JPRS ID: 9444 USSR REPORT ELECTRONICS AND ELECTRICAL ENGINEERING

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JPRS L/9444
15 ~7ecember 1980
- U SS R Re ort
p
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ELECTRONICS AND ELECTRICAL ENGINEERING
~ (F4U~ ~fi/803
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- JPRS L/9A44
15 December 1980
USSR REPORT
~ ELEC7RONICS AND ELECTRICAL ENGINEERING
(FOUO 16/80)
CONTENTS
~rrr~xx~s
Reduction of Nonlinear Distortioas ~n Reception of FM Signals by
, Using a ~ao-Ring Trackiag Filter Circuit . . . . . . ~ ~ ~ ~ , ~ ~ ~ ~
CIRC.UIT THEORY AND PRACTICE
Comment on the Article "Accuracy of MQasuring the Frequency and ~
Angle of Arrival of Signals Recaived by aii Antenna Array Agaiast
a Baclcground of Interfereace With Acoustic-Op~oelectronic �
Processing" g
� � � � � � � � � � � � � � � � � � � � � � � � � � � � 9 �
COP4IIJIJICATIONS, COI~IUNICATION EQIIIPMENT, RECEIVERS AND 1TiA1+TSMITPERS, NS~ORKS,
RADIO PHYSICS, IlATA TRANSMISSION APID PROCESSING, INFORMATION THLORY
_ A Study of the Stability of an Algorithm for the Filtering of a
Pseudorandom Signal Subject to the Action of Similar Capturing
Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Noncoherent Coxrelation FiltPring of Camplex Signals . , . . . . . . . . 25
Optimization of Coumunications S~stems With Noise-Like Signals aad
Correcting Codes . . . . . . . . . ~ ~ ~ , , ~ ~ ~ , ~ ~ ~ ~ ~ ~ ~ ~ ~ 36
Resolution and Compression of Space-Time Signals . . . . ~ ~ ~ ~ ~ , ~ ~ [~,l~,
- Three Scientists in Fiber Optics Awarded A. S. Popov Prize 54
COMPONENTS AND CIRCUIT ELEI~NTS, WAVEGIIIDES, CAVITY RESONATORS AND FII,TERS
Aspects of Design of Narrow-Band Filters of Surface Acoustic Waves 56
II~ECTROMAGNE`PIC WAVE PROPAGATION, ELECTRiODYNAMCCS
Evaluations of the Effectiveness of Determining Parameters of the
Marine Surface and Atmosphere by SVCh (Microwave) Radiometry,.,.,, 64
' a- [II~ - USSR - 21E S&T FOUO]
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INSTRUMENrS, I~ASURING DEVICES ArID TESTERS, MET~DS OF MEASURING GENERAL
EXPERIl~VTAL TECHNIQUES
Scanning Device for Contact-Free Measurement of Temperature 71
Light Beam Splitter for Calibrating the Photametric Scale of Uptical
Devicea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
- OPTOELECTROIIICS, QUASI-OPTICAL DEi1ICES
Precision Servo System for Optical Interferoaneters. v 80
PflOTOELECTRIC PHENOMENA AND DEVICES, ELECTROLi1t~IINESCENCE, ION DEVICES
Photocell With High Time Resolution for the Vacuwn IIltraviolet. 83
QUANI'[TM ELECTRONICS
Dynamic Holographic Monitoring of Internal Heterogeneities of Semi-
conductor Materials in the Near Infra-Red Region. . . . . . . . . . . 85
RALIARS, RADIONAVIGATION AIDS, DIRECTION FINDING, GYROS
Potential Direction-Finding Accuracy of Z`racking Goniometers Uaing -
Amplitude and Phase Techniques . . . . . . . . . . . . . . . . . . . . 91
~
Yu. B. Kobza~ev Awarded A. S. Popov Gold Medal . . . . . . . . . . . . . 97
SEMLCOPIDUCTORS AND DIELECTRICS, CRYSTALS IN GENERAI~
A. V. Rzhanov Awarded Order of Lenin . . . . . . . . . . . . . . . . . . 99
~
. ~
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ANTENNl~S
UDC 621.376.4.019.4
REDUCTION OF NONLINEAR DISTORTIONS IN RECEPTION OF FM SIGNA.I,S BY USING A
~4J0-RING TRACKING FILTER CIRCUIT
Kiev IZVESTIYA WZov: RADIOELr.~CTRONIKA in Russian Vol 23, No 2, 1980
pp 48-52 manuscript received 26 Jun 78, after revision 5 Jul 79
[Article by G. L. de-Ribas] ~ ~
[Text] An analysis is made of the operation of a two-
ring tracking filter that is a kind of threahold-
reducing circuit for FM reception. A system of non-
linear differentiaZ equations is derived that describes
the operation of the circuit. It is shown on the b~sis
of solution of this system that the proposed circuit
reduces nonlinear distortions of the received signal
as compared with conventional track3.ng filters.
~ One :aay to improve interference immunity in reception of FM signals is
- to include a tracking filter in the i-f channel of the receiver [Ref. 1].
The tracking filter is usually an isolated tank circuit K(Fig. 1) with
_ a central frequency that is tuned by a feed~ack
Input Outp t circuit consisting of amplitude limiter A0,
~X ~ A~ ~~~X frequency detector 4�Q, low-frequency filter
~F14, modulator M and adder C. The passband of
the tracking filter tank is narrower than the
M ~ spectrum of the received FM signal, which im-
proves the threshold characteristics of the
~ M~ receiver. However, because of the mismatch
between the instantaneous signal frequency and
the central frequency of tank IC that is inherent .
Fig. 1 in tracking filters, there may be considerable
nonlinear distortions of the received signal.
Such distortions can be redu~ed by supplementing the tracking filter with
another feedbar,k ring [Ref. 2J that includes a tunable frequency detector -
f14,q with central frequency tuned by modulator M1 and [low-frequency fil-
ter] ~F141. The main conditions of effective operation of the two-ring _
tracking filter are identical laws for tuning of the central trequencies
1
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~f the tu.nable frequency detector and tank circuit, and also fast action
- of the supplementary feedback ring. The first condition is met with the
relatively small t~:~ing band relative to the central frequency of the -
tank wli�~ch is the case for the proposed circuit. The second condition
is sat.tsfied by the wide band of the resonant system of the tunable fre-
_ quency detector and extra low-frequency filter [~F141). In virtue of the
identity of laws of tuning of the middle frequency of the tunable fre-
quency detector and the central frequencq of the tank circuit, the vol-

~ tage across the output of the tunable frequency detector is proportional
to the mismatch between the instantaneous signal frequency and the cen-
tiral frequency of the tank circuit. In the adder, this voltas;e is com-
bined w~th the main control voltage, reducing the mismatch, ar,d hence
redu~ing the nonlinear distortions of the received signal.
