 Hz. Nominal f ield scanning corresponds to the ratio ffi~ld = ZfZ/625 = ~
- =50 Hz. ;
The following lines are set aside for service nse: ~
~
16 and 329--identification signals; ~
17, 18, 330 and 331--test line signals; i
19, 20, 21, 332-333 and 334---signals for in-house use; '
7, 8, 9, 10, 11, 12, 13, 14 and 15 (in the first field), 320, 321, 322, 323, 324, ~
325, 326, 327 and 328 (in the second field of a frame)--color synchronization sig- ;
nals. Chrominance signals are a subcarrier modulated by two color-difference sig- ,
nals that alternate from line to line. The subcarrier frequencies used in di:Eferent
systems are: 4.429687 MHz (NTSC), 4.43361875 MHz (PAL), and the SECAM-3 systt~m
has two zero subcarriers (4.25 and 4.40625 MHz) located alternately on the trailing
flats of the line quenching pulses. ,
Test signals are used to monitor the white level by mesns of square pulses, ar~d
to evaluate: .
the amplitude-frequency response of the video channel by means of a signal with
six bursts of sinusoidal waveforms situated sequentially in ordpr of incr~asing ;
frequen,cies along the line (0.5, 1.5, 3.0, 4.5, 5.0 and 6.0 MHz); , ~
the transient response of the video channel in the video frequency range by means
of sine-square pulses with duration of 0.16 us;
nonli.nearity of the amplitu3e response of the video channel by means of a sawtooth
signal with superposed sinusoical waveform on a frequency af 1.2 MHz.
The television program is radiated by the telecenter on fixed carrier frequencies
- individually for the image and sound in separate radio channels. For the Moscow ;
Television Technical Center (TTC), the 1-st, 3-rd, 8-th and 11-th television broad- ,
cast channels are assigned. The nominal values of carri~r frequencies for image
and sound are summarized in Table S. ,
- Existing systems for transmitting dimensions of time and frequency units over tele-
visiun broadcast channels are differentiated into passive and active systems de-
_ pending on the method of coding information on the moment of time [Ref. 35, 36].
In passive systems, characteristic television synchropulses or apecial marking
pulses transmitted as part of the televiaion signal are used ae auxiliary signals
that are simultaneously registered at the synchronization points. Information
on measurement results is exchanged over an auxiliary communication channel, or
else the information on measurement results is transmitted from one point to the
other by a special code that is part of the televisior. signal.
In active systems, c?iaracteristic television synchropulses (most frequer~tly used ,
is the trailing edge of the first frame synchronizing pulse during frame quenching)
- 56
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TABLE 5
Nominal values of carrier frequencies
Channel fre- Carrier frequency, l~z
Channel quency ba~d,
MHz~ Image I Sound
~
I 48~5--5~i.5 49,75 5t~,25
2 Si$,0-b~i,0 59,25 f5,75
3 7f,~0-R4.U ?7,25 83.75
4. t34,0-92,0 85,25 ~1,75
5 92,0-100,0 � 93,25 9~ ,75
~ G 174,0- 182.0 i75.25 131.75
7 182.0- 1J0,0 183,25 It~,TS
8 190 , 0--1 ~J8 .0 I 91.25 1~) 7.75
9 198,U-206,0 199,25 205,75
10 20G,0- 214,0 207.25 ' 213,75
I l 214,0-222,0 215,25 221,7fi
12 `122.0-?'j0,0 223,2b 229~75
or seconds-marking pulses transmitted as part of the Celevision signal carry direct
information on the instant of time in the unified system of the State Time and Fre-
quency Standard [GEVCh]. Registration of these signals at the reception point
by an oscilloscope with drivQn sweep or a time-interval indicator makes it possible
to superimpose the the instant of output of the aecond~marking pulses of the local
clock with the second~narking pulses of the GEVCh clock (with consideration of
the time for the signals to travel over tl.~ radio relay line or intercity cable
line) without any auxiliary informati~n.
The error of tie-in c?f time scales reproduced at apatially separated points has
the same order of magnitude with use of either system since it is.determined mainly
by inconstancy of the time of signal travel over the radio relay or intercity cable
lines. ~
On the other hand, the systems differ in effectiveness from the standpoint of re-
liability of the results, simplicity of ineasurements, cost, flexibility, working
reliability and so on. The active system is preferable.
The method of synchronizing time and frequeacy standards over television channels
is realized by the State Time and Frequency Service [Gosudarstvennaya sluzhba
vremeni i chastoty; GSVCh] of the USSR [Ref. 37]. An active system hae been set
up at the Moscow TTC based on a precision time and frequency reference standard
that ensures constancy of instants of output of time eignals and frame synchropulses
from the television transmitter antenna in the unif ied eystem of GEVCh. A block
diagram of transmission of highly stable synchroniZation signals from synchrogener-
ators at the TTC and incorporation of titne signals into the television sigaal is
shown on Fig. 25.
The following methods can be used to control operation of the synchrogenerators
at the TTC from time and �requency reference standards: � .
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t~~(1R q}'F~C1a1I. l1b`~ pNl.~
~
~
_ _ _ :
C Q EVCh rn ~ I f
_ T~ _ T~ � ~ ~
~ r .J ~ 1 ` ^ y^~ ,
I -------1 ~>0 11 ~ i
~ ~ ~ .l ~ ~ ,
~ U-a--� 3 4 S 'j B 9 i!d f2 i ,
~GSVCh~ ~ Mos,~ow~C~; 6 ~ ;
~
Fig. 25. Synchronization by television: ~
1--GEVCh; 2--transmitting correcting device; 3--receptfon cor- ~
recting device; 4--reference frequency standard; 5--central ~
equipment room; 6--Os~ankino radio transmitter; 7--radio relay '
� line; 8--terminal radio relay station; 9--local telecenter; 10--
PShT-1P recording receiver; 11--selector for isolating first
cut-in of the frame synchropulse and time signals; 12--time-
interval measuring device; 13--digital printer ;
1) a voltage from the reference atandard is sent to the synchrogenerator instead
of the internal generator voltage;
2) synchrogenerator is changed to the driven mode from simplified synchronization
signals (SS or SSTs [expansions not given]) formed from a voltage with frequency ~
of 100 kHz from the reference standard.
These signals are used simultaneously for internal synchronization of all equipment
of the television center. The SS signal is a mixture of line synchrogulses with
duration of 2 us (fZ = 15625 Hz) and frame synchropulses with duration of 28 us
(fK = 50 Hz). In addition to these pulses, the SSTs signal also contains pulses ,
of 28 us duration (fSig = 12.5 Hz) intended for chrominance synchronization of the
telecenter equipment. ~ '
The second method of controlliiig operation of the synchrogenerator not only synchro-
nizes and cophases the line synchropulses, but also mainta3ns the temporal position
of the synchropulses and the field pulses of the television signal. The method
used at the TTC f or centralized synchronization of all equipment at the center
keeps the instant of output of the frame synchropulses from the television transmit-
ter antenna in re~ister with the signals from the time and fxequency reference
standard regardless of the nature of formation of television transntissiona (direct
a- transmission from a studio, motion picture film, magnetic tape). The automatic
control system used in present-day black-and-white video tape recorders sets the
- phase of synchropulses reproduced from magnetic tape relative to the phase of the
signal from the reference standard with an error of tU.2 us, and in color video
tape recorders--wiei~ an error of �30 ns [Ref. 38, 39, and also State Standard
GOST 7845-72].
In future, with full implementation of centralized synchronization of all image
sources in the telecenter, time signals introduced into line amplifiers of TTC
central equipment must be present in the television signal throughout tl~e working
time of the telecenter.
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Time signals and bursts of reference carrier frequencies transmitted as part of
television signals of reverse polarity to synchropulses~ are pulses of 2{~s duration
with recurrence rate of 25 Hz, the pulses arriving at the beginning of each second
being prolonged to 10 us. The time signals are accommodated in the central part
of the sixth line of the first field of the television sigaal (see Fig. 24). The
second-marking time signals fol.low 326 us later than the cutoffs of the frame syn-
chropulse~; this time can be different, and is established depending on the point
of insertion of the second-marking signal. The set delay remains constant during
all transmissions, and is determined by the GSVCh. .
Choice of Synchronization Method
Selection of the method depends on ~the type of registration of signals at the syn-
chronization point, and on the method of information coding. In the case of an
active synchronization method, a procedure can be used that is based on recording
either time signals transmitted as part of the television signal, or the first
cutoff, the pulses being transmitted from a scale synchronized with the GEVCh.
In the first variant of the method, the diacrepancy of the local time scale repro-
duced at a point to which a Soviet-wide television program is transmitted over
radio relay lines and intercity cable lines relative to the GEV~h scale is deter-
~ min~~d from the expression
_ r tTC + T~~ T:~~ S~
~T~~ = T� l Lc~ a P ~6. 3)
r
where TH is the time interval measured at the synchronization point between the
second-marking pulse of the local clock and the second-marking pulse differenti-
ated from the television signal; vZ = TP is the signal travel time over a radio
c
relay line oY intercity cable line from the Moscow TTC to the terminal radio relay
station; Ta~ is the signal travel time from the terminal radio relay station to
the antenna of the transmitting station of the local telecenter; Tp is signal travel
time from the antenna of the local telecenter to the antenna of the synchronization
point (see Fig. 25); T3 is the delay time of the recording receiver at the syncl:ro-
nization point; d is the error of establishing the inatant of output of signals
from the transmitting antenna at the Ostankino station.
For points located in the zane of direct reception of televiaion pr~ograms trans=
mitted by Ostankino, the discrepancy of scales of time standards can be determined
from the formula .
n~~f ~~N. T, ~ � a, ~6.4>
where Tpl is signal travel time from the Ostankino antenna to the reception antenna
at the synchronization point.
When using ttie second variant of the method, to elim3na~e ambiguity of readout
with discreteness of 20 ms on the one-second interval, it is necessary to pre-
~ synchronize the time scale with respect to signals transmitted by short-wave, long�-
wave and VLF radio stations with an error of 1-5 ms. ,
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~ i.
In the case of the passive method, a procedure is used in which synchropulses are ~
recorded at two points, where these pulses have not been synchronized and are not ;
tied in to the GEVCh, and the instant of output of frame synchropulses from the
transmitting antenna of the radio station varie~ by a random law. Time scales
for points situated within the range of action of a local telecenter or for remdte
points to which a television program is transmitted over radio relay lines or inter-
city cable lines can be synchronized under condition that the same frame synchro- '
pulses are recorded at both points. In this case, the inequality
i
~1TN (tP Tr -f- Ta c-~- T~) C 3~ ms ~ (6.5) ;
t
must be satisfied, where OTM is the error of presynchronization of the timE standard. ~
- The discrepancy of the scale of the local time standard relative to the GEVCh scale
is determined from formula (6.3) at TH = TH - To, where to is ~he time interval mea-
sured in Moscow.
In all transmissions, the temporal position of the cutoff of the first frame syn-
chropulse with respect to the GEVCh scale remains constant. The user gets the
values of T~, To and d by request accoraing to the procedure outlined in the Trans-
~ mission Schedule.
In mutual synchronization of time standards, when the standard to be synchronized
is any reference standard, and characteristic synchropulses are simultaneously
registered at the point of location of the time standards, the discrepancy of the
time scales is determined from the formula
l'~ 1
Tn ~r - ~E_r,t _ E~cTS) -f- T T -I- ~TA - 2~ ) (6.6)
r r ~ v +
r
where ET3A~and ET96 is the overall delay of frame synchr~oni~ation in the transmitting .
and rebroadcasting equipment between points A and B; ~T -!r is the difference
ar
of travel time of signals from the transmitting telecenter to the points where
the synchronizing and s}rnchronized time standards are located; vr is the group
velocity of radio wave propagation; is the difference of delays in the
recording receivers of points A and B.
Synchronization Error
~ The synchronization accuracy in such a method ia considerably dependent on the
operation of the selector and the circuit for gating the frame synchronization
pulses, and on the resolution of the time-interval measuring device.
The error of tie-in of time scales with the uae of active and passive methods is
of the same order of maonitude [Ref. 40]. This can be attributed to the fact that
the principal errors arise due to inaccuracy of determining the signal travel time
on the transmission p~ith from Moscow to the local telecenter, and from the tele-
center to the tie-in point, and due to delay in the equipment of the telecenter
and the tie-in point, which is equally detrimental to the results of calculation
of the discrepancy of time scales relative to the GEVCh scale.
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Error of synchronizing scales of time standards
BATT = 8~s� b~ BB~,. (6. 7)
v~P
Overall error
~ s
- oeTT - ~aT~J' + ~a ~ v~ + E ~aT,~~, ~6 . s) ;
. P
where dT is the registration error, 82 is the error of determining the distance
between Moscow TTC and the tie-in point, dv~p is the error of determining the mean
group velocity of radio wave propagation, dTg is the error due to instability of
signal delay time at the telecenter, in intermediate relay stations and in the
recording receiver.
To determine the possible error of synchronization of time standards when using
television signals, it is necessary to evaluate the influence of a11 destabilizing
factors of the transmission channel. The principal ones are the following:
1. Error of registration dl or measurement of time intervals between the signal
of the local time standard and the received signal. This error is determined by .
the error of the measurement method and the reaolution of the time-interval measur-
ing device.
2. Instability of reception equipment of the reception points d2.
3. Error of determining the signal travel time from the antennas of television
transmitters to antennas of the reception point~ 03 and d,,.
4. Change in temporal positio:i of signals during travel through the channels of
radio relay lines ds.
_ 5. Instability of delay of equipment at the television centers d6 and d~.
