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lACCESSION NUMBERI
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GIIIIIIIID
GENERAI- DYNAMICS
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A2136-1 (REV. 6-61)
R«port No. 543-1-65-40
Date 25 June 1965
Moo of ?•(••
42
FM RBCnVER
DYNAMIC RESPONSE
Prepared
Approved by ^-. .■ 'J
J. D. RluMar, ^43-^
Elect. Group Ekig
(This work waa perfomed at the requeat of
the Centaur RF Syateaa Group Dept 963-6
and funded by VAP K200594)
543-1-65-40
TABLE OF CONTWrS
SinmABY ill
1 INTNODUCTIOM 1
2 RECEIVER DBSCRIPTIOIf 3
3 ANTICIPATED DYNAMIC RESPONSE 6
4 EMPIRICAL RESULTS 8
5 ANALYTICAL TECHNIQUE 10
6 ANALOG COIfi'UTER SIMULATION 18
7 COMPUTER SOLUTIONS 26
8 CONCLUSIONS 38
9 ACKNOWLEDGEMENTS 30
10 REFERENCES 40
APPENDIX I 41
11
543-1-65-40
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This report d«scrib«a a study into tho dyiuuaic reaponae produced
by an FM receiver employing an aaplitude aenaitive diaeriainator.
A aiaple, graphical explanation of the anticipated response ia pre-
sented. Eaplrical reaulta obtained in the evaluation of an FM
telmaetry receiver are included. Analytical techniquea leading to a
■atheaatical proof of receiver behavior are diacuaaed. The appli-
cation of the analog coaputer to the problem ia outlined and the
analog aimulation of the receiver ayatem deacribed. CompuAer aolu-
tiona for a number of conditions are included in the form of graphic
recordings. Finally, it ia concluded that dynamic reaponse auch as
that exhibited by the AVCO range safety receiver ia the natural be-
havior anticipated from such a receiver.
iii
543-1-65-40
1. INTRODUCTICT}
A n«w receiver GO/C P/N 55-01233, ■anufactured by AVCO, is being
incorporated into the Centaur range aafety ayatea. The perfomance
1
requireaenta of the receiver are deacribed by GD/C apecification.
Evaluation teats of the receiver at NASA test facilities and at GD/C
revealed a dynamic reaponae characteriatic that initially appeared un-
usual to test personnel. Bange personnel were disturbed to the point
where they were reluctant to allow the receiver to be flown. The
dynamic teat was perfomed by supplying an rf aignal Modulated by two
tonea to the receiver. The rt aignal carrier frequency was initially
aet well outside the paasband of the receiver (frequency lower than
receiver); then, with rf level held conatant, the carrier frequency waa
moved toward the receiver passband wntil a command actuation waa
obaerved; this frequency waa recorded. The carrier frequency movement
was then continued until the command deactivated and that frequency
recorded. This process was continued until the carrier frequency waa
well beyond the paaaband on the high frequency side. The rf level waa
then changed 10 db and another aweep made through the spectrum observing
again the carrier frequencies producing command "on-off" statea. nroa
the reaulting data a curve such as that of Figure 1 was generated. The
curve shows two midm lobes and a wider center lobe where the co mm e n d
ia activated. Narrow command deactivate aonea (approximately one-
half the peak deviation in width) aeparate the center lobe and aidelebea.
The center lobe ia narrower than the unmodulated reaponae (aee Figure 1)
by an amount approximately equal to the peak deviation.
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The study described in this report was initiated to gain a better
understanding of the dynaaic response characteristic of the ¥H coaiuand
receiver.
2. RECEIVER DESCRIPTION
A brief description of the receiver is included in this section for
the reader's convenience. More detailed descriptive information is
2
available in the receiver handbook.
A simplified block diagram of the receiver is shown in Figure 2. The
three center blocks of the diagram are of greatest interest for the
discussion here for it is their characteristics that establish the
dynamic response of the receiver.
The IF filter features a sharp selectivity with a low 60 db bandwidth
to 3 db bandwidth ratio. The nominal filter transfer function is
that of a 4 pole Chebishev filter having a bandwidth of about 240 kilo-
cycles and 2 db passband ripple. The actual filter is a 4 crystal lattice
network. This type of filter does not have a linear phase characteristic
(a requirement for distortionless FX) in the passband and the phase
response changes violently near the bandedges. Figure 3 is a graph
of the anticipated phase response for the filter.