To analyze the two-ring tracking filter by the method of reduced coordi-
nates [Ref. 1J, the tunable tanlc circuit ~f the tracking filter must be -
replaced by a conditional equivalent circuit comprising two mixers, be-
tween which is a fixed tank circuit with passband and tuning frequency
respectively equal to the passband and central frequency of the tunable
tank circuit. In tr?e first mizer, the phase of the tank control voltage
0y is s~ibtracted from the phase of the output signal, and in the second
m3xer the control voltage phas~ 6y is added to the phase of the signal
_ passing through the tank. When FFi signal U(t~ =Umcos (~pt+0(t)) acts
on a fixed tank circuit with passband 2aH and tuning frequency wp, the
following system of nonlinear differential equations [Ref. 3] is valid
for phase ~K(t) and amplitude V(t) of the voltage at the output of the
tank circuit_:
~K ~ U v x SiFI (e - ey - ~K~ .
y~ + a,~y = aKUm cos (6 - e, - ~K) (1)
The phase of the signal at the output of the tunable tank circuit is
~m = ~r 8r� ~ 2)
If it is assumed that the amplitude limiter does not introduce phase-
frequency distortions, then the phase of the signal on the inputs of the
frequency detectors 4,q and Il4A is also described by expression (2). Then
we can write the following relations for the elements of the f eedback
rings that describe their operation:
*_he voltage at the output of low-frequency filter ~Fi4 with complex propa-
~ation ratio K(p) equal to U~(t) ~ SyA~~(t)K(p), where S,.~ is the dis-
crimination of frequency detector
the tuni.ng frequency of detecta~ f14,t~:va~cieB~gn accordance with the law
f~yA(t) = S~ySM~~(t)K(p), where SM is the discriminat3:on^ofmodulator Ml~
2
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the voltage at the output of the tunab].e frequency detector is propor-
tional to the difference between the inatantaneous frequency of the
signal and the instantaneous tuning frer~uency of the tunable frequency
detector: U~yA(t) = S~y,q (~~(t) - SMSyA~~~(t)K(p)), where 5~,~ is the dis-

- crimination of the tunable frequency detector;
the voltage at the output of filter o,~-~yl with complex propagation ratio ~
K1~P)~ U~l~t~ ~Snti,~Kl(P)~~~~t)-SM~yA~~~t)K~P~)�
Since the control voltage consists of the sum of the voltages on the
outputs of filters ~ti4 and ~Fi41, the tuning frequency of the two-ring
tracking f ilters varies in accordance with the law
f ~t) = SM~SyA~~~t)R(P) +S~y~~~(t) (1 - SMSyAK~P))K1 ~P) J ~
where SM is the discrimination of modulator M, which is equal to the dis-
crimination of modulator M1 under condition of identity of the laws of _
. tuning of the central frequency of tank circuit K and the middle fre-
quency of detector fl4,q. -
Accordingly, the control phase is
e
er - s t ~T~ dT = S~~P~ [S.aK (P) -f- Sp.AKs (P) (1- S�S.,aK (P))l� (3)
0
When the ~H found from (2) is substituted in (1) with consideration of
(3), system of equations (1) takes the form
- Sx~4 ~SaAK ~P) -F- Sn~~(`t ll+~ ~ 1 _ 'Sr~aR ^ lpl~ -
_ (Uma,~/V
) Sin (6 - ' (4 )
j/~ CxY ~ C~xUm COS ~e -
- Introducing the notation for the phase difference of signals at the input
and output of the two-ring tracking filter
9 - cp~ (5 ~ `
, and substituting (5) in (4), we get
; _ _ . _ _ _ _ e; .
~m~ S1Il ~
' ~ ~ ~ ~ ~ ~ `~li l"'9A" `PI ~ v714A�`~V'~ \~~~yJOV7l" V'~/~J ~ ~ � ~V/
V' ; ~j' _ ~cUn;COS ~ l
Thus the operation of the two-ring tracking filter circuit is described
by a system of nonlinear differential equations analogous to the system
~ that describes the operation of the tracking filter in Ref. 3. A com- -
parative analysis of these cir~cuits can be made with respect to the form
3
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of their equivalent frequency responses. The equivalent frequency re-
sponse is the ratio with ~hich the circuit propagates the frequency
deviations of the input signal Ky(p), and is defined as the ratio of the
amplitudes of frequency deviation of the voltage at the tank output �~p
and the frequency deviation of the FM signal at its input 0[Ref. 1].
The equivalent f~-equency response of the two-ring tracking fllter ia
found from solution of equations (6) in the linear eteady atate, i. e.
under the conditions that sin cos ~1 [sic], V'= 0. In this case,
the solution of (6) takes the form
A
� - 1-~- {(aA/P)/[ 1- KK (p) K,K: (P) KK~K Ks (P)J '
where SMS~ = K and SMS~yA = Kl .
Coefficient Ky(p) is found by transformation of expressions (5) and (7):
K, (p) = g ~ j ,i- {P~a*1[1-Kr (P)l} , (8)
- where Ky(p) is the propagation ratio of the controlling circuit:
Ky (p) = KK + K,K, (p) - KK1K (p) K, (p). (9)
Expression (8) is analyzed under condition that filters ~hi4 and ~I-141 are
integrating links with respective propagation-r~tios -
K ~P) = a/~a P)~ ~ 10) K~ ~P) = a~/(a~ P); . (l 11
After substituting (1`0) and (11) in (8) and making simpleb!ut cumbersome
transformations, we arrive at the following expressions for the modulus
and phase of the propagation ratio respective2y:
I K4 I= l~ AZ + B2,/(~-r~), (12) ~p arctg B/.A, (13).
where A = a.,~ [azoc~ac,~ ~ZacZ (a,~ - a,K, -f- a,KK~ '
-t- c~^~ai - aK uKK!) (aK - aK - aiKi)]~
- B = waK {aza,, (1- K - K, KK1) -
- ~2 [aatKKi - r~z a= (I - K) ai (1 - K!)l}~
C=�,�r - c~~~ D s~~~ a- Ka).
based on the known relation for the equivalent frequency response of a
tracking filter _
1
K4~~ = 1 -I- {P/~ [ 1- KY (P)l } ' ~ 14 ~
where Ky (p) = KK (p)~ (15)
4
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and substituting (10) in (14), after appropriate transformations, we can
get expressions analogous to (12) and (13) for the modulus and phase of
the propagation ratio of frequency deviations ~f the tracking filter, -
_ where
~ = aK ~a~ + Wza,~ w~acl~~ B = ~ ~w2 ac~ - ayl~;
(16;
C = ~ - WZ: D = c~ -I- a - Ka) ~ "
Shown in Fig. 2 are the moduli and phases of the propagation ratios of
frequency deviations of the two-ring tracking filter and the conventional
~racking filter as ~alculated from formulas (12), (13) and (16) for dif- _
ferent circuit parameters.
IK,I ~ p3 _~o -
/1 ~ ~ 6 94 _
.
,l0 ~ 60
pg 4 ~ 30
5
0.60 y B 12 /6 ZO _
Fig. 2
_ Curve 1 ie the modulus of Ky of the tracking filter computed at K= 0.9,
- a= aK = 10 kHz. Curves 2 and 3 are the same for the two-ring tracking
filter at ocl = 50 kHz and a2 = 5 MHz respectively. The addition of the
supplementary feedback ring, as can be seen from Fig. 2, ensures more
exact reproduction of the frequency deviation (less than the spread of
the modulus of Ky), and introduces smaller phase shifts (curve 5 for
the two-ring circuit as compared with curve 4 for the conventional
tracking filter). However, in this case there is an expansion of the
band of the equivalent frequency response of the two-ring tracking
filter, i. e. the interference immunity of the circuit is impaired.
Variation of al over a wide range (50 kAz-S MHz) has little influence on -
the band of the equivalent frequency response at the same K1, whereas
an increase in K1 ~eads to appreciable expansion of the equivalent fre-
quency response (curve 6, where K1= 0.3, al = 5 MHz). A reduction in K _
at constant K1 leads to impairment of the effectiveness of the additional -
~ ring. For example curve 7, plotted for the conventional tracY.ing f~lter
at K= 0.7, practically coincides with the curve for the two-ring filter
calculated at K1~ 0.1. Greater effectiveness of the two-ring tracking
filter can be realized by increasing K1, but in doing this, as can be seen _
from curve 8 plotted for K1 = 0.3, the band of the equivalent frequency
reaponse is considerably expanded. The influen.ce of the additional -
feedback ring on operation of the two-ring filter circuit shows up in
improvement of the control coefficient Ky(p), i. e. in an approach of
Ky(p) to unity.