Let us consider quantitative evaluation of the enumerated ma~or components of
errors of synchronization of time standards [Ref. 41-44].
1. In practice, di.can be reduced to 0.02 �s, conaidering that a counting-type
frequency meter.with high counting rate is used as the time-interval meas~~ring
device. If the count rate is 1 MHz, resolution will be 0.01 �s. The second compo-
nent of dl wi11 be determined by the rise time or fall time of the signals trans-
mitted through television channels, and by the aignal-to-noise ratio.
- The mean square error is
7',p .
o,~, ~ .
9 1~ 2rr
where T~ is the rise time of the signal, q is the sigrial-to-noise ratio,� and n
is the number of signals used for the measurement.
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For a rise time of 0. 3 us, n= 1 and q= 10, error Q~ = 0.02 �s .
2. Error d2= 0.06 us.
3. Errors 83 and 84 can be determined from the following considerations. ;
The value of -.P is determined either by. calculation or~�-exper.imentally.
ln calculation, v~p is taken as equal to the speed of lig'ht, and Z is found from
the coordinates of the reception point. .
- This merhod is most frequently used only for cases of intracity synchronization
when Tp is established with direct transmission through the ether from the tele-
center to the antenna of the reception point without re~ays. In intracity broadcast-
in~, rp can also be determined by using laser range finders or by measuring with
the parallax method. For Moscow points the parallax angles are differences of
zenith distances measured from the synchroni:;ation point to three tiera of the
TTC television tower. The mean square errors of the average values of the zenith
distances of one of the points as calculated from internal convergence of ineasure-
- ment results in receptions and semi-receptions are: for tier I ~_�2.6; II ~_�3.1;
III t2.9. The distance Z from the GEVCh to the television tower was obtained
twice from the values of reference bases (Fig. 26): with r~spect to basis I-III
of 260 m, Z'= 32681 m; and for basis I~-III 178.5 m, Z'~= 32756 m. The final value
is taken as the weighted average between these two results (~he weights are inversely
proportional to the lengths of the bases), Z= 32712 m. ,
Moscow TTC '
~ iii
il �
. /~1 ,
~ ~
Tie-in
point ~ ~
.
. ~
. o0
~L = 97/70 t 70 M
r . _ . - -
Fig. 26. Parallax method of distance measurement
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A 6 _
z~ _ 3
7q 1 2
start stop rpi ~
~ a
start
_z~ _
Tq S Z - - - - ~ ~ '
_ zA2 stop
- b ~
start '
TA S Z'pL,- 3 �
J
A '
2 ~ - - BtOp'
start - -
~ rpi 6 T~ ,
stop ~
Fig. 27. Diagram of determination of signal travel time over
main television chaanels:
1--pulse generator; 2, 3--relay stations; 4--counting-type fre-
quency meter; 5, 6--preciaion time atandard
For remote synchronization points to which television programs are sent via r~elay
rebroadcast lines or intercity cable lines, the loop method3.s used (Fig. 27a) com-
prising forward and reverse television channels, i. e.
A
~`v~ ~`v~ - eTA (6.9)
, ATA
~n _ .
when T~'~ - TP~; .p - 2 .
In the presence of a purely physical pair, where tp~ ~'r'~,,~ additional measurements
are made by the arrangement of Fig. 27b, whence
_ tr~-tn, i ~TA. (6.10)
Simultaneous solution of equations (6.9) and (6.10) gives

- . ATA ATa .
~ _ (6.11)
'CP~ - 2 ~
ATa - ~T~
. ,~q = 2 . (6.12)
In the presence of a single duplex channel, the measurements are done in the follow-
ing order: a loop is set up to determine the value of ~T~ at point B, and the
value of ~TS at point A. In addition, alternate measurements are made at points
6 and A by the arrangement of Fig. 27c, using synchronized precision time atandards
at point A(5) and point B(6) with registration of the received signal on the
local clock. From measurements
+ z~, e~�~, c6. i3>
. T~; cM - dTb~ ' (6.14)
b3
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from measurements by the loop
T~ + 'r, ~s~,~ = ATA~ ~ (6.15)
~ T~, + T~, + T~, = eTh� (6. ~6)
After solving equations (6.16)-(6.16)
.P, ~ oT; -eTb, ~6.i~~
T~, = eT~ - eT~. ~6. i~~
The error of ineasuring signal travel time in radio relay lines, as in the preceding
_ cases, is determined mainly by the error of registration, or by the instrumental
error of the recording device, which amounts to 0.01 us (for counting-type frequency �
~neter 4 at a counting frequency of 100 MHz).
4. Error ds is due mainly to instability of signal delay time upon passage through
radio relay stations; d5= 0.5~, where n is the number of relay points of a radio
relay line.
5. Error d6 = d~ = 0.4 us.
If we assume that all the factors determining the temporal position of television
synchropulses as they are recorded at time standard synchronization points have
a mutually independent random influence, the total synchronization error using
nonspecialized equipment is
a_= V$1z t,Z~ os~ oaa oaa a~ ~ 0,18 1-f- 0,2n. (6 .19)
A change in residual attenuation of radio relay line ch~nnels, deviation of ampli-
tude-frequency and phase-frequency responses from monotonic, and asymmetric limita-
tion of the spectrum of amplitude-+modulated signals (d5) occur fairly slowly compared
- with the duration of a session of time and frequency standard synchronization. In
this connection there is a possibility of reducing the synchronization error, par-
ticularly on transmission paths of 2000-3000 km, by measuring the signal transmis-
sion time through the radio relay line immediately during or after the synchroniza-
tion session.
in the case of intracity synchronizatior~, t?`.~ error is about 0.01 us.
Sibnal Reception and Recording Equipment
Fairly simple recording receivers are used in all methods of synchronizing time
and frequency standards. The principal components of this equipment are a standard~
television set, a counting-typ~e frequency meter and a selector for isolating the
required si~nal from television synchropulses.
Let us consider tl:e PShT-1M recording receiver. This instrtmment can synchronize
time and frequency standards from reception, isolation and recording of time sig-
nals (1 and 25 Hz) transmitted as part of a television signal; ,
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from reception, isolation and registration of the cutoff of television frame syn-
chronizing pulses;
from collating the frequency of a precision standard with the GEVCh scal~, using
television synchropulses or time signals or sine-wave signals, using the differen-
tial method of collation. For an averaging time inte~,val of 20 minutes on a fre-
quency of 1 MHz, the error of the collation method is (8-10) �10-11.
T _ _ _ _
! - ~ - - - . - - ~
_ r-r-rn _ 1 1
_ ~ ~ 25 Hz.
I I
I � S 6 7 ~ B
I ~z I start
- ~o >0 il � 17 1,T 14 !S 16
, ~i r~~ s~Eop 1 Hz
; li !r~ 1.9 2! ~ 12 ?3
~ - - - ~~i'
Y in ut external tri er ~
14 1S - 75 27
Fig. 28. Block diagram of PShT-1M:~
1--Video amplifier of Yunost'-603 television; 2--differential
amplifier; 3--coincidence stage; 4--gating pulse generator;
_ 5--kipp oscillator; 6, 10, 14--c3ignal amplifiers; 7--integrat-
ing circuit; 8--digital printer; 9--electronic clock; 11--shaper
stage; 12, 20--Schmitt trigger; 13--differentiating amplif3er;
_ 15--signalstop stage; 16, 21, 25--frequency dividers; 17-19--
freq~iency multipliers by 2.8 and 4; 22--phase d.~tect~r; 23--
_ time and frequency standard to be synchronized; 2,4--oscilloscope;
26--phase shifter; 27--chart recorder
A block diagram of the PShT-1M is shown in Fig. 28. A Yunost'-603 standard series-
produced television set is used as the receiver.
From a control point of the video amplifier with positive polarity and amplitude
of at least 1 V, the coYap_lete television signal goes to switch TIl. After amplifi-
cation, this sign~il is sent to stage 11 in which the level of the synchronizing
pulses is fixed with lim~tation on the quenching level. This ensures unchan_ged
amplitude of the signals from the output of 11 when there are fluctuations in the
amp]~i~tude cf the output signals. The aignals are then sent to Schmitt trigger
12 to make the synchronizing pulse edges steeper. After the Schmitt trigger, the
cutof~s of the frame synchronizing.pulses are isolated from the television synchro-
mixture by differentiating amplifier 13. The time constant of the differentiating
_ ~ircuit of the ampl~.fier is ~elected so that line synchronization pulses with dura-
tion of 5 us pass tl-xr~ugh it without diatortion, while frame synchronizing pulses
with duration of 30 ~as are differentiated, and stop signals are formed from their
cutoffs by amplifier 14 working in the limiting mode. '
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Under all working conditions, stage 15 is triggered from a seconds-,marking pulse
of the local clock. These pulses come from frequency divider 16, the stop pulses
being sent to the input of this divider.
To get reference frequencies of 10 kHz and 1 MHz, the device incorpora~es a system
of multipliers that convert the line frequency (15625 Hz) to 1 MHz, and a frequency
divider 21. A distinguishing feature of multiplier systems is that the first stage
has a quartz f ilter for frequency 2fZ = 31250 Hz, and signals of the complete synchro-
mixture are sent to the input o~ this filter after differentiating amplifier 13. ,
vifferentiation of the synchromixture is necessary to protect the frequency multi- ;
plier from the influence of tlie pulses that take care of conversion from frame '
synchronizing pulses to trailing controlling pulses.
~ Reference frequencies frcm the output of the instrianent can be used to check vari-
ous precision �reyu~ncy-measuring equipment and for prolonged collation of the
frequency of the standard (for example by phase detector 22 and chart recorder
27 or by oscilloscope, using Lissa~ou figur~s).
To collate the frequencies of high-stability frequency standards, it is suff icient
to take a few readings of the temporal position of frame synchropulses or time
signals relative to pulses of the local time and frequency standard through set
time intervals (in the active method), or to register the position of the frame
synchropulses for standard time intervals (in the passive method). ~
Synchronization by Television Channels Outside the USSR
_ In the Unitad States, specialists at the National Bureau of Standards (NBS) since
1969 have used a method of simultaneous registration of characteristic synchropulses
with subseauent exchange of information ~n the measurement results for synchronizing
radio st~tions that transmit exact time signa'ls and reference frequencies. Outside
the USSR, television signals were first used for comparing remote clocks in 1965
by specialists of Czechoslovakia (Prague) and East Germany (Potsdam) [Ref. 37].
In transmissions, television channels of three firma are used: ABC, CSS and NBC.
The method that is used does not require that the transmitting television station
be in�ormed of its participation in the measurements [Ref. 45].~
' In 1970 the NBS worked out a method of introducing code inforn?ation into a tele-
vision signal on time and frequency by binary phase modulation of a 2 MHz subcarrier
stabilized by a cesium standard for a passive system of clock collation. On the
- seventeenth line of the first and third frame quenching pulses after the'begin.ning
of each second, a 1-2-4-8 binary-de~imal code containing 32 binary digits tran;zmits
the hours, minutes and seconds of universal time. On the I7-th line of the second
frame quenching pulse a si~-bit code is transmitted'that corresponds to the number
of microseconds from the beginning of the preceding second to the beginning of
the code. On all remaining 17-i.h lines, sine-wave signals are transmitted on a
frequency of 2 MHz for phase synchronization of the quartz oscillator at the recep-
tion point. The synchronization error with use of this method did not exceed
0.1 us on a 45-km transmission path.
In 1972, th~ NBS did a series of experimental transmissions of "active" signals
in coded form over U.S. television communication lines. Running time information ~
66
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is coded into a bi~iary-decimal signal and transmitted in the second half of the
first line. A sine-wave signal with frequency of 1 MHz is tratismitted in the first
half of this line that is coherent in phase with the standard frequency signal
of the NBS and is used to get inforc~ation on~exact time and frQquency. In the
broadcast studio of the television network, an atomic~frequency standard is installed
to synchronize the television synchrogenerator and zhe generator of coded time
signals.
- 6.3. Usin~ Artificial Satellites
Some Information on Artificial Satellites
Artificial satellites of various types--communications, teJ.evision, meteorological,
navigational, geodetic--can be successfully used for synchronizing precision time
and frequency standards separated by great distances and situated in inaccessible
~ northern and mountainous regions or on ships. -
Exact time and frequency signals can be transmitted directly from the satellite
if it carr~es precision time and frequency standards (this kind of satellite is
cal.led "active"), or.reflected from i.he satellite, which in this case acts as a
passive or active reflector (relay). An exampli. of a passive satellite is the
Echo-1 launched in 1960 in the United States--an inflated balloon with aluminum
coating to ensure high reflectivity of radio signals. An example of an active
satellite is the Anna-1B launched in the United States in 1962 for mutual tie-in
of ground-based points (light beacon). Relay satellitea such as Molniya (USSR,
1965), Relay and Telstar (United States) operate ori the relay station principle,
rebroadcasting signals transmitted from the ground.
~ Depending on their purpose, artificial satellites move around the earth in diff~rent
orbits distinguished by the following parameters:
inclination of the plane of the orbit to the plane of the earth's equator (at an
angle ~f 90� the orbit is polar);
shape of orbit (circular or elliptical);
altitude of orbit above the earth's surface.
The shape of the orbit is determined by the velocity at which the satellite is
in~ected into a near-earth orbit. At orbital velocity (7912 m/s) a rocket becomes
a satellite and will move along an arc of an ellipse with eccentricity e< l, or
~ of a circle when e= 0. In the latter event, both foci of the ellipse coincide,
and are situated at the earth's center of gravitation. According to Kepler's first
law, one of the foci of an ellipse must be located at the earth's center of gravi-
eation (0 in Fig. 29). The second focus 0' is accordingly located at the same
distance from the apogee of the satellite orbit as the center 0 is from the perigee.