Limiting is accomplished in three amplifier stages that precede the
discriminator. Each stage reaches its limiting level at a different
rf input level to the receiver thereby providing a large overall
dynamic limiting range.
Report No. 543-1-65-40
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The frequency discrlBinator is a convrational Foater-Seeley circuit.
The discriainator bandvidth (frequency separation between reaponse
peaka) ia auch vider than the IF bandpaas of the receiver to aaaure good
linearity over the region of intereat.
3. ANTICIPATED DYNAMIC RESPONSE
The dynaaic reaponae exhibited by the range safety receiver (or any FM
receiver «nploying a Foster-Seeley discriminator) can be explained by
the *'conposite" frequency discrimination characteristic of the receiver.
The Foster-Seeley discriminator's output amplitude ia propertional
to input voltage and the frequency deviation of the signal; for this
reason, the discriminator is always preceded by one or more limiter
atages. The selectivity of the receiver is established by the bandpasa
filter located ahead of the limiter stages. Typically the IF bandwidth
is narrower than the frequency discriminator characteriatic. The com-
posite frequency discrimination characteriatica of the receiver can
be described by a auperpoaition of the IF bandpass and fM discriminator
characteristics. Figure 4 illustrates such a compoaite frequsncy dis-
crimination characteriatic for a hypothetical receiver to aid dia-
cussion. From Figure 4 it may be noted that the compoaite discriminator
output decreamas when the input frequency ia sufficiently offset from
band center becauae the IF bandpasa filter attenuation drops the signal
below limiting level. Again, directly from Figure 4, It is seen that
the composite discriminator characteristic haa alopea of oppoaite
algn at the bandedgea compared to the band center alope. The reault
ia that there are pointa near the composite discriminator response
Report No. 543-l>65-40
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543-1-65-40
peaks iriiere the dwaodulated output signal ia cancelled and any resultant
is a saall aaount of second haraonic. Iliere are two positions, one
on each side of the passband beyond the cancellation points, where the
discriainator output signal again increases but is of opposite sign
due to operating on the outside slopes of the coaposite discriainator
characteristic. A frequency sweep of a nodulated signal, therefore,
produces a signal such as illustrated in the lower portion of Figure 4.
(See also coaputer solutions in Section 7.) The center lobe is typi-
cally narrower than the width of the unaodulated passband because of
the frequency deviation and the difference in the laagnitude of the
inter and outer discriainator slope aagnitudes.
Pender & Mcllwan briefly discuss the dynaaic response of FM receivers.
4. EMPIRICAL iUSSOLTS
A Neas-Clarke R1037-A receiver was used to obtain data on FM receiver
dynaaic response. This receiver was used for the test to deaonstrate
that the dynaaic response exhibited by the AVCO receiver is not
peculiar to that receiver but typical of FM receivers eaploying the
Foster-Seeley type discriainator. Additionally, it was convenient
to use the Naas-Clarke receiver because of the availability of the
liaited IF, video and DC FM discriainator outputs at accessible
terainals.
Photographs of Figure S show null outputs as they occurred at the
points of slope reversal.
8
543-1-65-40
Low Frequency Null 214.668 MC
/«VVVVVVVVVVVVVVV
Receiver Video Output
)0000<KH>mK)0<KHM
Receiver Limiter Output
High Frequency Null 215.429 >JC
/^^V ^<Af^WV^ ? ^i |y!^ A >' M^^
Receiver Video Output
^piH^H MVHVH ><HH.><_^.
Receiver Limiter Output
Test Conditions (both photos)
Receiver: Nems-Clarke R1037-A S/N 355
Modulation:
RF Level:
(300 KC IF Bandwidth)
7.5 KC Rate 30 KC Peak
3000 volts
Figure 5.
Null Points Measured on the Nens-
Clarke Telemetry Receiver
9
543-1-65-40
The aMplituds ■odulation triiich caacals th* FM ia elaarly •rid«nt in
the liaited IF output (lower trace on the photos). The AM indicates
operation below the liniting level and on the IF filter akirt.