5
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After making simplifying assumptions about the frequency independence of
the feedback rings, i.. setting K(p) =1 and Kl (p) = 1, and from the
condition of circuit stability assuming K< 1 and Rl < 1, we can draw the
following simple conclusions by studying the expression fo~ the control
coefficient Ky = K+K1 - KK1 at the maximum:
The maxima of Ky at different K are reached when the condition K+K1 = 1
is met; the absolute maximum of Ky is reached a.s K approaches unity, and
as K1 correspondingly approaches zero. Hence it is clear that one cannot
realize equally good characteristics of the circuit by reducing the propa-
gation ratio in the main rdag-faiid increasing it in the supplementary ring.
It makes sense to introduce a supplementary ring only in a sufficiently
effective tracking filter circuit (K = 0.9 or more), where even a low
K1= 0.05-0.1 can produce a ga in with respect to nonlinear distortions.
One can detexmine this gain ~y comparing the two-ring tracking filter
with the conventional tracking filter that is equivalent in interference
immunity, i. e. a tracking f ilter in which the band of the equivalent
frequency response is equal to that of the t~wo-rrfng~~~~cking filter.
In the equivalent tracking filter the initial equivalent band of the
tank circuit 2aK 3He is not equal to the actual band 2aH, but is aider,
and is found from (16) by substituting the band af the equivalent fre-
quency response with respect to a level of 0.7 taken from the curves of
Fig. 2 for the two-ring tracking filter. The use of such a computa-
tional model is convenient fo r illustrating the physical processes in the
circuit since nonlinear disto rtions are determined mainly by the width
of the passband of the tank c iucuit.
To define the nonlinear disto rtions, we use a method [Ref. 4J according
to which the following expression is derived for the phase difference of
- signals at the input and output of the conventional and two-ring tracking
f ilters:
_
ec~ sin ~f 1 L(p) p+ 2 a` Acil'sins ~t
~ P.-F L ~P) 6 P+L ~P) P -F- ~ [P -~L ~P)1' ~ (17)
_ where L(p) = aH/Il - Ky(p)], and Ow is the maximum frequency deviation.
To calculate the nonlinear d istortions with respect to the third harmonic
the amplitudes of the third and f~rs~ harmonics are respectively faetored
out of (17) and divided; the calculation for conventional tracking f il-
ters was based on on aH 3H8, while the nonlinear distortions for two-
- ring tracking filters F~ere calculated from aH. The Ky for conventional
filters was found from (15), and for two-ring filters was found from (9).
Fig. 3 shows tne results of calcul~tion of nonlinear distortions. Curve
1 is the percent ratio of linear distortions in the conventional filter
to those in the two-ring fil ter on different frequencies, and shows the
b
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% -
/15
150
i75
/00
0 2 4 6 B f
~ Fig. 3
improvement in nonlinear distortions with introduction of an additional
feedback ring by 150-180X on frequencies below 5 kHz and about 150% on
high frequencies. Th~ effectiveness of a properly designed two-ring
tracking filter (K fairly high, and R+ K1 = 1) with various other param-
eters of the circuit is approximately the same as in the given compu-
tational example.
Measurements of nonlinear distortions of an FM signal (carrier frequency
6 MHz, upper modulating frequency 10 kHz, maximum frequency deviation 20,
50, 200 kHz) done on a pilot model of a two-ring tracking filter with the
same circuit parameters as used in the calculations without and with
activation of the supplementary feedbaek ring show~d good agreement with
the calculated data (curve 2). =
REFERENCES
1. A. S. Vinitskiy, "Modulirovannyye fil'try i sledyashchiy priyem ChM"
- [Modulated Filters and Tracking FM ReceptionJ, Mpscow, Sovetskoye
radio, 1969.
2. B. S. Troitskiy, G. L. De-Ribas, "A Receiver of Frequency-Modulated
Signals" Soviet Patent No 493925, Patent Bulletin No 44, 1975.
3. V. A. Dorofeyev, "Analysis of Filterless Systems for Tracking FM
Reception," Trudy NIIR [Proceedings of the Scientific Research In-
stitute of Radioj, Moscow, No 4, 1968, pp 18-21.
V. M. Dorofeyev, "Nonlinear Distortions in Tracking FM Demodulators,"
Trudy NIIR, Moscow, No 3, 1973, pp 5-12.
COPYRIGHT: "Izvestiya vuzov SSSR - Radioelektronika", 1980
_ [308-6610]
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CIRCUIT THEORY AND PRACTICL
I
UDC 621.397.193
COMMENT ON THE ARTICLE 'ACCURACY OF MEASURING THE FREQUENCY AND ANGLE OF
ARRIVAL OF SIGNALS RECEIVID BY AN ANTENNA ARRAY AGAINST A BACKGROi]rID OF -
INTERFERENCE WITH ACOUSTIC-0PTO~ECTRONIC PROCESSING'
Kiev I~VESTIYA WZov: RAI)IOELERTRONIKA in Russian Vol 23, No 7, Z980
p 104 manuscript received 22 Feb 80
[Letter to the editors by G. S. Nakhmanson]
[Text] In Ref. 1 in an analysis of the correlaCion function of distri-
bution of intensities of the light field in the output plane of an acous-
tico-optical processor when a linear antenna array receives a narrow-band
~ormal random process against a background of white noise (expression
(12)), a number of terms were left out, which in some cases leads to -
inexact results.
With consideration of corrections, the expression for the correlation
function of distribution of the light field in Che output plane of the
acoustico-optical processor (formula (12) [Ref. 1]) takes the form
_ _ . _ .
( (L t~)1,~ t~) - ( t~)> ( tJ) a
~ A~p sinc3 ~
N sinc~ { 4 IG~Z (X~' Y ~X~ )'1 I~�~?'
-t- (X~ )=1-f- (�i ) (�i ) f�~ ) (l+~~') (X~ ) (3C2 ) cos 2~,~oT'�Y
-r- 2Q ~(�i ) ~X:+) (W_~~') -I- ) (N~ ) ~X�)1 ~Z+) sinc 2 -f-
-F 2Q H�i ) (X�) ~�z ) -4- (�z ) sinc 2
-j- ~ I (Z+)' sinc~ 2 (Z-)' sinc~ 2 J 4 , ( ~ )
L ~
where all notation in (1) coincides with Ref. 1.
- Use of the corrected expression (1) in analyzing the statistical charac-
texistics of estimates of the frequency and angle of arrival of the re-
~eived normal random process in Ref. 1 leads to the following results:
the probability that the threshold will be exceeded at the output of the
8
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channel of the optoelectronic system (i, e. the threshold corresponding
- to the parameters of the random process to be analyzed) decreases mono-
tonically from 0.94 to 0.58 as the normalized threshold y changes from
' 0.2 to 0.9.
Graphs for the relative shift in the frequency estiu~ate /fp as a
fun~tion of Y are slightly higher than curves according to the results ~
given in Ref. 1.
It should be noted that the corrections that have been introduced do not ~
- influence the variances of the estimates of frequencies and angles of
arrival of narrow-band normal random processes.