The equation of the ellipse on the plane in polar coordinates is
u (I �-~z)
r I-}- r. cos Q;~~~ ~ ~ ( 6. 20 )
~
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I
i ~ ~y ~ :
- ~ '
- ` sate111te
I r earth
I (
0' p perigee
apogee X .
. I �
. I ' ( �
a
' yQ ' y~ � ,
Fig. 29. Satellite orbit
where a is the semima~or axis of the ellipse; QaH is true anomaly of motion; t:ie
eccentricity of the eYlipse is
~ : . O~, j~~, _ . _ f,,, . .
n- ~ 'lu '
- where b is the semiminor axis nf the ellipse; Ha at~d Hn are the respecti.ve. distances
from the apogee and perigee to the earth's center of gravitation.
As the initial velocity of in,jecting the satellite into orbit increases, the param-
eters of the ellipse change, and the second focus of the ellipse 0' approaches
the center of gravitation o f the earth, at a certain velocity coinciding in the
center of the earth with f o cus 0, which transforms the ellipse into a circle. This
is determined by Kepler's second law. The law of areas enables us to calculate
how satellite velocity wil 1 vary over its entire path, and states that the radius
~ vector of the satellite swe eps out equal areas in equal time intervals (shaded
areas~on Fig. 29). '
In undisturbed motion of a satellite revolving in a circular orbit of radius r,
using equilibr.ium of force s of gravitation and centrifugal force
k Mnr . mc?~ -
r~ ^ r '
we find the circular veloc ity of motion of the satellite in cm/s, ~
+ ~M (6.21) .
. t'K - l~ r.~ .
where k= 6. 67 � 10-~' cm 3/(g � s 2) is the constant of gravitation, M= 5. 974 � 102 ~ g is ~
the mass of the earth, and m is the mass of the satellite in g. �
, ~ ~ 68
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The velocity of a hypothetical satellite moving in a circular orbit with radius
equal to the equatorial radius of the earth Rg = 6.371�108 cm would be 7.912�105 cm/s.
The period of revolution of a satellite moving in a circular orbit of radius r~
T = 2vK� ~ (6.22)
For our imaginary satellite, T= 84.48 minutes.
The velocity of motion of ~a satellite in an elliptical orbit is .
l-I- 7.~~ ro~ Q-I- r~ ~(6.23}
J., =='Jw, a V ~-rs ~
li;i0
where z~K.,,== is t?~e velocity of satellite motion in km/s in a circular orbit
.
of radius r equal to the semima~or axis of the elliptic~l orbit; Q is the angle
between dire~tions from the center of the earth to the perigee of ~he orbit and
to the point where satellite velocity is to be determined.
Since Qa =-1, while cos Qn = 1, [subscript a= apogee, II= perigee J the velocity .at
- _ _ . _ -
' the apogee is z~;, 2~,;. 1/~ , and at the perigee it is v� = vK, ~ and the
~ ~ l -e
~ ratio of these velocities is inversely proportional to the ratio of the distances
~
H� ~6.Z~F~
r
v~ Hu
i. e. the velocity of the satellite at apogee will be lowest, and at perigee will
be maximum.
According to Kepler's third law, the squares of the time of revolution of satellites
are praportional to the cub~s of the semima,~or axes of their orbits
7'~s !r~ (6.25)
r"' Rs
since we always have a> R3, we have T3> To as well.
At a given gravitational constant, it is only the se~ima~or axis of the ellipse
that influences the change in period cf revolution of a satellite. ,
The flight velocity at which a rocket begins to move circumferentially over the
earth's surface is called tt?e orbital vetoeity. With increasing altitude, circular
vel.ocity decreases, at first sharply, and then more slowly. For example, at an
altitude of 200 km it is 7791 m/s, and at an altir:sde of 2000 1~? it is 6903 m/s.
- With a further increase in initial velocity, eccentricity increases: At e ~ 1,
the orbit of rocket motion becomes a parat*ola with focus coinciding with the center
of gravitation of the earth. At e> 1 the orbit becomes a hyperbola.
" 69 ~
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At an altitude uf 36,000 km above the the level of the earth, when the plane of
the orb~tt coincides with the equatorial plane of the earth, a satellite remains
- suspended over a definite spot on the surface of the earth; such a satellite is
called stationary. Its period of revolution is 24 hours. ,
When escape velocity is reached (11.2 lan/s) the rocket becomes an artificial solar
satellite.
The accuracy of synchronization of frequency and time standards~ is ~onsiderably
- influenced by the orbit of the satellite, its position relative to the location
of the points of synchronization, and its velocity of displacement in orbit. Most
favorable are satellites that have high-altitude elliptical orbit or with a sta-
tionary orbit.
L, thous. 1~? Tp, ms
1
>s / .~ao
10 ~ 200 ,
. /
S ~ f00 ~
/
- ~
- 10 20 ~0 .40'
Satellite altitude, thous. km
Fig. 30. Dependence of satellite poaition on distance between
standards being synchronized (1) and signal travel time (2)
Fig. 30 shows the dependence of satellite altitude on the di'atance between the
points of synchro~~ization and on the travel time of signals relayed by the satellite.
Ref. 45 gives the results of experimental synchronization of precision rubidium
clocks via geosta~ionary satellite ATS-1 and A~S-3 between NASA tracking atations
at Rossman North c;arolina and Mo~ave California in 1971. The method of aimultaneoue
transmission and reception ~f time signals (two-bea.m method) was used in synchroni-
zation. A frequency of 4119 MHz was used for transmisaion from point A to the
satellites, and frequency of 6301 MHz--for rebroadcsst via the satellite. Bandwidth
was 30 MHz. A check by transported clocks showed that synchronization error was
50 ns.
Molniya Satellites
In the Soviet Union, the Molniya-1 and Molniya-2 relay satellites are extensively
used for transmitting television programa and for communications. Transmission
of time signals via such satellites enables synci~ronization of time and,frequency
standards at a maximum distance between them of 14,000-16,000 lan.
70
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90 Tn 40 60 BO J00 f10 140 160 f90 >60 1f0 f10 100 BO 60 fi~ ~ ~
~ ~ ' ~ a - - ~n
;n ~ - - - ~
3' .
Sp - o; - - - SU
' �JO - - - ~ - _ - ~ 30
~ . _ - ~ 10
>0 . . _ - - ~
0 _ o . . - - - - _ >0
- -
. . S . -
0 �
~ ~
3n _ _..r i - - .
o I
_ . . ~ sa
so . - ,
_ _ _ _ 1 _ . ~o
~ i 90
?0 0 ?0 40 60 BO 100 /?0 140 160 >Bt7 160 lfi~ f10 >GIO BO 60 v11
k'ig. 31. Satellite orbit in Mercator pro3ection
Fig. 31 shows the orbit of a Molniya-1 satellite in Mercator proJection on a map
~ of the earth [Ref.~46]. Even and odd turns of the satellite are shown with ascend-
~ ing nodes of 60� east long. and 120� west long. The period of each turn is about
. 12 hours. The point of intersection of the equat~~r by the pro~ection of the odd
turn is d.enoted by 0(60� east long. The parameters of the orbit are Ha = 40,000
lan in the northern hemisphere and An = 500 lan in t.he southern hemisphere. The map
also shows satellite altitudes of about 6,000 km (points 1 and 5), Z0,000 km (points
2, 4), 15,000 km and higher (between points 2 and 4 and at point 3). From.O to 60�
east long., mutual visibility of the satellite between Moscow and Vladivostok lasted
7=10 hours. ~
With use of Molniya-1 satellites as relays over the territory of the USSR, a net~:ork
of Orbita reception points operates fo~ reception of television programs from the
satellites and transmission through Iocal telecenters and radio relay lines.
_ The energy characteristics,of the line can be calculated from the following formulas.
Power of ground-based transmitter
~~,.a,t~l2~.~~ . 6.26
. p� . ~ ( )
r/u~~~iquep^nop
where P~ is the sensitivity of the receiver, L= LTLHL is the product of losses
in the troposphere (LT), ionosphere (LH) and on phase ~luctuations (L~),
nxnaH~n= 2�2 is the product of losses due to nonuniformity of the antenna radia-
tion pattern (IIH) , inaccuracy of self-aiming (ITaB) and polarization losses (Tln) ,
Gnep is antenna gain, nnep is the efficiency of the antenna, Anep is the effective
area of the antenna.
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Sensitivity of the Rround-based receiv~.r . ~
P - ~~~~~~P'~~~~A~~P. (6.27)
- 4al?zl./1
1
[subscript np = receiver] . It is realized in prticular by using parametric ampli-
fiers and amplifying the signal on an intermediate frequency of 70 MHz. , ~
The ground-based station is equipped with a reflecting parabolic antenna installed
in rotating supports.
6.4. Using the Orbita Reception-Point System for Global Synchronization of Time
Scales ~
By using television channels via Molniya-1 or Molniya-2 relay satellites and Orbita
reception-point systems, time and frequency standrrds are synchronized with the
use of a complete duplex satellite television trunk and two-beam or three-beam
tie-in methods.
In this case, operation between points I' and B is possible under condition that
there is a transmitter at point I' and right of access to the satellite (Fig. 32).
_ _
B
8
T~T~C T~EVCh r~ ~.p6~ r~o -TC zP ~
~ ~ I
.
~ - - ~
~ ~ ~ 9 >0 -
~ ra 7 ~
~ 2 3 4 S ~ a o 6 ~ f1 1i ~
L_ s ~ I I I
LGS Ch,~ stankino � ~ ~ ~
_ I q ' I A transmitter ~ 6 ~ f ~ rs ~
~PShT-IP
~PShT_2M J
Fig. 32. Block diagram of synchronization over channels of the Orbita reception-
point system
1--GEVCh; 2--transmitting correcting device; 3--reception correcting device; 4--
reference frequency standard; 5--central equipment room; 6--connecting radio relay
line; 7--transmitting antenna; 8--Molniya satellite; 9--reception antenna; 10--
local telecenter; 11--television receiver; 12--selector for isolating cut-in of
frame syn~hropulses and.time signals; 13--time interval measurament device; 14--
local time and frequency store; 15--digital printer; 16--electronic clock
72
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Time and frequency standards are synchronized in the period of transmission of
a conventional television program at any point on the territory of the USSR and
other nations covered by the Orbita reception-point system. In 1975 there were
more than 60 such points analogaus to point I'.
Also used is a system that differs in principle from the time-scale synchronization
- system with respect to ground-based television channels. In this'case.a line oper-
ates on segment BI' with considerable continuous variation of signal travel time,
which must be takeri into consideration during the synchronization session. On
other segments, signal travel time always remains constant.
Transmission time is chosen in such a way that the television synchropulses and
time signal-. of 1 and 2S Hz are formed from the reference standard of the TTC
_ synchronized with the GEVCh, and are transmitted as part of the television s3gnal.
When satellites are used, the signa~. travel time Tp to the reception point may
be calculated or determined experimentally.
In calculation, we first determine the path of signal travel between transmission
and reception points from ballistic data of the satellite orbit during registration,
and the coordin~tes of the reception points, afte~c which we calculate
~~r
.~rr _ ! T~ (6.28)
n
t~i~
where Z is the length of the path of signal travpl, vp is the velocity of signal
propagation, T3 is delay time in the equipment on the satellite.
The error of determining Tpr in this case is due mainly to the error of the ballistic
data (since the orbital parameters of the satellite vary during satellite motion
as a consequence of the influence of various perturbations), and also to a change~
in signal travel velocity through the ionosphere depending on the state of this
medium. '
The experimental time Tp of signal travel is determined by the method of bilateral
~ transmissions and receptions.ur~ing a complete television trunk [Ref. 47].
According to the results of simultaneous registration of received signals at points
B and I', Tp is calculated from the fortnula
_
T~,r _r~rr.+.. z ~T~ _ �Ti: mrc _ (6.29)
i, ~ - ~ .
Formula (6.29) is valid for the case where the relay unit is nearly immobile (at .
apogee), i.e. TPBr =:~Br. If these paths are not equal, the value of TpBl'must
be additionally estimated. To do this, consider the seg~nent of satellite motion
~ in its orbit at the instant of synchronization (Fig. 33a). Since the distance
from points B and I' to the satellite is not the same, the signals will be relayed
~ at different instants (positions p' and p"), which results in inequality of times
Tp~, Tpsand T~p, 1pr. The calculation can be done with adequate accuracy by the ~
graphic-anarytical method of Ref. 47. In doing this, we first determine the velocity
of satellite displacement for d~~crete values of angle Q(Fig: 33b)
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- 4~ uo~
>s0�
, P� L
_~P
.
- -
~.~o - - -
�a~ r
90� . 0
~ ~ ~
6
;
a b
Fig. 33. Graphic-analytica.l method of determining synchroniza-
tion error: ~
a--segment of satellite motion in orbit; b--points of determining
velocity of satellite motion in orbit '
~ ~kA1( ! 2~> cos q ~
~ ( 6 . 30 )
t'uc:~ � ~ ~ " a (1 es) '
ri = Il� -~-11~~ 2r ;
2
- H, /I�
C 2a .
- [subscript xcs= satellite]
For each of the discrete positions of the satellite (value of Q discrete), Fig. 33b
is used for graphica~ly determining the maximum difference of ~3istances between
the satellite and points of the earth's surface ~r, which corresponds to the differ-
ence of distances from the satellite to the earth along the normal and along the
- tangent to the earth's surface (for example, for ~oint B, ~r ~ BB - IB). The signal
travel time over distance ~r is ~t = Or/c (c = 3�10 km/s), and distance ~H traversed
by the satellite in time ~t is ~H = ~tv.