Figure 6 illustrates the measured composite discriainator character-
istic, while. Figure 7 ahows noraal operation at band center.
5. ANALYTICAL TBCHNIQUE
A Batheaatical analysis was undertaken in an attempt to improve the
understanding of the dynamic response characteristics, for additional
verification of experimental results, snd to determine if any other
factors (such as the Chebishev filter phase characteristic) played
a significant role in the observed response.
The classical approach for the solution of a problem of this type
is examined. Wiile the actual mathematical solution of this
problem is quite formidable, the approach is simple and straight-
forward. A reaaonable simplification of the receiver system con-
siders only the IF filter, frequency discriminator and output tone
filtera (see Figure 8). The input to this system is easily described
as a time function.
{(t) = A ^-- (^c/i- -^^-^ ^' + -^ ^^ ^^^)
(1)
10
543-1-65-40
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Normal operation at band center 214.970 MC
Upper Trace: Receiver Video output
Lower Trace: Receiver Limiter output
Test Condition:
Receiver: Nems-Clarke R 1037-A S/N 355
(300 KC IF Bandwidth)
Modulation: 7,5 KC rate, 30 KC peak deviation
RF Level: 3000 volts
Figure 7. Normal Operation
12
543-1-65-40
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543-1-66-40
By Beans of th« Fourier integral the function (f (t) ) is transfonaed
to the frequency doaain.
(2)
If the IF filter frequency transfer function is H,(>;6j), thett the
filter output is
6, Cjto) = F,(^ui) l4,(jui) (3)
G,(j(a) is transfomed te the tiae donain by the inTorae l^urier
transfora
'^^^^'- IW <^'0'^)<^"'^^du)
(4)
Exaaining the arguaent of the function g(t) the phaae 0(t) aay be
deduced. The output ^(t) of an ideal discriainater is siaply the
first deriratire of ^(t) with respect to tiae
eu) = K -^ (5)
The discriainater output is then convelTod with the tiae response
of the tone filters to obtain the systea output.
It was iaaediately apparent that the aagnitude of the preblea was
such that a aanual solution was not eeonoaically feasible. This
14
543.1.«S>40
wac tru* mr9n for the aiaplor ea*« of a ■iaglo ■odulating tono.
Coaputor support, thoreforo, wmm eloarly la ordor if mi aiutlxtieal
aolutlon vaa to bo obtainod with a roaaonablo oxponditvro of tiao
and ■onoy.
First considoration was glvoa to tho application of tho digital
coaputor for solution of this probloa. "Cannod** prograas aro arail-
ablo that accopt tho Laplace fom of tho filtor transfer function.
Getting tho input drive function (see equation (1)) into a for*
appropriate for use as input data to the filter prograa presented a
probloB. It was noeossary to expfuid the function into its coaponont
parts I this would have entailed a now prograa. The procedure is
to expand the function of equation (1) by the sua of aagl** then
apply the following idMitities:
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Tho series are truaeatod arbitrarily at a point that includes all
significant coapononta. Because this would have required a now
prograa and because its general solution was required only once, it
appeared feasible to aceoaplish this by hand. This was actually
aoeoaplished and results are shon» in Figure 9 iriiere they aro evaluated
for tones 1 and S. The discriainator funetion appeared as another
problea for the digital eoaputer. It was finally dooidod that a rea-
sonable approaeh would be one that utilised the eoaputor to detect
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543-1-65-40
pesitlT* B*ro crossing of th« fuBctioni tho instantanoous froquosey
ia thoB doflnod as tho roeiproeal of tho poriod botwooi poaitlTo
xoro croaaings. Tho inataataaooua doTiation would thoa bo tho
differenco botvoon the instantanooua froquoncy and tho earrlor fro-
quoncy. If loaa than an idoal diaeriainator function voro doairod
(a roquiroaont for tho probloa of intoroat) tho liHitlag function
■uat alao bo lncludod| thia appoarod rolatiroly oaay to aeeoapliah.
SoBo rough oatinations of tho required conputor tiao for a solution
indicated the digital approach night bo exponaive depending upon
the nunber of ateady-atato aolutiona required.