REFERENCE
1. G. S. Nakhmanson, "Accuracy of Measuring the Freqi.iency and Angle of
Arrival of Signals Received by an Antenna Array Against a Background
of Interference with Acoustic-0ptoelectronic Processing," IZVFSTIYA
- WZov: RADIOII~EKTRONIKA, Vol 23, No 1, 1980 p 3. ~
COPYRIGHT: "Izvestiya vuzov SSSR - Radioelektronika", 1980
[308-6610J
6610
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_ COMMUI~CATIONS , (AI~lIJNICATION EQUIpME~NT,
REC~IVERS AND TRANSI~ITERS, NET6~pgRS, RADIO
- PFiYSICS, I~ATA TItANSrQSSION AND PROCESSING,
~ ~ ' _~iF~~tAT~CQ~i THEORY
UDC 621,391.2
A STUDY OF THE STABILITY OF AN ALGORIT~i FOR THE FILTERING OF A
_ PSEiTDORANDO~i SIGNAL SU~JECT TO THE ACTION OF SIMILAR CAPTURING
INTERFERENCE ~
Moscow RADIOTEKANIKA I ELEKTRONIRA in Russian No 8, 1980 pp 1629-1638 _
manuscript received 5 Dec 78
, [Article by V.P. Ponomarenko]
[TextJ The stability of a two circuit synchronization
- system which realizes an optim~n f iltering algorithm
for a pseudorandam radio signal subject to the action
of a similar capturing~'interference is studied. The
dqnamic characteristics whf~h make it possible to esti-
mate algoritl~ stability with a change in the system
and ir.terference parameters are determined.
_ 1. Introduction. Formulation of the Problem
The solution of the probleffi of synthesizing an optimcmm filtering algo-
rithm for wideband pseudorandam phase keyed signals (ShPS) for a broad
class of cases where the processes of change in the information para-
meters of the signal are that the phases 6(t) and delays T(t) are modul-
ated [1, 2] by Wiener and gaussian exponentiallq correlated random
processes respectively, leads to the following equations [1, 2j for
estimates 0* and T* of the parameters 0 and T:
A'= k'[R(T-T')sin(8-6")+n,(t)],
P
(1)
k=
7"-To= ID(T-T')cos(6-9')+nz(t)}.
4+T`=~

~~r 10
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Here, p- d/dt; R(T - T*) is tl~e autocorrelation function of the signal; ,
D(T - T*) is a nonlinear characteristic def ined by an algorithm for
generating the error e~ T- T*; TD is the known constant value of the
delay T; T1 is a time constant; kl and k2 are parameters; nl(t) and
n2(t) are the noise camponents of the signal.
The technical realization of algorithm (1) is realized [1] in a two-
_ circuit tracking system with crossed feedback loops, consisting of a
filter-free autamatic phase tuning syst~ (FAP) [PLL - phase locked
loop] and an inertial static delay tracking system (SSZ) with s f irst
order integrating filter. Camplicating the models of the information -
_ parameters 0 and T, as is well known [1, 2] influences only the type
- of filters in the PLL and static delay tracking subsystems, without
changing the fundamental structure of the optimum filtering system.
_ A study of the quality of algorithm (1) without taking into account the
action of interference (nl(t) = n2tt) = 0) for the purpose of estimating
the stability in a large two-circuit filtering system which realizes
this algorithm was made in paper [3). One of the imporr,ant problems
- which came up in studying the noise immunity of systems for tracking
signal parameters is protectioa against intentional simulating inter-
ference [4, 5J which is intended to disort Xhe useful information and
make automatic tracking of the signal parameters impossible. A wide-
spread type of such jamming in ShPS [wideband pseudorandam phase-keyed
signal] systems is a capturing ShPS similar to the useful signal, but
differing frc~m it fn a~plitude, frequency offset with respect to the
~ carrier frequency and having a time shift which changes monotonically
with the c~urse of time.
- Under cnnditions of exposure to similar interference, along with the
problem of filtering algorith~n optimization, which leads to more -
complex correlational compensation processing algorithms, there also
arises in connection wi. the probl~ of realizing these algorithms
that problem of estimating the stability of algorithm (1) with respect ~
to the s~milar interference. The property of stability is understood
to here to be the capability of algortliim (1) of ma3ntaining its own
characteristics within a specfied range when the interference parameters
change (intensity, frequency and time differences).
A characteristic feature of ShPS filtering algorithms is the presence -
of aperiodic nonlinearities R(T - T*) and D(T - T*). Under conditions
of exposure to capturing interference, this leads to the fact that the
stability of algorithm (1) depends on whether the system is synchronized ~
or not at the point in time when the interfereQCe arrives. In the case
of simultaneous arrival of the useful and interfering ShPS's, the
interfering signal influences the process of locking the syst gn into
synchronization. In this case, the stability of algorithm (1) can be '
disrupted at certain values of the interference parameters because of
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the impossibility of eatablishing the signal tracking mode for these
values of the parameters. In a number of situations [5], the inter-
ference can lag the signal so much that at the moment of its arrival,
the search can be completed and the useful ShPS parameter tracking mode
- established in the filtering system. The impact of the interfering
, �ShPS can lead here to a break in th~ tracking, which also entails a
loss of stability for algorf.thm (1).
_ The solution of the problem of the imonunity of algorithm (1~~ is campli-
cated by the substantial nonlinearity of equations (1) and the presence
of the noise components nl(t) and n2(t) in them. For this reason, to
ascertain the general laws governing the influence of similar inter-
ference on the stability of algorithm (1), it is expedient to limit
ourselves to the simplest case where the noise components nl(t) _
= n2(t) = 0 are absent. The results of a study of the stability of
algorith~ (1) with exposure to simiiar capturing int~rference are
given in this paper, which were obtaiaed by me~ns of studying the oper-
ational modes of a model of (1), and determining the regions for the
preservation and loss of tracking as well as the capture range.
2. A Mathematical Model of the Syste~m
In accordance with the problem posed here, we shall assume that the
input signal has the form:
~2~ y (t) =A,i[t-T,(t) ]cos 6.(t)+A�f [t-T.(t) )cos 6�~t), .
where AS, TS, Os and An, Tn, On are the amplitudes, time delays and
phase angles of the vseful and interfering ShPS's respectively; f[�]
is a function which defines the law goveming the phase keying and
assumes only two values: 1 and -1. We shall consider the amplitudes
As and An to be constant. We shall adopt the following linear function
as the model for the change in the delay Tn of the interference:
~3) - -
_ T;, (t) ~T, (t) +T.+act,
where T~ is the initial diff erence between the delays Tn and TS;
a is the rate of change in the deiay Tn. With the ass~ptions made
here, the equations for the estimates 68 and B of the parameters of
the useful ShPS are written in the fo~n:
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- . . . . -
~4~ ~'s p' (R~T-T')sin(6.-8.')~'F~~~'.-~'.')sin(6~-9.')
_ k, ~
T.~-T.= ID(T,-T.')cos(6.-6.')+
i +T, p
+W~ (T�-T.~).cos (Aw-6: )
where u= AnAsl. By introducing the instantaneous phase tracking error
OS - OS and delay tracking error x= Q'1(Ts - s), where ~ is the
width of one element of the ShPS code sequence, and taking (3) into
- account, we derive the follow~.ng equations for algorithm~(1) when sub-
jected to similar capturi~g interference:
__aT . -
d~ - ~ -
~5~ =Y-R(z) sin ~-�R (a-Fso-F8i) siu (g~h~"9'~),
'dr
- = b [~-z-aD (z) cos ~-�aD (a-f-z,i-st) cos ~p+9T) J,
dT
where T= klt; Y= p0~/kl and S= A-1(TS - TpP are the relative initial
frequency and delay differences; a~ = Tp~-1; b=(k1T1)-1; d= akll; -
- q= Stkll; S2 and ~ are the frequency difference and the initial difference
in the phases of the interference and the signal respectively; a=
= k2A'1 is the maximum relative delay selected bq the SSZ [in~rtial
sta~ic delay tracking system]. The nonlinear characteristics R(v) and
D(v) for one period of the change in v are determined in the following
fashion [3]:
_ - _
f -v, . 0~v~1~ .