Distance ~H is laid off to scale along the tangent to tl~e orbit at the point of
observatio~ of the satellite, and the difference of the paths af signsl cravel
to either s~.de is ~raphically determined,
A/!' = AH cos al ~FI cos a2,
where~,t and a2 are the angles between the tangent and directions of the~satellite
to points on the carth. �
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Then the tie-in error due to inequality of paths with transmission to one side
or the other will be
' 61i (cos a, -{-cos . (6. 31)
e~ ,
_
Table 6 summarizes results of calculation for an orbit with parameters Ha = 4Q,000 km
and Hn= 550 km and for the most unfavorable location of points at different angles Q.
TABLE 6
Synchronization error using bilateral method
~---~1 ~-I mJs_ km I ms I m/ I em , I us , ~
~U ~,4 4;;00 14.3 135 210 O,:i5
IIU' 7,4 ~i200 17,3 12$ 215 0.~
I;~O� ~i,fi 5ti(x) IR,i 10? IG8 0~28
I~i(1 :4,7 li0(H) 20,0 74 115 O.IJ
' 17U' 'l, I ,;200 20,G 43 35 O,Ofi
Thus the maximum error OTp upon emission of signals at the same instants does not
exceed 0.4 us, and when the apogee segment of the orbit is used (in a range of
Q= 150-210�), it does not exceed 0.2 us.
In the case of nonsimultaneous emission of signals by driving and driven points,
an additional error ~T~on arises that depends not only on the coordinates of the
ground points and the satellite, but also on t~e mismatch of the driving and driven
clacks. When the mismatch is less than 10 ms, ~T~on does not exceed 0.25 {ts even
in the most unfavorable cases. Therefore tie-in should be done in two stages:
prel iminary tie-in with error of no more than 5 ms, and final tie-in when the error
- may be of the order of 0.1-0.2 us.
In synchronizing time and frequency standards over channels of the Orbita reception-
point system, it is necessary to distinguish channels with constant signal delay
in the equipment and radio relay line (AS and I'A), and variable delay (IBI') during
signal travel from the transmitting point to the antenna of the Orbita reception
point (see Fig. 32) .
The discrepancy of the time scale at point A with registration of the seconds-
mark ing signal transmitted as part of the television signal will be, determined
by the expression �
n'1'lt T11 (.~P~�~_ .~r -'r~t -~-'~;t)~
(6.32)
where T~~ is the discrepancy of the seconds~marking signal of the local scale of
~ point A relative to the signal received in the Orbita network, Tp-T~ is the time
of signal travel from the antenna of an Orbita reception station to the antenna ~
of the local telec~nter.
The user determines the value of Tp at the point of the standard to be 9ynchronized,
and the total travel time of of signals Tp, tpr', Tp-T~ is given to the consinner
by request at the recommended syachroniza~i~~n time.
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Recommended recording sessions most generally correspond to a satellite positia~n
close to apogee, since in this case there is an imporvement in accuracy of determin-
ing the position of the satellite in orbit, and a reduction in requirements for
accurate determination of the time of registration of the received signal relaCiv,~
= to the local scale. .
7700 ~30D - - - - - -
~M tN
- 1R00 1915~ - 'T" - . - -
1rr / GM GN
F .,i7.~~ - ' - - .
i
t T
~nan -'~zmu - - - -
_ I ~ CN `
~T -
Fon -~>>mo . _ . _
~oa ~,~on - - .
' OB 09 IU 1f 12 1.~ >4 !S >6 17 1B 19
hours of the day
Fig. 34. Range difference from satellite +to synchronization point
Fig. 34 shows range differences ZM ZH (satellite-Moscow) -(satellite-Irkutsk);
ZM Zti (satellite-~Ioscow) - (satellite-Novoaibirsk); ZH ZH (satellite-N.~vosibirsk)
- -(satellite-Irkutsk) as a function of time of location of the satellite near apogee.
As we can see from Fig. 34, over a two-hour period, ZH ZH changes by 9 km, which
amounts to 27 us� Consequently, mutual synchronization of two points under these
conditions can be done with high precision. ,
Signal travel time on section BI' (tP~ is computer-calculated for the recommended
synchronization time in accordance with data of a network of precision TV orbit
monitoring [PTOM] and regularly reported to the user. Users for whom the error
must not exceed ten microseconds are provided with nomograms and periodically given
necess3ry initial data. ~
PSh~-1M and PShT-2M equipment can be used for. recording instants of time signals
or synchropulses transmitted through the a~bita reception-point network. In con-
trast to eqi~ipment used for recording the instants of time signals or synchropulses
transmitted over channels of radio relay lines and intercity cable lines, reception
of time si;3nals with variable delay necessitates exact (with deviation in a range
of 0.1-1.0 ms) marking of the time of signal registration. Therefore the PShT-2M
equipment is provided with an electronic clock (see Fig. ~2).
6.5. Synchronization Error due to Inconstancy of Radio Wave Propagation
,
In determining Tpr it is necessary to evaluate the influence of ionized layers, ,
since signals will travel through these layera at different angles for different
synchronization points, and the signal travel time in the ionosphere as a result
of reduction and variation of group velocity will change as compared with the speed
of light; this time can be written as follows:
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L1.~~~~ _ :i~f' _ ~ ( ~
f )a~ (e)[ 3 h�~~:-I- h~], (6.33)
where fKp is the critical frequen~y for the ionosphere, f is the carrier frequency
of the radio station, h~X is the half-thickness of the layer in the parabolic
.approximation, he is the constant of ineasurement of electron densitq above the
maximum. The coefficient A(0) shows by how manq times the equivalent distance
traversed by the radio wave changes with oblique incidence as compared with vertical
~ ~A~ ~ R (h)
~ (6.34)
V R' (h) - R~ cos=A
where R(h) = R3 + h is the altitude of the poinr the ionosphere. ~
Values of A(0) in the range of altitudes where the inf~ae.nce of the ionosphere
is appreciable are:
Angle of elevation 0� 10� 15� 30� 45� 60� 75� 90�
A 3.00 2.57 2.40 1.75 1.40 i.13 1.03 ?.00
Analysis shows that signal delay on frequencies of 200-300 MHz with passage through
the ionosphere may be 15-30 us, and on frequencies higher than 10 GHz may be 1 us
and be detennined with an error of 0.1 �s.
As the carrier frequency of the transmitter increases, fluctuations decrease in
proportion to the square of the frequency. The delay of time signals in the ionos-
phere on frequencies below the UHF band reaches appreciable values that are diffi-
- cult to take into consideration because the distribution of electron concentration
above the.maximwn ;?as not yet been adequately studied.
According to CCIR documents, carrier frequencies of more than 4 GHz are now being
used for satellite relay broadcasters.
CHAPTER 7: RECOMMENDATIONS ON SYNCHRONIZING TIME AND FREQUENCY STANDARDS
7.1. Synchronization Facilities
The choice of the means (as well as the method) of synchronization depends on the
predetermined accuracy of synchronization, the rela~ive location of the synchronizsd
and synchronizing standards, the conditions of operation of the synchronized s~tan-
dard and the makeup of auxiliary equipment.
Frequency standards can be synchronized by the carrier frequencies of Soviet short-
wave stations (with ca31 letters RWM, RAT, RTA, RKM, RID, RCH, RIM), long-wave
~ stations (RBU, RT'!., RW-166), by television channels, and by signals t~ansmitted
by Soviet and non-Soviet radio stations in different radio wave bands. The times
and programs of transmissions by these statfons are published by the Interagency
Unified Time Service Committee in "Schedules of Exact Time and Reference Frequency
Signal Broadcasts." ~
77 ,
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~
Time scales can be sy-*!chronized by time ~ignals transmitted by the same stations,
and also over wire channels, ground-based television channels, satellites and mete-
oric communication.
~
Fur purposes of automatic synchronization, use can be made of carrier frequencies '
and time signals transmitted in the long wave, VLF and UHF bands with an error
that is determined by the station.
Time standards can also be automatically or manually synchronized with error of !
10-100 ms (depending on the point of location of the standard to be synchronized)
by using time-check signals (six points) transmitted via wide broadcast stations
- in the same '!'[JC system as the exact time signals. The beginning of the last (s3xth)
~ signal corresponds to 00 min 00.00 s--the beginning of the hour. In contrast to
exact time signals, time-check signals are transmitted without consideration of
their travel time from the supply scale to the radio broadcast stations. These
signals can be received by using standard recording receivers.
It is also possible to indicate running time to 0.1 s in a current-ttme code trans-
mitted as part of the time signals of some radio stations, or as part of television
si~nals.
- Table 7 shows comparative characteristics of major transmission facilities for
synchronizing time and frequency standards that are in use and under development.
As can be seen from the Table, the highest accuracy can be achieved by using:
a) wide-band systems (in virtue of ccnstancy of the characteristics of the trans-
mission channel, the steepness of the leading edge of the pulse signal at the recep-
tion point and hi~h signal-to-noise ratio); b) stable narrow-band systems with
registration of the phase of transmitted sinusoidal signals.
- When standards are located at a distance of up to about 30 km, synchronization
should be done by signals from the synchronizing standard that are transmitted
via ground-based television channels, wide-band wire lines and radio stations in
the long-wave and VLF bands (for short-wave radio stations, it is recommended that
frequencies below 2.5 MHz be used).
- When standards are located at a diatance of 300-3000 km, it is more advisable to
use signals from the synchronizing atandard that are transmitted over ground-based
television channels, and radio stations in the ahort-wave, long-wave and VLF 'oands.
At distances of 3000-6000 km transmission should be by radio stations in the short-
wave ar.d VLF bands and via satellite with operation in the UHF and microwave bands.
At distances of more than 6000 lan, signals are used that are transmitted via short-
wave radio stations and sa~ellites (active and relay) in the UHF and microwave
bands.
In general form, the transmission channel consists of transmitting devices, antennas,
the medium between antennas and the recording recep~ion equipment.
Auxiliary facilities include radio receivers for various bands, televis~.on receivers
with special attachment for isolating time signals from the synchromixture, counting-
type frequency meters (in the case of pulsed signals) or phase meters and phase
78
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79
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80
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comparators (in the case of a sine wave), synthesizers, chart recorders, timers and
- other indicator devices. ~
, During signal travel, electromagnetic waveforms undergo changes ir~ amplitude and
- phase. The function with signal transmission through a channel made up of n links
is equal to the product of the transfer functions of the links, i. e.
K ~ lz,hZk, !t� (kl/:~/ta k I(~~-I-~~+. . .-I-w~? = ke-1p '
n ,
where kl, k2, k3,..., kn are the moduli of the transmission coeff icients; ~1, ~2,
�n are the corresponding p~:ases.
In a system with distributed parameters, instead of the phase ~k we have the phase
constant ak multiplied by the length of the k--th link of the line Zk or by the
product vkTk, where vk and Tk are the velocity and time of signal travel in the
given litik. Then at the end of the channel
n n
~ f (wl ~f ' ~l~~l `I ~
Sn S~t' f~ ~ 1-~~ r
n
- where So is the signal at the channel input, ?,'cpc is the total change in phase
~
due to the lwnped constants of the channel, and the sum a;v:'r~ is the same quantity
, ~
due to the distributed constants of th~ channel.
In transmitting high-stability frequencies and time intervals, the constant phase
shift due to lumped and distributed constants of all elements of the channel does
not cause any change in the transmitted high-stability frequency only if all param-
eters are stable thorughout the measurement period. When transmitting time signals,
there is a change of signal times due to phase shifts in circuits with lumped con-
stants, and as a c.onsequence of the finite value of the radio wave propagation
velocity.
All these changes during synchronization of frequency standards or time standards
must be strictly accounted for, and their resultant effect responsible for�the
synchronization error must not exceed a predetermined value.
7.2. Synchronization Methods
The choice of synchronization method depends in great measure on the working con-
ditions of the standard to be synchronized, and the capabiZities for receiving
signals from the synchronizing standard. For example if the standard to be synchro-
nized operates periodically, and synchronization is required each time it is ener-
gized, The method must ensure one-time synchronization with error no greater than
the permissible error. On the other hand, if the standard to be synchronized oper-
ates continuously, synchronization with the permissible error can be achieved by
averaging the results of repeated sequential comparisons of the frequency of the
standard to be synchr~~nized with the signals of the synchronizing standard.
The requirements placed on the channel fo~.: synchronization of frequency,standards
are not the same as those for time standards. When synchronizing frequency standards
81 '
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it is necessary to take consideration of the inconstancy of lumped and distributed
= constants of all elements of the channel Qnly for the time interval of synchro-
nization. In synchronizing time standards, consideration must also be taken of
the constant phase shift caused by systematic and random�changes in the parameters
of the channel from the instant of establishing the signal tra~lel time in the trar.s-
mission channel. ~ ~
Synchronization of time standards (or tie-in of time scales) must be distinguished
from tie-in of the instants of time signals. Tie-in of time scales includes two
operations: synchronizing the frequency of electric oscillations or time intervals,
and tie-in of the instants of time scale signals. Tie-in of the instant of the
time signal amounts to one-time phasing of the signal of the standard to be synchro-
nized without synchronizing the time-scale intervals. After one-time tie-in, the
instants of the time signals will be continuously shifted relative to the instants
of synchronization by ~o= Yo ~the relative error of the frequency of the synchroniz-
ing measure), i. e. ~
= t~,.,. r,,.~oo, . i>
_ where tH,o6 is the interval between time signals emitted from the radio transu~itter
antenna from the reference standard, tH,~ is the interval between time signals
of the standard to be synchronized. ~
Synchronization of frequency standards or time-scale intervals is done by a method
of direct measurement of the frequency of the standard to be synchronized or by
the method of frequency comparison u~ing counting-type frequency meters, the hetero-
- dyna or phase method in transmissions of sine waves or time signals from the syn-
chronizing standard; synchronization of time standards is done mainly by the phase
method, using special synchronization signals or time signals.