Conaidoration waa then given to the application of tho analog ooaputor*
Bxaaination of the roquiroaenta for the syatea ainulation on tho analog
computer revealed no unauraountable problona. The aolution of
CO— iinication probleaa by use of an analog coaputor ia not nov, auch
4,5
techniquea being described aa early aa 1961, It appoarod that use of
the analog coaputor for thia probloa would be loaa exponaive and aoro
quickly accoapliahod than by digital, and it offered additional inaight
in underatanding tho ayatea because of "live" graphical output and on-
line adjuatability. This was the coaputor approach finally utilisodf
the ainulation is described in tho following section and tho coaputor
aolutiona are diacuaaed in Section 7.
17
S43-l-eS.>40
6. AIIALDQ OOWnJTlR »IIIUL4TI0W
This ■•ction d««erlb«s (1) th« ■•tkod of ••lutioB by analog eon^utor,
(2) technical dotaila of aoa« of th« circuits •■ployed, and (3) inatrue-
tions for calibration which will aaaiat poraonnel at another laboratory
in putting thia aiaulation on their coaputer quickly. Pigvre 10
ia a coaplete block diagram of the ayatea, uaing conventional analog
notation. Dotted linea indicate connect iona for ealibration pnrpoaea,
and aolid linea indicate the basic WH ayatea aiaulation.
Initial conaidorationa indicated a frequency acaling factor of 10 or
10~ for analog alaulation of thia FN receiver. Since frequency scaling
by 10~ would require leas coqniter solution tiae (a factor of 10)
this approach waa invent igated first.
Unsuccessful Att— pts to Dse Scaling of lO" i A 107 CPS constant
aaplitude oscillator capable of boing firequsncy Modulated was iqr>tkssis»d
6
first. This Miplitude stabilissd oscillator was later na at 1/IOtt the
frequency and proved to be quite atable at either frequsnay. A second
order ayatea in the fora of a three aaplifier loop waa tried for sian-
lating each aet of pelea in a Chebiahev filter, but the Q adjustaents
were unatable for large values.
The next atteapt uaed a twin "T" circuit as a quadratic filter (see
Figure ii) The general range of deaired frequMiciea were eaaily sbtainad
and Q*a ia excess of the aaxiawa Q desired were attainable.
18
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Pltur* 11. Twin "T** Piltsr
20
543-1-65-40
A test was conducted by frequency modulating the 107 cps carrier with a
single tone geneiator and then denodulating the filtering to re-
obtain the tone. Except for a DC drift out of the demodulator the re-
sults were very encouraging.
A four pole Chebishev filter was synthesized using twin "T** networks.
The FU carrier was driven with a sweep generator and the output of the
filter was amplitude detected. The sweep generator drove the x axis
of an x-y recorder and the amplitude detector drove the y axis. The
output from this filter circuit was never satisfactory . The following
problems caused the termination of this approach: (1) Q and frequency
measurements were made with considerable difficulty. (2) Q and fo required
too much time to adjust because of interaction between these two para-
meters. (3) Frequency pulling or shift in frequency was noted when
the individual poles of the filter were connected in series. (4) Lack
of sufficient isolation between filter stages was detected. (5) Major
factor which caused this line of research to be abandoned was the
apparent non-linearity which was detected with a change in gain; the
cause was undetermined, but the d v/dt limitation of the operational
amplifier was suspected.
Success in Using Scaling of lo" ; The next alternative required fre-
—6
quency scaling by 10~ and subsequent chemges in the existing circuits.
Two computing boarus were used because of the number of amplifiers required
and the availability of integrators with different RC time constants.
Amplifiers in station two had RC time constants of 0.1 sec auad station
three had one second time constants. With the exception of the carrier
21
543-1-65-40
oscillator all 10 cycle circuits were on station two and all tone
circuits were on station three. The exact location may be foimd by
noting the station number posted with the anpllfier nui^er on the main
schematic in Figure 10.
The peak follower in Figure 10 serves two purposes: 1) calibration of
the Q of the filter sections, and 2) peak reading of the filter output
to the X, y plotter. It is not used to simulate any function of the
FM receiver. The detailed operation of this circuit is given presently.