R(v) = i-}- i;, - i C v~ 0, _
0, i~lv~~M-1,
' U~ 1~1~1~ -
2-v, ! ~v~2,
D = ~
-(~-~-a), -2~v~-i,.
a~ 251v~~R~-2*
where M is the number of elements of the code sequence i~n one signal
period. The case where M� 1 is the most practical real case; then
it can be assumed that R~v) = 0 for ~v~ > 1, D(v) = 0 for ~v~ > 2, i.e.,
one can assume the nonlinearities R(v) and D(v) are aperiodic with
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,
respect to v. ~'hen the right sides of equations (5) are aperiodic
- with respect to the variables x and 'Thus, algorittmn (1; with the
assumptions considered here is written in the form of a nonautonaonous
system of nonlinear differential equations (S~ in the phase space
X, T.
3. Steady-State Modes
To solve the problem posed in this paper, it is necessary to first of
all ascertain what steady-state modes of the filtering system are
dete~ined by the established motions of the model (S). In the absence
of interference (u = 0), the dynamics of the system are describ~d by
the autonomous system of equations:
- - - -
a~
= 7-R (z) sin
~7) c?T
ds
- =b[~-x-aD (z)cos
dr
10 ~=0
r
a, e
-a
0, 6
-J, S `
- 0, 4
O, 2
~
! /0 !0 Z � !03
k, T,
Figure 1.
In this case, the steady-state synchroni2ation mode wfth a constant
phase difference ~s and difference in the delays xs is determined by -
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the stable equilibrium state [3] of A1(~s, xs) on the cylindrical
phase surface x. For value of the parameters from the capture `
range of DS: Y< Y*(g, b, a), the onset of the synchronization mode
accurs for any intial values of the phase difference ~ini 8nd inftial
_ values of the delay diff erence xini a R. The curves for Y~ Y*(S, b, a)
are shown in Figure 1 in parameters of Y, k1T1 where a= 5 for values
of the initial delay difference of s= 0, -0.5 and -1.5. It can be
seen that size of the capture range falls off with an increase in the
_ absolute value of the difference S. Sho~wn in Figure 2 are curves of
B= B*(Y, b, a) where a= 5 for a number of values of the d~mensioniess
- time constant k1T1 of the eystem, which define the region ~Q~ < 6*~Y~
b, a) of permissible values of the initial difference S; for which
synchronization begins at any initial values of the phase difference
_ _ - -
a _
? - .
x~T �10
\
ZO ~ .
!00 SO \
~p ~
~
~
J000 ~ ~
~
p 42 44. 46 48 Y
Figure 2.
For values of Y< Y*(S, b, a), the phase picture of the system when
S< 0 is shown in Figure 3a; with theae values of the parameters, there
, is stability on the whole for the equilibrium state A1 on the phase
cylinder x. For value of Y> Y*(S, b, a) on the phase surface
x, in the case of the presence of a stable state of equilibrium A1, there -
is a stable ultimate cycle of the second kind (Figure 3b); with these
values of the parameters, a beat frequency mode of the second kind can
also be established in the system besides the steady-state synchroniza-
tion mode, where the phase difference ~ increases without limit, while
the difference in the delays x varies periodically about a certain -
value.
It follows from the results presented here that when u= 0, the stability
range of algorithm (1) with respect to deviations from the steady-state
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is governed by the values of the parameters Y, b and a whicY? belong
to the capture range DS.
X X
Z
~
-n - 0 A, a-at D A~ A
1 / i ~
~ (,a~ Cb?
Figur~ 3.
When u# 0, by virtue of the aperiodicity of the right sides of system
(5) with respect to x and T, the steady-state modes of the filtering
system are determined by the 13ffiited steady-state motions of system (5)
in the phase space x, z, i.e., by those motions during which the
mapping point where < T 2 is an sutono~ious system (7) with a known
picture for the behavior of ti~e phase tra~ectories. A stable trajectory
LS, which is bounded with respect to the phase coordinates ~ a~d x
when < T 0(or d< 0)
coincides in the region x+ xp + dT ~-2 (or x+ xp + 8T > 2) of the
phase space x, T with the ray RS~~ _~S, x= xs, and when T-?
it tends to the ray RS:~ _~8, x= xs in the re~ion x+ x0 + ~T > 2
(or x+ xp + dT 2 is
equivalent to the following system:
. _ -
d~
dT, ~7'~R~Z~sin 6,
(9) .
dz ~
=b,~~,fb,i,-s-kD(a)cos 61,
dz,
where fl=~+~+ qT and z= x+ xp +.ST are respectively the phase
difference and the difference in the delays of the interference and
reference signal; Y1 -~7 + q)u-l; S1 = g j- xp + 8b-x; bl ~ bu-1;
81 = du-1; k= ua; T1 =}IT. The tra3ectories of system (9), when the
- time T1 increases, enter inside the phase space regions 61 + d1T1 <
< z< Si + d1T1, where S1 = R1 - 81b'1 - k and ~i =~1 - dlbll + k.
_ It follows from this that all of the solutions of system (9) are not _
bounded. By virtue of the absence of bounded solutions f or system (9),
system (5) does not have any steady-state motions which are bounded
with respect to the variables v and A when < T
~ 4, the parameter d is less than zero and the initial phase difference
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varies in a range of (0, 2n]; the parameters of the system Y, b, s and
a belong to the capture region D8 of the autonomous model (7), while
the initial state of the system at the point in time T~ Tp is determined
in the phase space by the point bn the straight line RS, i.e., by the
equilibrium states (�8, xg) of model (7). Then when T> Tp, with the
influence of interfe rence, the mapping point in moving in the phase
space along the trajectory L8 is deflected from the steady-state status
(�g, xg), hawever, with the course of time mones out into the region of
x+ xp + dT i; F"- xN~".
~ T
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As implied by (9), smooth cyclic scanning of radiation pattern (3) with
quadratic phase response for predetermined deviation of epace frequencies
2w�! leads to time modulation of the space-time signal with deviation of
the "time" frequencies equal to 2FM.
Let us consider a system that realizes an algorithm for shaping signal
(9) for the case of utilization of a discrete aperture. In this case,
we have on the basis of (7)-(9)
~ ~
- ~ nr t-xT/~-i2T lx
S (t, e) = s,1, ~ fi---~
(lo)
Z
Xexp ~ j f 2n f~t 2:skOxA n T" (t kOx i2~'l -f- ~o
~ \ r I ~
where ~X is the dis'tance between elements of the antenna array, and
2m + 1 is the number of elements in the array.
~
~ yy ~
~M
PSl ~By _
Fig. 2
A block diagram of a system for shaping s(t;6) is shown in Fig. 2.
Signals s(t) - Sp exp { j(Wpt + Qp) } from rf oscillator PBy are sent to the
radiators of the array through distribution device PY and controllable
phase modulators Qril. The controlling voltages for the phase modulators
are shaped in accordance with t.10) by control device YJ~.
The signals shaped by the system are uniformly distributed on plane
~t{ < T; (A~ ~ 6r,i (have a constant amplitude), are linear-frequency modu-
lated with respect to both time and space coordinates, have identical
shape in contrast to discrete-coded space-time signals [Ref. 5], and
differ for different directions Ai, 6~ only in the time displacement of
~ s(t;8i) =s(t+~t; A~) by an amount
~t 9i-8 f I ~"~ent.
The possibilities for resolution and compression of signal s(t;6) and
evaluating its parameters are determined by the space-time uncertainty
f unc tion
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_ _ _ _ _ -
T ~ - _ T
~~T~ Tl) = C I � s~t; g) ~~t t; 9-F- r~ dtd6 = sinc22nFx T- t~ eN (11)
~J ~ ,
? _r
" sin x
where C is a normalizing factor such that Y~ (0; 0) =1; sinc x= X. Un-
certainty function (11) has one main lobe and a comparatively low level
of side lobes. Since the uncertainty function describes signal behavior
at the output of an optimum processing system, the width of its main lobe
with respect to axes T and n will characterize the degree of compression
of the space-time signal. The width of the main lobe with respect to
axes T and n respectively on the zero level is
_
e~ - i ~2FM = 2T/2X,~,26~.: e,~ = i/2x� ~/2x~,~e~.