7.3. Synchronizin~ Frequency Standards
Order.and Conditions of Synchronization
Frequency standards are synchronized in the following order:
a) the optimum method and means of synchronization are selected from among those
summarized in Table 7, depending on the metrological characteristics of the fre-
quency standard to be synchronized, the makeup of the recording receiver equipment
and rhe location of the frequency standard;
b) the time for synchronization is selected with consideration of the maximum con-
stancy of parameters of the transmission channel;
c) the necessary time interval of frequency comparison is determined (see Table
8 or 9) ;
d) the error of the recording receiver is determined;
e) �requencies are comFared, and the principat metrological characteris~.ics of
the standard are determined under selected measurement canditions;
82
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f) the frequency is corrected by a regulatin~ element or a special frequency ad-
3ustment module.
Synchronization Error
In synchronizing frequency standards, errors should be accounted for and minimized
- that are due to: change in the state of the ionosphere during t~+p synchronization
interval; the synchronization facilities that are used; the method of reception
and registration; the error of the frequency standard to be synchronized; the se-
lected time for synchronization.
The error of synchronizing the frequency standard is determined by errors of the
transmission cha:nnel (dQlf), the synchronizing standard wit~ consideration of trans-
mitting equipment (d02f), the standard to be synchronized (do3f), the method of
synchronization and the receiving recording equipment (do4f) $nd frequency regu-
lation of the standard being synchronized (8osf)� Since these errors are indepen-
dent of one another, and each of them is random, the relative synchronization error
o~ ' Fiii~ ~ ~oz/ so:,J ao~ f-~- s~;s~� (7.2)
The transmission error due to inconstancy of the char~cteristics of time and fre-
quency signals in different radio wave bands, as has been shown above, is due in
large measure to the state of the atmosphere surrounding the earth, including the
ionosphere, to the conductivity of the underlying surface, the geographic location
of the transmission path, time of day, season of the year, solar activity, magnetic
sttsrr~as in progress and oscher factors that inf?sence conditions of radio wave propa-
gati~n in various bands.
Approximate values of errors of the transmission channel Solf for different bands:
Equilw~ninant Non-equiluminant
path ~path
Short-wave . . . . . . (1-5)�10-9 (1-8)�10-e
Long-wave . . . . . (1-5)�10-11 (1-10)�10-11 '
VLF . . . . . . . . . (3-8)�ip-11 (5-40)�10-11.
UHF . . . . . . . . . (1-10)�1Q-is (1-10)�10-is
The values for the long-wave range are cited for a surface wave when the duration
of the measurement time interval is in accord with the data of tables 8 and 9(see
below); the values for the VLF range are cited for transsission paths of 1000-
3000 km.
Fi~. 35 shows an example of the results of daily comparison of the frequency of
a standard being synchronized with the carrier frequency of short-wave radio stations
on 10 and 15 MHz situated at a distance of 2000 km from the reception point. Con-
sidering that the instability of the carrier frequency on the antenna of the radio
station is ef the order of 10-11, we can state that the given curves characterize
mainly the inconstancy of conditions of radio wave propagation. As we can see
from the graphs, during the period when the tranamisaion path is totally illiuninated
. or totally in da~~cness, the difference of frequencies being compared re~ches
(1-5)�10-9, while this difference is (1-5)�10-e when the path is un~~venly lighted.
83 ~
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i W/~1M ' 10'9 .
r
I /A I ----I- - I
, ~
~ ~
sc 3 r----+---~- , , o
- , 1~~ ' ; ~ i N I I
N~ ' I
Y~ - ~ ~ ~-~~~-j- ; ; , ~
, ,
~ Z~
~ ' I
~
~ ' ~ I Hours of day
� ' ~ ~
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' ~ ~ ~ ~ ! ~ ~
:a , ~ --i--- ~---1----.- ; r ~
I ; ! ~ ~ ~ /
~ _ _:----~..i..^_ . :_.._--I
- Fig. 35. Frequency comparisons with respect to a short-wave
radio station (carrier frequency 10 MHz) on Moscow-Novosibrsk �
transsniseion path (June):
1--calculated date; 2--experimental data ;
In Novosibirsk, Sverdlovsk and Ttiilisi during a solar eclipse when the complete
shadow of the moon crossed over the territory of the USSR, measurements were made
of the changes in the carrie~ frequency of r3dio station RWM (15 MHz). The maximum
chan~e in frequency was noted for the Moscow-Tbilisi route (6.7�10-8), and for
Moscow-Novosibirsk the change was 5.3�1C-e.
To synchronize frequency standards, a radio station is used that ensures prede-
termined accuracy, and provides sufficient field sCrength at the reception point
for reliable synchronization. For the VLF band, the field strength must be~at
least 300 uV/m in the receiver band of 500-1000 Hz, and 20-50 �V/m in the band
of 20-50 Hz; for frequencies of the long-wave band (50, 662/3 and 200 kHz)--at
ieast 100 uV/m in the band of 100-500 Hz, and at Ieast 50 �V/m j..~ the band of
10-100 Hz; for frequencies of 2.5, 5, 20, 15 and 20 MHz and those displaced from
the nominal frequency by �4 kHz--at least 2-10 uV/m, depending on the interference
level.
If frequency reception is impeded by the presence of interference, special devices
are used: quartz bandpass filters, external or loop antennas, shielded antenna
housings.
The time of day that is suitable for radio signal reception wt?en the path of radio
wave propagation does not cross the terminator (the boundary between.the daytime
and nighttime sides of the earth) can be determined by a nomogram (see Fig. 36).
Sin:e the terminator line is a fairly broad twilight zone, the boundaries of the
' favorable part of the day are to some extent uncer.tain, resulting in an error of
the order of �(20-30) minutes.
The error of the synchronizin~ frequency standard d02f i~ determined by the error
of the frequency standard set up at the transmitting point (radio station), and the
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TABLE 8
Min3mum time intervals for comparing frequency standards
(values of TH are approximate)
Relative error of Time interval tH, s for band
standard being
synchronized short-wave long~wave VI.F
10-11 - 60,000 86,400 '
10-10 - 10,000 36,000
10-9 - 1,000 3,~~0
10-8 - 200 400
10-~ 20 `v~ 120 .
10-6 10 20 ~ 60
. 10-5 5 10 30
10-4 2 5 20
TABLE 9 .
Minimum time intervals for comparing frequency standards
~ ~ with respect to exact time signals
~values of TH are approximate)
Relative error of Time interval Tx, s
standard bein~
= synchronized short wave long-wave VLF TV channels
10-'1 - - - 3,600
- 10-10 - - - 1,600
10-~ � - 86,400 - 120
10-~ - 12,000 30,000 30
10-' 800 500 1,200 10
10-6 200 100 300 5
10-' 80 40 100 2
10-`` 40 20 50 1
ir.istability of parameters of the radio transmitter and aneenna. To reduce these
components, devices are used at the transmitting atation that stabilize the phase
of the signal on the antenna. The overall error d02g is usually indicated in
- "Schedules of Exact Time and Reference Frequency Broadcasts."
The error of the synchronized standard do3f is indicated in nameplate data.
Error d~yf is determined by the equipment used, and the error of time of registra-
tion and synchronization.
The error of frequency regulati~n of the synchronized standard Sosf is determinined
- by the resolution of the tuning element in manu~l alignment, and by the stopband
in automatic alignment. .
85
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~
a
~
~ ~ ~
_ O' ~ ~ ~ b q
~ ~ ~ ~ r o
~
b~0 . ~ ~ n. ~
_ ~ r O ~ ~ ~ ~ :dOc o t~tl
- m r-1 G' O � CS ~ w Q,
W F~~ Fb~ F^I 'b ~~b~ O t ~i
m q ~
C ~ ~ ~
~ F~ ' ~3 c v t~i~
. . O h fA
~ w ~
~ ~~0~+~~~ ~d ~ ~ ~ ~
_ o ~ ~
~ ~ d~ ~I
~ O w w 1~
~ ~c.~ ~c i.~
- - - - - N ~ C:
o U - - - - y. ~ ~ ` ~i-I
_ ~ ~ ~
a 't1:� - - - - - - - ~a ~ i . ,
~
o y 41 ~
C j. .ro. ~b _ ' ' _ ' ~ ~ ~ ~ ~
h' O~4 ' _ C ~ . 1~ Q
r ~ �
N ,b0
r"~ O ~o q
_ � A H - - ~ r - ~ r7
O 0 r"~ J..~
c
~ h ~ - - - - - - w i . h~ b~.I0
4 ^ ^ ~
~ ' ~ 'b - - - - - - b ~ * b ~ . .
y 1~
^ ~ - - - - - ~ f:
, .,i ~n - m ~ - ,av~
3~+ ~ ~
~ - - H N o0i 'd
:
t ~ - - - - - - - N. ~
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" ~ C e
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t Ql C7 GIIN ~ QU
~ ~ ~ ~ ~A .u ~ . g
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ti ~
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- 'i. 'fi i ~ tii tV ~J ~O r.~~ ~ l.~ b ~ ~5 ~ .
~
' ~ w8T � ~T w ~~T ~ S ~ ~
~ L l~l
< c~ ~ ~-I i e M
`1" - b
� �
~ ~ ~ ~ ~1
r .r e
~~�;~..~q ~ ~ _O
86
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Synchronization of frequency standards with error from 10-4 to 10-~ is done'With
respect to carrier fr~quencies of short-wave, long-wave and VLF radio stations.
In the case of short-wave radio stations, a heterodyne method is used for camparing
the reference frequency with the freqLency of the standard to be synchronized or
with its harmonics; when long-wave or VLF stationa are used, frequencies are campared
by a heterodyne or differential method.
Synchronization of frequency standards with error from 10-~ to 10-10 is done with
respect to the carrier frequencies of long-wave and VLF stations, using phase,
� differential or heterodyne methods of comparison. Use of the first method is pref-
erable.
Synchronization of frequency standards with an error of 10-10 and less r_an be
achieved only with strict accounting for destabilizing factors of the transmission
' channel, the error of the phase method of comparison, registration and processing
of the results of comparisons.
The time intervals for comparir.g frequencies to be synchronized when using reference
_ frequencies transmitted via radio stations in the short~wave, long-wave and VLF
bands are established by Table 8 with consideration of the fact that the total
error of the synchronizing standard and the synchronization method must be at least
three times lower than the error of the standard to be synchronized.
Table 8 gives data with consideration of inconstancy of conditions of. radio wave
propagation for an equiluminant transmission path and recording error.
The time interval for comparison when using time signals as dependent on the rela-
tive error of the f.requency standard to be wyncnronized is established by Table 9~
The data in Table 9 are given with consideration o~ inconstancy of the conditions
of radic~ wave propagation for equiluminant paths or in the course of a da; (86,400
seconds). The error of signal registration: for the short wave band 40 ?ts, for
the long-wave band 20 us, for VLF 100 us. for TV channels 0.1 us.
The actual value of the frequency of the standard being synchronized is calculated
- from the followinfi formulas.
When using a counting-type frequency meter in the fre~quency measuring mode
jn.'rac ~+~t~r., (7. 3)
where f~,~3C is the reading of the frequency ~eter in Hz, and ~?~3C is the error
of the frequency me~er in Hz. ,
When the differential or heterodyne method of ineasurements is used
~r - -I- C -I- (7.4)
where fH is the nomina] frequency of the standard being synchronized in Hz, C=-0
is the correction to the frequency of this standard in Hz, equal in magnitude and
opposite in sign to the difference between the nominal and actual frequencies;
87
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The quantity ~ may have either a positive or negative sign; is the error of the
method in HZ.
When using the phase method of ineasurements
i
f (1 s~ � 10-6~ -1= ~ ( 7 . 5 ) :
N
where TH is the interval of ineasurement time in s, d~ is the discrepancy of signal
phases in us over the interval of time measurement.
When using a counting-type frequency meter in the mode of ineasurements of time ~
- intervals between pulses of rhe synchronized and synchronizing frequency standards,
or measurements with respect to time signals '
tn f~~ (1 + ~iT 1 (7.6)
~ t~~ 1
wherE~. dT is the change in the time interval between signals over time TH, s.
The relative error of synchronization ~o.~ m~~/fH; it must be an order of magnitude
less, or at least three times less, than the relative error of the frequency of
electric oscillations of the standard to be synchronized, i. e.
< a ~o�
Formulas (7.5) and (7.6) are used for calculations of the actual value of the fre-
quency of the standard to be verified over the time measurement interval, while
the averaged actual frequency over the course of a day is determined froiq the formula
lA = fx~l Ob864 ' 10-~~1~ (7.7)
~
where d~~ is the phase dis~repancy of the signals in us over a day. .
When the phase discrepancy is measured in degrees,
f f n~ (7.8)
! 1 - / II ~ ~~tll �
The method of processing the results of comparison by the phase technique is ex-~ ~
_ plained in Section 7.5.
lletermining the Time of the Equilianinant Transmiasion Path
To determine the time of the ec~uiluminant path it ~s necessary to know the hours
of sunrise ar.d sunset, which depend on the season of thP year, and on the coordi-
nates of the points where the transmitting radio station and the standard to be
synchronized are located [Ref. 48].