Integrator 19-2 is the time generator.
This time generator should be checked with the EPUT Meter (combination
Events per unit time and time interval meter EPUT and TIM) . This will
eliminate the possibility uf an incorrect RC time constant from being
perpetuated into other measurements.
The Qis of the individual filters which makes up the four pole filter
are adjusted by using a peak follower, a comparator, and a time generator.
The technique is to excite the filter and measure the rate of decay of
the sinusoid. The quantity actually measured is the time required for
the exponential envelope to decay to one half of its initial value.
This time and the circuit Q are related by the easily derived expression
In the circuit the damping is tweeked until the t corresponds to the
desired Q. (At the high Q values employed in these circuits the fre-
quency '*fi' is essentially independent of Q.)
22
543-1-65-40
Output of aap 3 1-2 is the initial condition for the pole being adjusted
and also the output of the peak follower. The comparator has 1/2 of the
initial condition as a bias. When the computer is set to "operate",
the peak follower tracks the output of the filter being adjusted to the
half voltage point where the computer is switched to hold. The output
of the time generator will agree with the computed time when the proper Q
has been set. An initial setting of the pot may be computed from the
relationship Mo/<j = the pot setting. At the same time the Q is being
tweeked in, the Mo pots may also receive final tweeking.
The TIM is connected to the output of the filter being tested for Q.
The initial condition behaves as if it were an impulse function causing
the filter to ring at the natural frequency. Both frequency and Q
may be adjusted simultaneously.
The peak follower is an instrumentation circuit irtilch is used for cali-
bration and envelope detection.
The peak follower is a sample hold circuit that samples the f(t) term
when it is at a maximum. The circuit is included with the analog com-
puter F^i receiver diagram (dashed enclosure). The input labeled "j"
is connected to the filter point whose value is k(f(t))/S. The 1/s
shifts the phase of f(t) by 90» so that when k(f(t)/s is equal to zero,
f(t) is a positive or negative extreme. Pot 40 is used to bias the in-
put to amplifier 9. Amplifier 9 has a cathode follower limiter around it
so that its output can only be negative. If f(t) is negative then
the input labeled "K" is negative and the output of amplifier 9 is
23
543-1-65-40
blocked or zero. If f(t) is positive and k(f(t))/s is equal to zero
the output of 9 will generate a pulse. The electronic switch between
amplifiers 14 and 15 will close for the duration of the pulse.
Integrator 16 and aaplifiers 14 and 15 have a R.C. time constant
of 1/2 millisecond, but this value can be made smaller if desired. From
the previous text it has been implied that the peak follower is polarity
sensitive. This may be eliminated by appropriate use of absolute
value circuits.
Pot 47 on station three depends on relationship of voltage to
frequency. The servo pot varies the RC time constant of the amplifier
by changing the input resistance. A way to detezmine this pot value
requires the multiplier to be set with fixed voltages and the correspond-
ing frequencies. The ratio of the change in voltage to the change in
frequency can then be normalized to give .01 cycles per volt of
modulation. This normalizing coefficient is the setting for pot 47 in
Figure 10,
The following Table may be used to change the Chebishev filter into a
linear phase filter.
Pots
2 - .6663 30 - .6738
4 - .6663 31 - .6738
6 - .0907 32 - .1450
27 - .6701 8 - .6776
28 - .6701 10 - .6776
29 - .1459 12 - .0997
The rest of the pot settings should remain the same.
24
543-1-65-40
Pots 42, 43, 44, and 45 were changed an equal amount to increase or
decrease the gain of the filter. The change in pot value is approxi-
Biately equal to the fourth root of the change in gain. A linear change
in gain at the output can be oade by pot 38.
25
543-1-65-40
7. COMPUTER SOLUTIONS
The analog coaputer sinulation of the range safety receiver system
was accoaplished by scaling frequency by a factor of lO" . The
receiver IF freqaency is 10.7 negacycles and the computer simulated
IF frequency 10,7 cycles.