The curtailment factor [Ref. 2] in the given case is determined by the
product of the width of the space frequency spectr~ 2~ multiplie~ by
the duration of the space interval 2A1�1, which by definition [Ref. 4] is
the spatial bas~ of the signal. The temporal base of the signal, defined
as the product of the width of the time frequency spectrum 2Ft�i multip.lied
by signal duration 2T, coincides in the given instance with the spatial
base 2FM2T = 2~26M.
Let us proceed to examination of the particulars of optimum processing of
linear-frequency modulated space-time signals. As in Ref. 5, we will
assume that a field y(t;X) arrives at the aperture of the reception
antenna system on intervals of time [-T~; T~] and
space j-9~,,~ AI,~ with distribution density with respect to angle
coordinate
- - .
y~r; e~ S, ~r; e~ a~e - et~ -f- n~t; e~,
which is a mixture of space-time signals (5) reflected or re-radiated by
objects located in sector [-6j,~; 6nq] with thermal additive normal inter-
ferences uniformly distributed in space and described by the correlation
function [Ref. lJ
- (n ~t~~ ei) R"` ~tr 8~) = No8 (t1- t~ 8(6t - 8~�
We will consider processing of space-time signals on the same intervals
on which they were formed: T~ ~ T~; AI�I 9M ~q; Xr,i r~g~ = Xr,R t~pR�
We will also assume that the angular spacing of the received signals
exceeds the Rayleigh limit ~9i - e3~~ i/2~, and taking consideration
of situations that actually occur, we will disregard the influence of
signal envalope delay over the aperture.
In this case the expression for the optimum output effect of the process-
ing system takes the form
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M
Y ~e~ ~ ~ S~n~ ~e - kee~x
- ~12~
r
1z
X f So exp i- j~2nf ~t n T" (t - 8 8 I+~o ~ Y(k~8; ~ dt ~
\ ~
=r
x�
where Y(1t09; t) = f y(t; x) exp { j2nk~@x} dx;
2m 1= 2A~ oP,,,2~ DA =1/2y,~
Optimum processing algorithm (12) is ~ealized by the same system (Fig. 3)
as in Ref. 5. The system contains an antenna array with pattern shaper,
each of the (2m+1) outputs sending waveforms Y(k~A;t) to temporal pro-
pattern ,QOC shaper
~ ~ ~
Q ALl A,Q
H
Fig. 3
cessing channels that consist of optim~ filters (GYD) and amplitude de-
tectors . The resultant aggregate of discrete values of Y(1c~6) of
the output effect
T .
2
Y (k~8) = . f Y (k08; t) So exP { -1 2n
f
ot -4- n ~ (t 9 ~o ~ ~ -
-T `
goes to the interpolator (1~ which shapes output effect (12).
Let us consider the signal component YS(~) and the interference compo-
nent Yn(8) separately in output effect (12) . In doing so, we will assume ,
that the only significant parameter of the received signal s(t;9) is the
' direction of its arrival
z
S~~; e~ = So eap ~ 2nf~ + n~." t- e~~+~a,} s~o - e,>. ( ~ 3~
l~ ~ .
Substituting (13) in (12), we get
L
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~n P -
Y, (9) sinc 2n~ (A - kA6) ~ So exp l- j f 2rcf ~t -f- n T~~(
~ _r l.
e�
E
x(r - e e~+~o J~ d~ y S~~; A) sinc 2n~~ (A - k~9) dA =
--e~ (14 )
~ I So2Te~~~~-~'~ sir1C 2JCgy ~(9 - 8,) sinc 2n T" (t - 6, g 7X
~ y .
Xf 1- I t-9,T/Ay~ ll.
~ T ~
~ Expression (14) implies that the signal component at the output of the
optimum processing system is determined both by the characteristics of
the reception system and by those of the space-time signal shaping
system. The maximum value of the output effect YS ~X = S~2T is formed
for the direction that coincides with the direction of arrival of the
received signal. In contrast to systems with discrete-coded space-time
signals [Ref. 5] where the shape of the signal component of the output
eff ect depends on the direction of arrival of the signals, in the given
case no such dependence is observed, and the processing system forms an
output effect of identical shape regardless of direction ~6~~ 9M. Shown
in Fig. 4 is an example of the form of envelope of output effect (14)
S~(tl
_ ~
- ~ I
I ~
I ~
� T t~ r2 T t
Fig. 4
for the case of reception of two space-time signals arriving from direc-
tions 61; 92F [-0M; 6M]. The time position of each of the pulses at the
out~ut of the processing system as read out relative to some fixed time
is uniquely related to the direction of signal arrival ti = AiT/6M. In
this relation, the spatial distribution of objects in sector [-AM; 6r,s]
is transformed to temporal distribution on interval [-T; T], and curtate
(compressed) signals (14) are produced at the output of the processing
system. The resolution with respect to the time coordinate ~T= 1/2FM
corresponds to angular resolution An = ~TAM/T = 1/2~.
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The interference component of the output effect is defined analogously to
the signa] component
m. T . _ _
(A) _ ~ sinc 2nx� (6 - ke9) So exp { - j [2~
f ~t
k~-et � - T
e�
:~F�/T !t - 6T/8�)z ~o)} cit ~ n (t; 8) sinc 2~cx~ (6 - k06) d6
-e�
and is a normal random process with zero mathematical expe~tation and
- with correlation function
- m - m
~ Y,a (e~) Yn (e:>; = Z ~ S~n~ ~X~ ~e~ - koe~x _
k+.-m q~-m
T
n
- Xsinc 2~,~ (6~ - q~A) ~ ) So exp j `2~fo ~ts - t:) -f- n T" ~ (t; - 81 Q ~Y -
L ~
-r
e~
z,
- - 82 eM J ~J1 ~ J ~ n ~t>; n` ~fs; e~ )X
-e~
(15)
Xsinc 2ny,~ (8, - k~8) si:,c 2~xw (62 - q~9) d6,d8t I=
So2T 2~ sinc 2n~ ~pM ~e~ - 8,~ S111C 27[%r npA ~@, - 8~ I 1- ~ d' e~ eY ~l I.
~ i J
Analysis of the energy characteristics of processing system (14), (15)
shows that despite unification of all processing channels into one, -
in contrast to systems with complex radiation patterns and simple space-
time signals [Ref. 6], the influence of the interference acti~ig at the
input of the processing system (Fig. 3) is attenuated by a factor of
2~�~26r,i. And with respect to its energy capabilities, this system is
equivalent to an optimum multichannel system that realizes parallel
- scanning of space. The reason for the reduced action of interference,
as in the theory of linear-frequency modulated time signals [Ref. 2],
is the increased resolution of the system with respect to angle coordi-
nates.
It should b e noted that output effect (14) can be shaped by a system
that uses a scanning radiation pattern FcK(6) of the type
F~(6) = sinc 2n~(6 - tBh,I/T) ,
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- which maximizes the output effe~t when the maximum of the radiation -
pattern F~(6) coincides with the direction of signal arrival. However
the throughput of such a system will be limited since at the same instant `
of time the signals arriving from other directions of the scanning sector
will not be received by radiation pattern F~(8). -

- Thus the proposed algorithms for shaping and proressing space-time sig-
nals enable shaping and compression of complex linear-frequency modulated
signals with respect to both time and space coordinates, ensuring high
angular resolution by extension af the spectrum of space frequencies
without narrowing the radiat~on pattern.
The proposed algorithms are distinguished by comparatively simple hard-
ware realization. And in fact the circuit that realizes the algorithm
for shaping linear-frequency modulated space-time signals is even simpler
. than the analogous circuit for shaping discrete-coded signals [Ref. S].