- 'to plot the nomogram (Fig. 36), a BESM-4 computer ie used to calculate times of
suarise and sunset for latitudes fror~ +85� to -~5� with a step of 5� for the middle
- 88 ~
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c~t e~,cl~ month by the follQwing approximate formu9.as of spherical astronomy:
tg Zo = tg e sln ao~
to = arcc~s tg ~ tg So); (7 . 9)
7'� t n; T, = 2 4'' - to,
where aa, So are the time of right ascension and declination ~f the sun, e= 23�.4
is the tilt of the ecliptic to the equator, ~ is the geograpltic latitutde, to is
the hour angle of the sun at sunrise, TB, T9 are times of sunrise and sunset. ~
The values of ao were calculated from the formula for mean right ascension. To
calculate values close to the middles of the months, the formula was transformPd
to the approximation
ao 17~'.6 2~'m,
where m is the ordinal number of the month. The error of the resultant value of
ao does not exceed 17 min.
The curves of ttie nomogram plotted by using the values calculated from formulas
_ (7.9) are graphs of the times of sunrise (sunset) as a function of tatitude with
respect to the local mean timy scale. To cor,.~rt to universal (G~ :enwich) timey
it is necessary to consider the Ton,~{-tude of the point (subtract ` v~lue of east
longitude or add the value of west lur.gitude). This operation ~ccomplished
by using the upper and lower longitude scales. The ctiange in times of sunrise.and
~ sunset from month to munth increases with increasing latitude. And at the same
time, there is an increase in the twilight period at higher latitudes. Thexefore,
considering the physics of the phenomenon, it makes no sense to interpolate bet~aeen
curves of two successive months, and it is sufficient to take the curve relriting ,
~ to the middle of a given month.
Work with the nomogram should be done in the following order:
find the point of intersection of the horizontal line corresponding to one of the
points (for example the transmitting point) with the ct~rved line that corresponds
~o the given month;
go up or down from this point to the midline of the nomogram 0", i. e. find the
pro~ection of this point;
~oin the pro~ection point to the point of the upper scale of the nomogram that cor-
responds to the longitude of the site, and beneath this point read uut the time
of sunrise TH1; ~oin the same point of the pro~ection to the [appropriate] point
of the lower scale ~f longitudes, and read out the titne of sunset T91 above this
_ point. ~
The time of sunrise and sunset fcr the other point (TH2 and Tg2) is determined .
~ in exactly the same way. .
89
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To determine the part of the day that is favorable for measurement (equiluminant
path), it is necessary to construct a cyclic diagram of order of succassion of
sunrises and sunsets at the two points [see example to the right on the nomogram].
If the sunrises and sunsets succeed one another in the order "rise-rise-set-set'~,
- the equiluminant path will lie between times TB-Tg and T-TB. If the order of
succession of sunrises and sunset~ is "rise-set-rise-set~, the equilwninant path
will lie in intervals TB1-T32 an~l TB -Tg or Ts2-TBi and Tgi-TB2, i. e. between ~
neighboring sunrises and sunsets at ~he ~i.fferent points.
The following must be taken into consideration.
1. The nomogram gives universal (Greenwich) time, and 3 h must be added to convert ~
to Moscow time. '
2. If the horizontal scale corresponding to the latitude of the site does not
intersect the curve of the corresponding month, this means that it is polar day
or polar ni~ht at the given point at this time of year (in accordance with the
inscription on the nomogram). In this case, the only favorable interval for mea-
surements is the part of the day when it is daytime or nighttime respectively
at the other point.
3. Measurement conditions are ulfavorable during twilight, and therefore the period
of the equi]umina~:t path should be somewhat shortened on both ends.
7.4. Synchronization of Time Standards (Time Scales) f~~
Order and C~nditions of Synchronization
J
Time standards are synchronized in the following or~ier: .
- a) dependin~; on the metrological characteristics of the time standards, the makeup
~ of the recording reception equipment and the location of the standard to be synchro-
nized, the optimum method and means of synchron~Lzation are c:~osen from an:~ng those
cited in Table 7;
b) the time of synchronization is aelected with consiaeration of maximum constancy
of the parameters of the transmission channel;
~ c) in ~ccordance with tables f3 and 9, the necessary time inter~�al is determined
for synchronization.of the frequency standard that is the basis for setting up the
i time scale;
d) the error of the recording reception equipment is determined;
e) the signal delay is determined in the recording reception equipment;
f) the signal travel time from the antenna of the transmitting station to the an-
tenna of the locati.on of~ th.~ standard to be synchronized is calculated or experi-

_ mentally determined; .
g) th%~ frequencies are compared, and the principal metrological characteristics
of the standard are determin~ad under selected measurement conditions;
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h) th~ instants of the signals of the time scale are brought together with the
signal transmitted fram the synchronizing standard;
i) corre~~Cions with respect to the frequency and instants of the time signals sre
calculated and introduced by means of regulating elements (frequency control,
phase shifter or discrete delay module);
j) synchronization of the time standard is checked by one or two other radio sta-
- tions;
k) synchronization results are marked on a graph.
Synchronization Error
In synchronizing time standards, it is necessary to account for and minimize errors
due to: change in state of the ionosphere on the transmission path during the
interval of signal registration at the reception point; selection of the time and
tin~e interval of synchronization; error of determining the signal travel time in
the transmission channel and its change during synchronization; the error of de-
~ termining the time of signal delay in the receiving and recording equipment; the
error of the method of comparing, recording and processing measurement results;
the error of the time standard being synchronized and the periodicity of synchro-
nization; the error of regulating the intervals and instants of the signals of
~he time scale to be synchronized.
The error of synchronization of time standards is determined by errors of synchro-
_ nization of the time-scale interval or the frequency of the reference standard .
for f ormation of the time scale (see Section 7.3)--~of; of determining the time
of signal travel from the antenna of the synchronizing standard to the antenna
- of the synchronized standard--dotl; of the synchronizing standard--SQt2i of the
standard being synchronized--8ot3; of recording the instants of time signals--
aot4; of determining travel time delay of the time signals in the recording receiver
equipment--dot5; of determining and making the correction to instants of signals
of the time scale to be synchronized-~ot6:
'~nl - Y~ O J~- ~0~ 1+ AO! 2~ SO! 3+ AUf 4~ EO! 5"'I- fiUf fi' ~ 7.10 )
In sele~ting the radio station, consideration is taken of the fact that the time
signals from this station ~ust be c.learly audible, the leading edge of the signals
- should not be distorted by interference and multibeam propagation of radio waves,
and the transmission path should be equiluminant.
Time standards with error o� 10-100 ms can be synchronized with respect to signals
of civil time (six pointsj transmitted by radio broadcast atations; with error
of 100-300 us--with respect to time signals of short-wave radio stations on the
territory of the USSR and the neighboring seas; with error of 40-70 us--with re-
spect to time signals of long-wave radio stations RTZ and RBU (radius up to 1200-
1500 km fro~r. Moscow and Irkutsk) and other non-Soviet long-wave and VLF stations,
including the Loran-C long-wave and the OQaega VLF navigation systems; with error
of 0.5-2 us--with respect to TV and satellite channels. Time-scale intervals or
frequency of the reference standard are synchronized in the order given in Section

~ 91
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7.3, and Che instants of signals of the time scale being synchronized are normalized
with respect to exact time signals, or with respect to the phase of the carrier
frequency marked to resolve ambiguity. ~
In some cases, where high precision of synchronization is not required or where
a single tie-in of the scale is to be done (in the case of a periodically energized ~
time scale), the operations of synchronizing time intervals and normalizing the
instants of local time-scale signals are combined by repeated sequential regis- '
. trations of the instants of received time signals with the sign~ls of the time ~
scale to be synchronized. Each time after determining the deviation, corrections
are made by correcting elements without correcting the frequency of the reference
standard.
T}ie error of travel time of the signals dotl is determined with consideration o�
all destabilizing factors (see chapters 4-(s), or is evaluated from experimental
data. For the short-wave, lor.g-wave and VLF ranges the most appreciable influence
is from illumination of the transmission path. As an example, Fig. 37 shows the
change Ln signal travel time of signals during the course of a day on a transmission
path from Moscow to Rugby (U.K.) in the summer (radio station GBR, frequency
16 kHz). The greatest change in signal travel time between day and night is ~
45 us.
- _
~ nigh day night day nigh
_ - _ --1. _ ---I - - - -
r9J91s
i > i _ 1
RJ7l1 , _ . . - - -
~
R~.SO - - . ~ _ . _ _ - - _ _
BJJU
~ 4 ,4 1, 16 70 14 4 B JZ f6 10 2f 4 6~
L _ 9 Jun_ 73_ _ 10 Jun 73 ~
~
Fig. 37. Change in signal travel time on Rugby-Moscaw
transmission path
- The travel time of time signals can be approximately determined for the shart-
wave band from Fig. 38a, and for the long-wave band--from Fig. 38b. The curves
are plotted from experimental data. The error of determining Tp by using Fig. 38a
is �150 us, and for 38b--�50 us.
_ Error dot2 of the synchronizing time standard is determined by the error of the
time standard set up at the transmitting point and by the instability of delay
of signal travel time'in the transmitting equipment with consideration of a special
stabilizing device. The total error is usually indicated in "Schedules of Exact
Time and Reference Frequency Signal Transmissions."
Error dot3 of the standard being synchronized is indicated in the nameplate data.
The recording error dot4 is determined by the resolution of the recording device,
the method of compar'ng time scales, the shape of the leading edge of the signal.
and the signal-to-noise ratio at the reception site.
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tp us
/
f4000
/ zp, 3
i ~
11000 ~
i i
- i I 5000 , ~ �
= 10000 ~ ~ ~ 2 I .
; ~ 4000
i / ? ( ~ ,
8000 I I ' I
.~oao , ;
600U I ~ ~ ~
~ ~ ! 2000 ~ ~ '
400l1 ~i----..~ I ~ ; ; I I
I ; '
1000 ~000 J000 4000 G~KM ~`~~~J00 SOG 700 900 Jf00 1T00 G, KM
a b
- Fig. 38. Signal travel time as a function of distfince betweet~
antennas of synchronized and synchronizing standards on an equi-
luminant transmission path:
1--daytime; 2--nighrtime
For short-wave radio stations, this shape will vary because of multibeam propagation �
= of radio waves. Fig. 39 shows the shapes of time signal pulses at the reception
point. In recording time (Fig. 39a) the recording error may reach 50-80 �s, and
in recording the signal (Fig. 39b)--300 us or mbre. For practical purposes, a
signal of th~s shape is not recommended for synchronization. -
'
~ ~
'
~
_ +
a b
Fig. 39. Shape of leadin~ edge of signals at the reception point
_ with transmission by short-wave radio stations
Fig. 40 shows the leading edge of a signal in Che long-wave range at the antenna
of i�adio sta~ions RES--10 kHz (1) and RBU--662/3 Hz (2) .
?n the case of interference witr~ ratio of 5:1 and realistic phase fluctuation at
the reception site, the recording error is 30-50 us at a distance of up to 1200 lan.
If the exact time signals being used to synchronize the ~~time standard have some
- spread at the reception site characterized by variance vE, reliable det~i-mination
of the instant of the received signal necessitates averaging the instants over as
- 93
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~n - - - -
a~
~ '
~ a1 O,B . _
_ a .2
o
~ ; Q~ . _ . J. _ ~
~
; a - - - ; '
- u.,
~ � ~;2 . - - -
~
a 0 ~ '
fU0 2l,'0 ,~i70 T, � s
Fig. 40;. Leading edge of time signal on antenna of long-wave
_ radio stations
long a time interval as possible, consistent with QE and depen3ing on reception :
conditions,inte�rferenae level and the fluctuations of the leading edge of the
signal.
If a time ~cale i5 to be synchrronized for a time during which the instants of sig-
nals of the scale being synchranized must not deviate from the instants of exact
time signals by a predetermined value of QE, an interval can be established during
which it is advisable to carry out averaging and synchronization of instants of ;
the time scale si~nals.
If the error uf synchronization of time signals is preassigned, the average time
during which it is advisable to carry out tie-in after the (2n - 1)-th received
time signai to the average value of the instant of these signals is
~�--i -
-
- ~ ~;E
_ t~�~, _ ~ ~ _~~.~~o~~(lt- 1)-f- to '2ro t l ' . ~7.11) ,
_ 2n-Y
where n is the number of recorded instants of time signals; ~i is the fluctuation
of time signals at the reception site; t~,B is the interval between t3.me signals
radiated from the transmitter antenna.
- But t~,IIdo3f(n - 1) + to is the correction at the n-th instant, and cansequently ~
is the more exact the greater the n, since its variance is equal to QE/(2n - 1).
If we displace the instants of the time-scale signals by t~P after the (2n - 1)-tfi
signal, then the interval between the new position T2n_1 and T2n_1 will be equal to
_ ~E' ~~A~~~,~,G-- 1), The spread of values of this interval obt.ained from the
`ll1 ~ ,
possible values of ~i and 8o3f is w;~at deter.mines the accuracy of synchronization.
Then the recordin~; error due to averaging of the fluctuation of instants of the
signals at the reception site is .
a2
E (7.12)
~ Q'~' - 2n - l +~c.a ao3/ ~ n- 1)a.
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It can be seen from formula (7.12) that there is an optimum value nopt that ensures
_ maximum recording accuracy with averaging of the recording results.