Prior to making the actual computer "runs" it was necessary to
verify that the computer did indeed include the proper transfer
functions and that the accuracy of simulation was adequate. The
static linearity of the modulator was measured first with the result
that the ntnyjimii deviation from a straight line through the end points
was 2 parts out of 464. The IF filter characteristics were then
measured by driving the modulator with a ramp (at a very low sweep
rate) and using the peak follower and an X-Y plotter to record the
response. Figures 10 and 13 illustrate the results for the Chebishev
and linear phase filters respectively. The mathematical description
of the filter transfer functions are:
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Chebishev:
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J67.89
^t =
-.0788
-
J67.89
Linear Phase;
P, s -.4984 t- J66.63
■p, s -.4984 - J66.63
Pi = -.7296 + J67.01
ft > -.7296 - J67.01
8 = -.7296 + J67.38
fi = -.7296 - J67.38
5 s -.4984 + J67.76
4 ■ -.4984 - J67.76
26
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Ex
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S43-1.6S-40
The frequency discriainator characteristic was detemined also by
a sweep of the aodulator over the frequency range of interest.
Figure 14 is an X-Y slot of the discriainator voltage vessus fre-
quency characteristic.
The first case evaluated on the coaputer was a single tone case.
This case is equivalent to the unsealed condition where the signal
is Modulated by a 7.5 kilocycle sine wave producing a peak deviation
of 30 kilocycles. A raap voltage, suMied with the aodulation, drove
the Modulator slowly over the frequency range of interest (each run
required approxiMately two hours). The sweep range was chosen such
that the liMiter preceding the discriMinator dropped below liMiting
level at both ends of the sweep. Figure 15 is a recording of run
results. The output froM the IF filters (Chebishev transfer function)
is recorded as are the outputs of the liMiter, discriminator, ramp
generator, tone filter. Modulator, and tone oscillator. The modulator
output was included in the recording for the purpose of showing that
it was free of aMplitude modulation. The tone oscillator was included
to provide a phase reference for coMparing tone filter output. A fairly
high level signal was provided for this run (liMiter input was 30
volts peak-to-peak at bandcenter) and limiting level was reached
quickly. It may be noted from Figure 15 that the tone filter output
is large and approxiMately 180* out of phase with the tone oscillator
output when operation is below the liMiter level. When the
carrier frequency is moved into the pass band where liMiting is con-
tinuous, the tone filter output is in phase with the tone
oscillator. Null conditions occurred on
29
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FIGU»^ 15 aXJCtTS 30aTI<W TOR 3IIKLE T0N2 CASE
31
-^1-6
543-1-65-40
the skirts of the passband and are measured at frequencies of
10.58 cps and 10.86 cps for this ceise. For proper evaluation one
mist consider the storage associated with the tone filters; for
the circuit Q*s used, a storage of two cycles is reasonable. Correct-
ing for tone filter storage the null points are more accurately
located at 10.565 cps and 10.835 cps. Another interesting observa-
tion one can make is to note the large signal distortion present
in the discriminator output when operating near the bandedges of the
Chebishev IF filter but at a point where limiting is continuous.
This distortion is attributed to the non-linear phase characteristic
of the filter.
Data of Figure 16 is similar in all respects to the data of Figure
except that the IF filter output (limiter ini<ut) is reduced 10 db.
The effect is that the frequency range in which limiting is con-
tinuous is narrowed and the null points are closer together.
The case of two modulating tones was rtm next. This condition is
equivalent in the unsealed situation to sinusoidal modulating tones
of 7.5 kilocycles and 12.14 kilocycles each producing 30 kilocycles
of deviation. Figure 17 includes data for a high limiter input
level while Figure 18 data has a limiter input 10 db lower. The
modulator output was not included in the run shown in Figure 17
because of the lack of recorder capacity. The higher frequency
tone oscillator output was recorded to allow phase comparisons. To
demonstrate that the modulator was free of amplitude modulations
under two tone modulation , it is again recorded in Figure 18 data
32
10.9
CABRIUi FK£wUENCT
10.3
TC.VK riLTER OLTPIT
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^<o
543-1-65-40
and the high frequency tone oscillator output omitted. Basic data
characteristics are the sane as those for the single tone case.