Elimination of the rather complicated and cumbersome pattern shaper in
the given case (Fig. 2) not only simplifies the hardware realization,
but also improves the ~uality characteristico of the system ~y reducing
energy losses and signal distortions in the pattern shaper circuits.
- As for the circuit used in processing linear-frequency modulated signals
(Fig. 3), it sl~ould 'oe noted that this is not the only possible con-
struc[ion of a system for processing space-time signals. Analysis of the
_ output effect of the space-time processing system [Ref. 1, 5J shows that _
with the same constraints as used in deriving (12}, space and ti.me pro-
cessing can be accomplished independently, and the design pecuiiarities
of the system will be determined by the processing sequence. For in-
stance in writing (12), preference was given to carrying out operations
of spatial processing first, which led to the necessity of using a
pattern shaper in realization. On the other hand, carrying cut the �
temporal processing opezations first leads to a system without a pattern
shaper [Ref. 6], which in many cases simplifies the processing system
- and improves its characteristics.
REFERENCES
1. S. Ye. Fal'kovich, "Otsenka parametrov signala" [Evaluating Signal
Parameters], M~oscow, "Sovetskoye radio," 1970.
2. Ya. D. Shirman, "Razresheniye i szhatiye signalov" [Resolution and
Compression of Signals], Moscow, "Sovetskoye radio," 1974.
3. Drabovich, Orbi, Bonnas'ye, "Compression of the Radiation Pattern of
an Antenna Ai=ay by the Method of Space-Time Coding," ZARUBEZHNAYA ~
RADIOELEKTRONIKA, No 3, 1971.
4. A. I. Pogorelov, "Using Complex Radiation Patterns in Direction-Finding
Systems for Resolving Signals in a Broad Scanning Sector" in: "Radio-
tekhnika" [Radio Engineering], Vishcha shkola, No 37, 1976.
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5. A. I. Pogorelov, "On the Theoxy of Nois.e-Like Space-Ti.,me Signals~~'
IZVESTIYA VUZOV: RADIOELEKTRONIKA, Vol 22, No 7~ 1979 p 3.
- 6, A. I. Pogorelov, "Analysis of Syatems with Complex Radiation Patterns"
in: "Metrologicheskiye voprosy prikladnoy elektrodinamiki" [MeCro-
logical Problems of Applied Electrodynamics], Proc. ~�f Metrological
Institutes of the USSR, Leningrad, 1978.
COPYRIGHT: "Izvestiya vuzov SSSR - Radioelektronika", 1980
[308-6610]
661Q
CSO: 1860 ~
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FOR OFFICIAL USE OHI~Y
TfIItEE SCIENTISTS IN FIBER OPTICS AWARDED A, S~ POPOV PRIZE
Moscow VESTNIK AKADEL~I NAUK SSSR in Russian No 8, 1980 pp 135-6
[Arti.:le: "A. S. Popo~v Prize Awarded to G. G. Devyatykh, Ye. M. Dianov and
M. Ye. Zhabotinskiy"] _
[Text]
, ,
g j ~ ~rs~-
~ ` i ! ~f ~
` ~ , .
_ i'~ - - , y~~ ~t~- ~ ~ ~
~ ~ ~ . : , t ~ f"~'rtlF~. ~ . . . ~
pY +
1.,.. ~
~
~
~ ,y
�aY,
~pSt, i41
.'�t ,~p F .
L
f
~ 4 . _ .
~
G. G. Devyatykh Ye. M. Dianov M. Ye. Zhabotinskiy
_ The Presiditan of the USSR Academy of Sciences has awarded the A. S. Popov prize
for 1980, in the amount of R 2,000, to Academician Grigoriy Grigor'yevich Devyatykh
{Institute of Chemistry, IISSR Academy of Sciences), Doctor of Physics and
Mathematical Sciences Xevgeniy Mikhay?nvich Dianov (Physics Institute imeni
P. N. Lebedev, USSR Academy of Scienc.:s) and Doctor of Tectinical Sciences Mark
Yefremovich Zhabotinskiy (Institute of Radio Engineering and Electronics, USSR
Academy of Sciences) for research in the development ot low-less fiber optical
conductors for information tranamisaion systems. _
The series of works which was awarded the prize is a camprehensive study of the F-
physical and infoxmation characteristics of fiber optical conductors, the develop- _
ment of the methodology and technology for manufacturing low-loss fiber optical
_ conductors, including purification and analysis of the initial materials, as -
- well as development of the metrics for fiber opltical conductors and control over
the manufacturing process.
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Results of this work opened the practical possibility of creating wide-band
optical co~nunications systems having the following significant advantages as
compared with existing ones: 1) Being wide-band in nature while maintaining
low loases (about 10 gigaHz/km) with lossea of lesa than 1 dB/km;
2) Immunity ta electranagnetic interference;
3) Small size and weight;
4) Replacement of scarce materials (copper, aluminimn, lead) by glass; and
5) the Possibility of wide introduction of standardized digital information
tranamission systems (because of the grzat wide-band nature).
The results have been introduced into industry. The fiber optical conductors
which have been developed will fimd broad application in telephone systems, in
cable television, in computer technology, in sircraft infonnation txansmission
syatems, in systems for automating industry, transport and power engineering and
in a n~ber of special devices.
COPYRIGHT: IzdaCel'stvo "Nauka," "Vestnik Akademii nauk SSSR," 1980
[307-9194]
9194
C90: 1860
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CO~ONEN'rS AND CIRGUIT EL~II~I~S, WAV~G"JIDES,
CAVITY RESONATORS AND FILTERS
IIDC 621.37 2 .543 .2
ASPECTS OF DESIGN OF NARROW-BAND FILTERS OF SURFACE ACOUS~IC WAVES
Moscow RADIOTEKHNIRA in Russian No 5, 1980 pp 22-26 manuscript received 18
Apr 79
[Article by A. Ye. Znamenskiy, Ye. S. Muratov, V. N. GulinJ
(Text] Ir designing narrow-band filters of surface acoustic waves (PAV)
with relative bandpasses ~,f/fp ~ 5 x 10'2, particular attention is given
to the choice of filter structure, methods of reducing spurious triple
passage signals (TP) and volumetric waves (OV), the need for accurate
realization of inean filter frequency, accountinq for the effect of loads
and destabilizing factors on fi?ter parameters. Let us exami~e each of
these problems based on the specifics of design of narrow-band filters in
particular.
Choice of filter structure
The primary material for sound guides of narrow-r,and filters is a quartz
slab of thermostable ST-section (xyl/42�45').
At the preset mean frequency, the lower limit of bandpass (PP) of the ~
filter is constrained by the possibilities of photolithography on large
surfaces (since the expanse of the interdiqxtal transducer (VShP) is
inversely proportional to its PP), the increasing level of parasitic
signals in expanded VShP (reflection, diffraction on apodized structures,
signal attenuation in propagation) and the limited dimensions of existing
sound guides made from the ST-section of quartz.
Thus for relative PP L~f/fp about 10-2 and small intermediate fre~uencies
fp, where long duration of pulsed filter response is necessary, it is more
advantageous to use a cascade connection of individual links with a _
nonapodized VShP structure (Fig. lc) instead of the traditional one-link
narrow-band filter PAV (Fig. la) consisting of apodized and nonapodized
VShP [1]. This makes it possible to greatly reduce the effect of the
aforementioned constraints. Figure lc depicts a two-link filter structure
which theoretically permits production of a responoe curve of the type
sinc4 x, where x=?L(f - fp)T, sinc x=(sin x)/x. ~
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With cascade connection of links of the type shown in Figure la, the
overall dimensions of the device can be reduced somewhat by compactly
arranging the apodized VShP. A natural bevel is produced on each slab
which effectively reduces the level of signals reflected on the end face
(Figure lb) .