One of the appreciable components of the synchronization e�rror is the error of
determining the signal tr.avel time in the radio reception equipment dots, which.
depends mainly on the width of the passband, and can be detennined for each specific
r.~ceiver. Fig. 41 shows Tg,np =~(~F) for the R-250 M radio receiver.
T3.np, us
.
- i
800 ~ ~
~
600 - - -
~
~ ~
400 - -
~
~
20U - -
2 4 6 B >0 ~F , kHz
~ Fig. 41. Typical behavior of signal delay ti-ne in receiver for
different passbands
+ Signal delay time in the receiver equipment is
t,.~~,~ = T~.~ OT,~ (7.13) ,
where T3,~, L~T3 are the systematic and random components of delay time of the phase
or envelope Qf the signal
The time T1 of travel of a sine-wave signal through the cir.:uit correspon~s to
- the phase angle ~=c~T. If T is constant in the frequency band, the phase shift
in the circuit in this band varies linearly as a.function of frequency. Deviation
of the phase shift wT3,~ from lir.earity is comprised of the systematic and random
changes of T3.
When a pulse signal is being transmitted, T3 must be constant for frequencies in
the passband for retention of pulse shape in the phase relations. Otherwise it
is diffi.cult to determine signal delay time due to distortion of the envelope.
During si};nal transmission, the signal envelope depends on the steepness of the
phase characteristics of the tran~mission chann~l; the average phase delaS~.is usually
= determined from ttie relation T3.~p=~/~:, and the signal envelope delay ("signal
delay time" or "group signal travel time") is defined as
_ ds ~ � ~
~ 7 14
dw - 2`~ w d~ '
i. e. the delay of the envelope is equal to the phase delay on the fund'amental
frequency plus a term that accounts for the change in delay in the frequency passband
95 ~
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- and that is determined by the passband of the channel, the accuracy of tuning to
the carrier frequency, and to a lesser extent by signal arnplitude and shape.
The foregoing arguments show how difficult it is to exactly measure the delaq time
of the signal envelope.
It would be possible to get the most exact results in measuring the phas~ shift
- with respect to poinrs in a predetermined frequency band and plotting a graph of .
the delay characteristic. But this is a very laborious process.
We give below a bl.ock diagram of practical measurements of~.the time delay of a
, time signal in radio reception devices either when a low-frequency voltage arrives
directly at the radio receiver input from an oscillator (voltage keyed by squai�e
_ pulses), or when antennas are used for radiation and reception through the etller.
3 ~3 `
~ ` nr i~ ii nz ~ nf
1 S'
/ ~ ~
~ ~
n4_
~OHz -
. 7 6
Fi~. 42. Diagram of ineasurement of signal delay time in radio
receivers:
1--standard signal generator; 2--time signal simulator; 3--antennas;
4--receiver; 5--oscilloscope with external triggering; 6--device
with variable delay; 7--pulse generator
In the former case, a signal from a simulator (Fig. 42) n~ay be sent directly to
- the receiver input, all sFTitches [171 T14] being set in position I. In the latter
case, the switches are set in position II.
R.?
j);j R1 -C7---' fr4 p3 ~t"
o Tr1 ~
l output
n.2zo v' C1 ~ D 2~�2 T1 C.~ R6
k~ R,S
1 2z
nputll SSG input ,
Fig. 43. Schematic diagram of time signal simulator
. Fig. 43 shows a schematic diagram of a time signal simulator. Time frequency gener-
ators are provided by an rf-oscillator operatir~g in the ban~ of the radio stations,
or televisi~~n broadcast channels. The time signal simulator is an el~ctronic sw~.tch
based on a semiconductor diode. In the initial state, the transistor is closed, and
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the negative potential from its collector load is fed through resistor R4 (lU kSZ)
to i.he cathode of the diode. When a negative pulse arrives at the base of ~he
transistor, it is opened, and the blo,:kin~ voltage is remcved �rom the diode. Tr.e
high-frequency voltage from the rf-osci]lator passes to 'the output plug of t.he
simulator. 'rhP duration of the output radio signal of the Simi~lator is determined
by the duration of the lnput pulse.
Signals from the simulator output are fed to the antenna in~L= of the receiver
being studied. The delay time of the receiver ts measured by an oscillosco~e with
calibrated scan. Signals from the output of the intermediate-frequer_~y amplifier
of the r.eceiver are fe~ to the vertical ampli�ter input of the osci7~loscope. The
oscilloscope is triggered by the se~onds-marking pulses of =he local clock. The
zero-amplitude po3.nt of the signal is shifted away from the reference line o:: the
oscilloscope screen, ar~d the time :3 is read out with respect to the calibrated
scan of the osciiioscope.
When more accurate measurements are needed in tbe record~ng receiver, che s~lgnals
from the simulator are se~t to the antenn3 of the receiver. The measurements them-
- selves are made in the same order as in the first case.
When determining signal delay time in e~quipment, repeated measurements must be
made, and each ti.me the recelver must be tuned and the amplitude at the in;.ut must
be regulated. The arithmetic mean of thc group delay time is
n
~
t:~.~�~ (7.1~)
- ~--i
-
n ~
and the error of detennining T3 is ` .
n
~ ~ta.r 1 t~.r~a 16~
- ~
� ~ n ^ ~
As we can see from Fig. 41, for th^ frequency band from 4 to i2 kHz Tg is nearl;
~ constant, and it increases sharply for the frequency band below 3 kHz. Therefore
when signals are being received in the frequency band below 3 kHz, T3.r must be
accounted for and precisely monitored sinca it will have an appreciable ef�ect
on tt~e overall error of time-scale tie-in. -
The error of determining and making the correction to the instants of the tim~
scale dot6 is determined by phasing and precision of registration of the instants
of signals of the syn^_hronizing znd synchronized time standards, and by the,defi-
nition of tine correcti~n.
The instants of the time signals axe considered siriultaneous when the instants
of signals of the local time scale lead the received time signal by the signal
travel time from the reference time standards (radio stations) to the standards
bein~ synchronized.
A time standard will ue syncl~ranizeZ if the following equation is satisf ied and
: all components of the Lotal synchronization error have been minimized: .
~ ~M (T:i.np -I" ~p~ = nTM~ = U~ (~.1~~
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whrre ~'C~M is the dtacrepancy of inetanta of time-scale si.gnals.
' To increase accuracy, all synchronization operations must be repeated 10 times,
and the average shauld be detennined
~
~TM
N W (7.18)
07~~~~ ~ n �
' If exact time signals transmitted by two or more stations that are equivalent in
accuracy can be received at the site of the recep~tion point at a given time, and .
the.leading edge of such signals is of the same quality (signal-to-noise ratio
, more than 5:1), then tie-in should be done with respect to two or three stations
, for greater rQliability. Fox this purpose: '
a) the beginning of the received signals must be combined 10 tiQ~s with the signals
- of the time standard to be synchronized with respect to the first and secoMd sta-
tions, the readin~s recorded, and AT~~~~ and nTu2 muat be calculated;
b) if th~se values do not differ by more than 10~, the arithmetic mean ahould be ~
calculated:
M
DTu~i -I- AT",2 . ( 7 .19)
AT~~~~.s 2 .
on the other liand, if the mean values with respect to the two stations differ by
more than 10%, all synchronization operat~ons should be repeated.
After determining A7'M,~, 2 or nT",i~ r, 3 a phase shifter or discrete delay should be
used to change the instants of the time-scale signals by the resultant amount
taken with the reverse sign.
, When using the phase method of time scale synchronizaLion, only one station should
be used, and to improve the accuracy and reliability of the results of the measure-
ments, the synchronization time interval must be increased.
1 2
4 S 6 ~
a
_ ' . 7 ~t S -Q .
B
4 s ~ .
b
Fig. 44. Block diagram of equiFnient for synchronizing time stanciards wi.th respect
to time signals: ,
1--radio receiver; 2~-i-f or low?-frequency amplif ier; 3--slave-sweep oscilloscope;
4--discrete deZay device; 5--time-scal~ shaper; 6--frequency standard; 7--two-beam
electronic oscillo~cope; 8--count~ng-type frequency meter
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, Fig. 44 shows block diagrar.is of equipment for synchronizing time standards with
: respec~ t~ exact time signals. Let us consider the one that uses devices with
discrete delay (Fi~. 44a).
The voltage of the received time signal goes from the output of i-f or low-frequency
amplifyer 2 to single-beam oscilloscope 3 with slaved sweep. Signals from the
ti~ne scale to be synchronized with recurrence rate of 1 or 10 Az, dQpending on
the repetj.tion rate of the received signalare sent through device 4 with disczete
delay (type Ch6-37) to che trigger terminal of the oscilloscope (slave sweep B~ode).
By varying t.~e delay with which tfi~e b'eginnin~g .of~ tlie rise in the leading edge
of the signal is fed to the beginning of the scar.., we. determine the. discrepancy
- of the instants of time signals of the standard to be synchronized relative to
the instants of the received time signals.
Fig. 44b shows a block diagram using a counting-type frequency meter in the ~ode
of ineasur~ment of time intervals with different rec~ived wavefor.ms. In t~.e presence
of. two-beam oscilloscope 7 and a second divider channel with phase-shifting device,
synchronization is done in the following order. Tne received time signal is sent
to two-be~m oscilloscope 7 with slaved sweep. To synchronize the oscilloscope,
a seconds-marking pulse is s~r.t from the time scale to be synchronized, which is
simultaneously the start signal for counting-type frequency meter 8. Time signals
(reference mark) from the output of the additional divider channel are sent to
the second beam of the oscil.loscope anc~ to the frequency meter (stop). By rotation
of the phase shifter, the seconds-marking signal (reference mark) is fed to the
beginning of the rise in the leading edge of the received time signal. The value
of T~i is determined from the readings of frequEncy meter 8 in the mode of time
interval measurement.
7.5. Methods of Processing Results of Measurements Made by the Phase Method
i
When the phase method of syr.chronization is used, the phase difference of signals
of the synchronizing and synr_hronized standards is regist.ered by conventional phase
meters. The measurements are taken over standard time intervals T~.
The average frequency of the standard to be synchronized is
~ ~
f
~P~~)~t� ~7.20)
'laT,.
_ i,
~ The principal advantage of this method is in continuous averaging of the p~hase
of the Erequency standard.
If time standards are synchronized discretely rather than continuously, the mea- .
sured real value ~~f the frequency is determined as 3 function of phase dispersior..
at the reception site and the preset accur~cy of synchroniz~tion.
The averaged real value af the frequency over standard time intervals normalized
to the middle of a measurement time interval of N days is determined as follows.
The established measurement time interval t~^~~--1~~~`'~' is broken down into n identical
_ interval.s 1~~i'~ - ~ t~^'~ . where i = ~ y 1~, 2, . . . , (n - 1) .
At time t~N), a measurement (in us) is n.ade of the phase difference between the
reference frequency and the frequency af the standard to be synchronized (the phase
time lead is determined) ~~N~. .
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Then no ~I~
f"- on intervals t1~~'~ 1~~ti? will be defined as
- _ (M
_ . t1a;~~ = i~M~ f~^,~ 10-~. (7~21)
� fFl~" !
~ the average value of this quantity on the interval 1MN~ - to^'~ normalized to the mid-
dle of this interval is
' (~'I (y3
- AU~,~ + ^1 ~ ~~-~i ~e~ - 10' (7.22)
n ~,u t~+j �--tiN~
~ M days after these measurements, a standard measurement interval t~N+,~ty j~n~-{-M) is
selected that is equal to the N-day measurement interval and is situated at the
same place of the time scale, i. e. l~N-~-,N) _ 111N�FM) _ t'Nj t~N) where l~N~-~�> = l~~`'~.
~ Then analogous measurements are made and used in the calculat~on of
a n-1 (N-I-,N) _ (N-I-M)
- ~(N
I M) ~ `~'�I-~ 'Pi lQ-~'. �7.23)
0 n ~'~l0 �
~ . (7.26)
2
If the time interval is expressed in daysS and the phase advance in microseconds,
the av~raged relative 24-haur change in freq,uency is
0 _ ~P (t} --~p (t- 10-i~~ (7.27)
� 0.864
_ when the phase advance is measured in degrees
n~_ ~p(~)�--~(~-�~~ . ~7.28)
/n~n3fi0
- By determining the ~~alues of Qo over equal ti~e intervals (24 hours) in a set period,
we can calculate all principal metrological characteristics of the frequency standard
by the formi~las, using one of the methods of frequency measurements. �
- Experience has shown that the methods of mathemat9.ca1 statistics provide the best
means of determining metrological characteristics of time and frequency standards.
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- Practical formulas are given below for calculating the metrologic,al characteristics
_ cf. frequency standards from the results of continuous testing over severaJ. days.
~ In processing experimental data with a cot~.siderable inherent randc~m spread, the
best result is attained by constructing a line of rpgression [Ref. 49] using the
method of least squares. The specific nature of frequency stlndards is such that
the systematic change in their frequency with time as a rule ia very well described
by a linear law, or at least by a square law. Besides, in prolonged testing of '
frequency standards, measurements are u5ually made every day at the same time,
- so that a standard measurement interval can be intrAduced.
Let i~s select some standard interval of ineasurement i(e. g. 24 hours) that takes
integral values i= 1, 2, 3,..., n(usually n= 15 days).
- Let - f"--~ ~"-1 --T ~ be experimental values of the reiative deviati~ on of the
R~~1fK1
effective frequency fa~ of the standard away from the nominal value fH at peints i.
, Then the iinear regress~on
oocl)=e~+v~ c~.29)
is determined by parameters ~o, vo calculated frot~. forinulas
v~- n~n~2 ~ t~ot-n 2~ ~j~o? ~ (7.30)
t-.i i~~
/~n = R- J 2~ vo. ~7.31)
~--i
In the case of a square law of systematic change in frequency, the line of regression
; De~l) - On -I- Yoi 9012 (7.32)
is determined by parameters ~o, vo, qo that in this case are calculated by formulas
-
,t
. � ~ (,tri' ~:iit I'l) J~n? G(2n 1) J' iA�~ IO ~~~~`n~~~ . ~7.33)
r,~i~ I)(ir I i ~ t ~
~ n
_ _ ,~~ll-~ ~~~11�~ l~~lll-~-~~~l~oi__'
'o
A(i~~ ~i~~~" ..q~ i I
~ n
' - 'l(`lr~ 1)(;tn~~~ 11) ~iA�i-~~ 3Q(n-~ i)~~i=A,,; , (7.34)
li ri
n n n
~1~~ ...---,tn- (~i I~ I )(?i I- 'l) }Jn~~~ - fi(~i I) ~ l~orl- G iZ~ur . (7.35)
~r~i~_'....I) I~l= - 4) i ~ ~ `J
1-1 '
- As to the dimensionality of the quantities: ~o is dimensionless, vo [day+l],
Qo Lday-a~.
For linear regression, the rate of going of tt~e time scale of the investigated
- time standard (in microseconds) relative to the reference scale is
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. 7~~ I ti,li~ ~ IO~u(/1~~1 ~_l-v~in,, (7.36)
~
and for square-law regression
T ( i ) 7',? 8,69 . 10~~ (A~i 2 �~�i~ ~I- 3 [/�ia), (7. 37)
~
where To is tlze instant of the time signal at i= 0. Dimensionality of the quan-
tities ~a [us/daYl~ ~o Ius/daY2l. 90 ~usjday3].
Let us give a specific example of investigation of a rubidium frequency standard
- over television channels 1300 laa from the GEVCh. Me~surement results ann processing
data are summarized in Table 10.
TABLE 10
- Results of ineasurement processing, us
~ > ~ An(~) X 1�~i ~ ~�o~
~ ~ ^~~r ^n1 io In~~ ~ In~~ Io~~ �-s~(~ ~ x - MU)~}
i~ ~ x io ~
- _-2.- -~--I-~~- a ~ in
`0 --2'1.,,~ _ . _ . _ - - -
I -�17,4 5.~--b~0 ~ fi,0 I I 6,0 6.0 0,0 0.00
'l --�13, I Q,:i >,0 10,0 4 20,0 5,3 --U,3 0,0~1
_ :i �-�9,5 3,(i 4;2 12.a fl 37,8 4,G -0,4 O,iG
4--~f,R 2,7 :i,0 12.U If 48~0 4,0 - 1,0 ~ 1,00
. 5-�4,7 'l,l 2,5 12,5 25 fi2.5 3,~ -O.R O~~.i4
G -..3,5 1,2 1,4 R,4 :i(i 50,4 2.7 -1,3 1,G9
. , 7-`l,8 0,7 O,R ~i,fi 19 3?,2 2,1 -1,:1 1,69
V_.2,:i U,5 ~,ii 4,8 fi4 38,4 1,5 -0,9 0,81
9--I,~ 0,4 :1,Fi 4,> SI 40,5 1,1 -O.fi 0,36
10 -_I,fi 0,3 0.3 3,Q 1pp 30,0 O,E -0,2 ~,04
11 ~1,3 0,3 0,3 ;i,3 121 36,3 0,2 0,1 O,Qf
- 12 ---n,7 O,G 0,7 8,4 144 100,$ --0,2 0,9 0,81
is - .i ,n ._~,3 --a.s ir,~ _-~0,7 -o,s o,s o,o~
' ~q _ _2~g ~ ,g _I ,5 ,0 19C, -2'.)4~0 --0~9 -O,G 0~36
~ Iri ...3,(i --�1,3 1,5 --22,5 225 -382,5 -1,2 -0,3 0~09
. I(i -~i,6 --2.:) ._.2~3 -�3(i,8 2.riri -5$8,8 -1,5 -U,S O~fi4
17 --7,2 -I,t~ _..1,R -30,G 28~ -52Q,2 --1,7 ~�0.1 O,OI
Far the case of linear dependence, we sum colu~nns 4 and 5, and substitute these
- sums in expressions (7.30) and (7.31) at n= 17: ~
n~~ . . ~'j~~) � ~Q ~ � ~~r~ ~ ~~~12 _ ~ � ln...ll~
- 17
�
12----( -'l3,?� 14-ii._g.17,9� 10-~i~=---4,5� 1Q-~i~
o - 17 � 'lRti -
17
_ Summing columns 4, 5 and 7 for square-law dependence, we get E Do~ = 1,79�10-10;
- i~ i~
Zin,,; ~~--~,;37 � 10'"'; i'~am =--1,32 � 10-A. Subst~tuting these values and n= 17 in formulas
i~-i ~ i
- (7.33), (7.34), (7.35), we get
- , e__ 3~ 13�'l89 51 -I- 2)17, 9� 10-}i 210�23,7. 10--;~-13200� 10-~~~ = 6� 10-tt.
� I?� 16. If> '
fi~3� Iri. I!)� 17 10�-1l-}-70(8.17-~-I I)23,7� 13-1l-540� 1320� 10-~tj ? 4� 1(r~~;
17�28(i�2~.> - ~
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Y
:i0~ IR. I~.17,!1.10 :~.f -IOH�'13,7� lil t3'l0� f0-~~) ~ i
~1~~' - ~ 7 � 2AB � 2H.~i = 1,6 � 10 .
The rate of going of the time scale of the given standa~d, us,
' 7' ( l} - To 5,2i - Q,321~ 0,041~', ( 7. 38)
from which we see that the daily rate of going of the time scale is equal to +5.2
us/day, the change in the diurnal variation is -0.32 us/day2, and the deviation
of the chang~ in the diurnal variation is +0.004 �s/day3.
To calculate the mean square error, we sum column 10, and then calculate
a , /~8 .49 � I(~-z~ ~ 7,3 . 10-~2,
i s
_ to determine the linear de~endence, other ~ralues must s*_and 1.n colimmns 8-i0. These
~ are calculated by the formula
On(1) (5,1 4,~ii) 14-~t (7.39)
The mean square error v= 8.5�10-12. From a comparison of these two values we see
that the square-law dependence should be given pr~ference.
The metrological characteristics of the frequency standard can be calculated by
a method of graphic interpolation.
If dependence 0o(i) can be interpolated by a straight 13ne [see formula (7.29)],
then we can write the following two equations for deterniining parameters Go, vo:
+ ~ a~t c ~ . ~~o>
A n~ - 0 '
o o- on
and solving these, we get
neoi Ao� ( 7 . 41)
~o= n^~ ~
Y �o~ --eo, (7.42) -
o- .
- n-I
If dependen~:e 4o(i) is intErploated by a parabola in accordance with expression
(7.32), the~i we determine parameters Oo. vo, qo by solving the three equations
n o -1- "o -I' 90 ~o~
t!o m.vo nr9q� _ ~o�, , ~ (7 . 43)
60 nvo 'I- rta9e ~on
n~� (n m) tloi --n (n-� 1) ~ont I nt (m - I) ~on
~0 ~ (n -m) (n -1) (m - l ) ' ~7 .44)
( na - ~n' ) ~oi - ~ n~ - ~ ) ~onr 'I- ~ lri9 ~ ~ ~On
~ (n-m)(n--1)(m-I) ' ~7.45)
' (n--m)doi-(n--I)Qon,-I-~~-1)~en �
90 (n -m) (n- 1) (m- 1) ~ ~7.46)
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In formulas (7.41) and (7.42) we substitute n= 17, ~01= 6�10-11, ~~r~= -1.8�10'll
- (see Table 10), and we get
0._ i~ � s_� io-11 ,_i ,s_ io..,~ _ s 5� lo-u
- !G ^ ~ > > .
~ _ I,g..t0:.~~ - 6 � ~0 ii _ ~,~~q . 10_~zday i.
� Ili
In formulas (7.44)-(7.46) we substitute n= 17, m= 9, D01= 6�10-11, O09 = 0.5�10-11,
~01~= 1.8�10-11 (see Table 10), and we get
l7�9� 8�ii� IU--ti I?� lG�0,5� 10-11-9�8� 1,8� 10-f1 _ 5,? , 10-~~~
_ ` 1024
7.Uf3 . li � I l}-tt ._.'l88 . 0,5 � !0-~~ gp . ~ ,g� Ip-~l _ .
: 1u24 -9~4 � 10-r~ day-i ~
8� ti � IQ-i~ Ili � O,Fi � 10 1=-- 8. 1,8 . 10-11_2 10-~a day-2
~~0 ~ v 1024 ~ �
Experimental data show that parameters Go, vo, qo are calculated more accurately
by the method of least squares than by the method of graphic interpolation.
7.6. Constructing Trapezoids of Changes in Tp From Results of ths Differential
_ Measurement Method
Synchronous recording of f~eld strangth and difference frequency is de~uonstrated
on the example of operation of radio station RES in Moscow (100 kHz) and a local
s radio station at a reception site in Omsk (Fig. 4S}.
~ I ~ 31 I
i ~ ~ ~
- ~ ~ i ~I
~ ' ~
~ I ~ ~ ~
` pi
1., ,1 !G v
v ~6 S' 06 OS ~?r O,i 02 Ol 2- ~ 3 ~ 2 =
0 '9 '8 1' ~ t6 ;
S 4 l,i ;1
~ ' a ~
- ~ I
~ ~ I
~ I i
~ pha ~ ~
I slip ' ~
l t I 1 I 1 I ~L ~ ~ ~ I I ~ L ~ ~ ' l i I I I I I 1 I
1? 11 /0 .^9 ~B c" G6 ~
S ~
~ O.i 0? Of ~ 4 Z,~ 22 : ;
~ :0 ;
~ .'B ; 7 .'6 >S "
- b time of day
- Fig. 45. Synchronous recording: ~
a--uf field strength; b--of difference frequency (bea~ frequency)
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I~rc~m I~ ly;. ~i5 wc crin Kcc thut durinq the couree of a ciay the field sttength at the
re~~c~~~t I.oii point vnries stran~ly, and thxt during sunrise, when there is a sharp
increase in field strength, phase slip takes place at the reception site due to
a ~hange in du-ation of the period of the difference frequency.
If the instants of zero amplitude of the difference frequency to, tl, t2,..., tn
are recorded, the difference of two displaced instants determines the duration
of the beat period, i. e. tl - to = T1, t2 - tl = T2,..., tn- tn-1 = T~. The beat fre-
- quency is defined as ~n = 1/Tn, or in relative quantities ~an = 1/TnfH
The relative error of the averaging frequency over ten beat periods (for the case
shown in Fig. 45--for 14 periods) is calculated from the formula
n 14 = 1 69 � 10-9.
~0 ~ - � 23 � 3600 ' (7.4')
fH Tt
r~~
The duration of the average period T~p = 5914.3 s, and since each of the ~eat periods
differs by ~Tn from the average period T~p, this means that the phase changes by
p~ _~1 - 2n. The total phase change in radians over n periods is
A %'i,
Z^ _ (7.48)
~~�p ~
For gr.aphic representation of the change in phase on measurement time interval
AT~p, a~raph is plotted (Fig. 46) from tabuiated values of ~Tn = Tn - nT~~, F~here
n= 1, 2, 3,..., 14 (Table 11). Plotting is ruled by ths formula ~Tp = Tn�
n?,,.us
s � . .1 - - ~ -r''"'i
;;','i'i;; ; ' (i// ~j;
.
i'~ j',';;. . ; , ~
. ~ .
~4~1;~ Jh , %i0 ~ / i4 ~ ~ R OL1rS
, 4,/ ~ ~ :.~y~/~ ti f day
_ , : nigh~ ~ ay I r.
J . ~ ~ / ,
~ l r;",' . ' ,~j
. ~ i 7
' .�.,'i~ J,~i i/ /
x . ; , .j:~ . _ _ ~ ~~f
/ / ; , ~ ~
~d.~ / , i. .
~ ~ ~ ~ /
~1/ / ~ ~
~ ~/~r ~!i . . ~ ~ - L~~ T /Y ' ~ i
~ ~
; . ~ ~ . l-~ I . I r~/ ' < 1~;~
IY ' . . : _
Fig. 46. Cha*~ge in signal travel time of radio station RES on
Moscow-Omsk transmission path as a function of the time of day
Considering the high stability of the standard being synchronized, all changes
_ in ATn can be attributed to inconstancy of the conditions of radio wave propagation.
The curve of Fig 46 shows a practical reflection of the way that signal travel
time depends on the time of day.
~ 105
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_ TABLE 11
Processing measuremez~t results
n I/r~, I ir%~.~,. S I A7'n~/n.. nr�r'gIl n( Pn' gl nT~~~. 3 I A%'R T~ nT~Q. S
I Fi7(1(1 b914 --214 R 9:i2~ 9T312 -~-4112
2 1()};00 11828 -1028 9 q9200 5.'i22fi --402f~
3 Ib(~00 17742 -2142 10 ~00 59146 --3340
4 210f10 2:~i5(i -2fi,~iG 11 f>1200 (i.5(~54 --3354
5 `l~iHOG 2!a570 --3770 12 f>tiGOp 7096fi -43('~3
fi ;12400 :i,~i4R4 --30}~1 13 72000 ?fi8A2 -4882
7 ~7200 41'39R ---4198 14 7f1000 8279G -479fi
REFERENCES
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- END -
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