QI
b~ 2T
2T
el r ~z, r
- FTT
~R~
I.-~"~o +~a/4 -
Figure 1

- Spurious TP and OV signals
- Existing methods of reducing TP signals, e.g. by arranging a metallized
coating in the path of wave propagation resulting in a 180~ phase shift of
reflected waves with 1.6 dB powec lass [2J or reduction in TP level (which,
however, involves an increase in losses [3]), may be successfully usen for
the structure in Figure Ia.
For the structure in Figure lc, in [1] a method of TP signal compensation
is used with introduction of the appropriate shift between VShP in each
link:
NP - H, (P - t ) a�12k.
where H1, HP are distances between the transmitting and receiving VShP in
the first and pth links of the ."-ilter, respectively; p= 1,2 k; k is
the number of links in the fitter. This method does not introduce
additional power losses. '
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For narrow-band filters PAV, the family of spurious OV signals situated in
the direct proximity of the PP is the most hazardous; for example, for ST-
quartz the nearest quasitransversal mode has a frequency which is 4.5
percent higher than the mean frequency of the filter f~ [4]. The relative
� level of OV depends on the relationship of sound guide thickness t and
surface wave length lambda0: thus for t/lambda~ = 152/Z ?r, the relative
level of these signals is no greater than -30 dB. Furthermore, a family
of rapid quasitransversal and quasilongitudinal modes is excited with
frequencies of 1.61 fp and 1.82 fp with relatively high levels (about 7 and
10 dB, respectively, below the primary signal). These spurious ~V signals,
aside from the methods of suppression noted above, can be effectively

~ reduced by the filter's external matching circuits.
In [5] a method was considered for suppressing spurious OV signals by
tapering the lower surface of the sound guide with respect to the upper
one. Thus, in the example of a filter considered in [5) with a mean
frequency of about 200 MHz and bandpass at a level of -3 dB of around 5 MHz,
manufactured on a slab of ST-section quartz with a bevel of 3�, spurious OV
signals were suppressed by more than 30 dB as compared to their initial
level. Among the shortcomings of the method is the abrupt drop in
effectiveness for relatively low frequencies 10-50 MHz. A method is also
known for supressing spurious OV signals by construction of special two-
channel receiving and transmitting VShP and a delay coating on one of the
channels to support synphase reception of PAV and compensation of OV [6].
This method requires very precise parallelism between the surfaces of
the sound guide and high precision of treatment of the lower edge to
achieve effectiv~~ suppression of OV: this makes manufacture of sound
guides complicated. Furthermore, high identity of channels is required to
achieve total compensation, and this is also difficult to do for expanded
strutures. ~
In tests run on narrow-band filters of the structure shawn in Figure la,
the mean frequencys in the 40-90 MHz range, the level of spurious signals
of the most hazardous OV (with frequency of about 1.045 f~) was reduced
12-15 dB by putting notches on the bottom side of the sound guide. When the
sound guide is 2 millimeters thick, the depth and spacing of the notch
constituted 0.8 millimeter and 1 millimeter, respectively.
~ ~
~
Figure 2
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In combination with the absorptive coating applied to the notch which
simultaneously is used for attachment of the sound guide to the housing,
sugpression of these spurious OV signals was greater than 45 dB.
For a two-link (cascade) structure of the filter shown in Figure lb and lc,
spurious OV signals are no special problero, because with this design their
relative levels in decibels are added. But when links are arranged on one
sound guide to prevent OV t~ansition from one link to another (due to

� overreflection on the bottom or side edges) it is necessary to use one of
the met:iods considered. For example, in a two-link filter (Figure lc) made
from ST-section quartz slabs 5 millimete~s thick, with a mean frequency of
12 1~II~iz and bandpass of 62 kHz, application of the aforementioned notch on
the bottom edge and an absorp+tive c~ating on the lower and side edges
decouples the links by at least 45 dB.
Methods of adjusting mean filter frequency
Deviation of inean frequency of a narrow-band filter from the theoretical
level is due to: straggling of the rate of propagation of PAV Vp from
specimen to speciemn on the order of+ 3 x 10-4; change in the rate of
propagation V on the metallized surface of the VShP due to technological
scattering of the wiuth of the digxts and thickness of the coating; by the
relationshp of the rate of propagation V as a function of the angle of
misalignment of the piezocrystal and photomask during photolithography,
etc.
Current methods for adjustment of inean filter frequency [7,8] are based on
altering the rate of propagation of PAV in VShP by changiny the thickness
of the coating. This is achieved by etching an already existing coating or
by applying a new dielectric coating by the va~uum method of deposition.
- Use of this methods for adjustment of Lhe frequency of narrow-band filters
with expanded VShP causes some problems related to the constrained
technological possibilities of producing homogeneous and identically thick
coatings on large areas.
A simple and accurate method for adjustment of the mean frequency f~ of
narrow-band filters represented by a combination of a comb filter (GF) and
matched filter (SF) with double bandpass (Figure 2) was described in [9]�
_ The essence of adjustment consists in changing the frequency of the
"working" peak of the comb filter traveling inside a wider lobe of the SF
with doubled b;a;,~t,a3S. This is achieved by changing the delay between GF
sections by mea~s of eli~nination (application) of a section of inetalliza-
tion M. Therefore, in the case of narrow-band filters, the problem boils
down to approximatioa of the required response curve by selecting SF with
different bandpasses.
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As illustrated by the resulting function sinc`~ (x), let us consider the
process of synthesis of VShP ensuring fp adjustment of the entire filter.
1. The function H(f) = sinc4(x) is product of the response of four
identical SF: -
h ~ Mec (x). (1)
2. Let us represent expression (1) in the form of a product of GF and -
doubled bandpass response:
sin x sin a( f- J�) T sia x( f- j~) T/2
sinc (x) - X � a(!-I�)T A(
-1~ cosx(I-I�)T12. (2)
Expressi.on (2) coincides with the ~dulus of filter response as con-
structed in Figure 2 to within a constant ccefficient.
3. Let us define the unknown pulsed filter response from AChKh:
N (n - si~ (x).
For this purpose let us represent H(f) = Hl(f)H2(f), where Hl(f) and H2(f)
are products of AChKh of GF and SF, respectively.
Le~ us then use the known theorem on the product of two functions (11~:
~ �
S 8(S) I(l- s) dt S F(M) Q(��) �i�r d��' ( 3)
~
where F( ~,J ) and G(~) are spectra of two signals f(t) and g(t),
respectively.
In this case, for pulsed reponse corresponding to H1(f), F(W) = G(cJ) _
- cos T('(f - fp)T/2; for pulsed response corresponding to H2(f), F(~.a) = G(w)
- sin s (f-I�)Ti2
xc - r.~T~2 �
By alternately performing the geaaetric operation of convolution in
accordance with the left side of expression (3), for all four comb filter
structures, we find one apodized VShP. By carrying out convolution for two
equidistant structures, we find another apodized VShP. As a result,
together with the remaining two equidistant structures, we have four .
pulsed responses (four VShP) which We will combine into a two-link
structure in Figure 3, where VShP 1 corresponds to convolution of pulsed
responses of all four comb filters; VShP 2 corresponds to convolution of
two equidistant structures; VShP 3 and 4 ccrrespond to equidistant
d~ubled-bandpass SF structures; M are sections of inetallization, whose
removal (application) ensures adjustment of ineanfilter frequency; Ap is an
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arbitrary unit of length.
Table 1 shows the theoretical values (in decibels) of change in levels of
the first three side lobes of the function sinc4 (x) as a function of
frequency detu?~ing of the "working" peak of function H(f) and mean
frequency of the central lobe of function H2(f), in percents of the
bandpass at a level of -3 dB. The tabular data show that this method of
adjustment of the mean frequency in a very wide range of detuning has only
a sl~ ,