The tone filter outputs are out of phase with the tone oscillator
outputs when operation is below limiting level and in phase in
the center portion of the band where limiting is continuous. The
apparent distortion in the tone filter outputs is the result of cross
talk between channels and is due to the low Q*s of the tone band pass
filters which limited separation. These tone filter Q's were chosen
as a compromise to provide reasonable separation yet allow a computer
run in the two hour time period.
A single run was made using the linear phase IF filter characteristic.
This data is included in Figure 19 . The two tone condition was
utilized for this run and filter output was at low level. The
purpose of using the linear phase characteristic was to demonstrate
that the dynamic response observed was not peculiar to the Chebishev
filter. It is readily observed that the tone filter outputs experience
the same phase reversals observed with the Chebishev and null points
are clearly evident. The spacing between null points has increased
slightly because the linear phase filter's skirt slope is nut as
steep immediately beyond the pass band. Comparison of the discriminator
output using the Chebishev filter indicates that distortion is not
significant near the bandedges with the linear phase filter.
36
SSfS
1 I? FXL3ER CUTPCT (LD!E*H PSASE rLUEB)
" " 5V/0 r;"Z."3
LIKETEB tVTJ"JT
IV/CX
"1 EISCPIKBATCB CUTR-
■ ' iv/a
10.3
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- - /
^^
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TC.TS OSCILLATCP OUTFIT '"
V.SZ OSCILLATOR OtnVT ^ '
(LCVi rRZliUHiCI) 1
f
■:s3 riLTER oLTPirr
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FIJl-RT 19 CCKPimS SCLLTIOit PCS T-0 TOHE CASE (LCeAS KASS Tlir
\/^V
3-7-6
S43-1-65-40
CONCLUSIONS
As a result of the arguaents and coaputer results in this report,
the following conclusions are reached.
(1) The dynaaic response characteristic exhibited by the AVCO
range safety receiver is the natural response anticipated
from a receiver utilizing a Foster-Seeley discriminator.
(2) The IF filter phase characteristics do not have any significant
influence in the generation of the dynanic response observed.
(3) The Chebishev filter introduces significant distortion into
the m system when signal frequency is near the filter band-
edges.
38
543-1-65-40
ACKNOWLEDGEMEMTS
Th« contribution* of Mr. George Coopor, Mr. John Rhavy and Dr. Allan
Wilson are acknowledged. Mr. George Cooper set up the analog
coaputer simtlation and prepared the Material of Section 6 of this
report. Mr. John Rhaay contributed the explanation for the natural
behavior of FM receivers (with amplitude sensitive discrininators)
as described in Section 3. Dr. Allan Wilson assisted in resolving
siaulation problems and developed the "proof" of FX simulation as
included in the Appendix.
39
543-1-6S-40
REFiamiCES
1. Coanand R«c«iver Dacoder, Vehiclebome Specification o5-01233-l
2. 80045 XRW 10/964 Uandbaok of Operating and Maintenance Inatructiona
Comnand Receiver Decoder, Vehiclebome Part No. 185010-1 thru -ISl
AVCX) Corp. Electronica Division, Cincinnati, Ohio 45241 10 Septea-
ber 1964
3. Electrical Engineera Handbook Fourth Edition P8-29 Pender and
Mcllwan
4. Proceedings of the Western Joint Computer Conference May 9-11,1961
p. 490
5. Missiles and Space December 1961 by John M. Lambert "G£*s Electronic
System Evaluator."
6. Simulation January 1964, p. 31
40
543-l-6S>40
APPiMDIX I
Siwilatlon of Ffquancy Modulation by Vb9 of an Analog Cowptttcr
(Dr. A. N. Wilson)
lU±(i.)\ u-
± d f2L)
Asstuting carrier frequency £0, , modulation frequency p, and the desired
deviation ^^cO, the necessary instantaneous frequency of the resonant
elenent is AJ = zOo -t- ^4>co8 pt.
The analog loop gain above is cJ (aaplifier gains are assured to
be unity, for simplicity). The instantaneous oscillator frequency is
thus /Z?-=oJ , which may be identified by analogy with i//Cc of the
conventional tank circuit used in a frequency modulator. This analogy
should constitute sufficient "proof" of proper simulation of FM on the
analog computer.
An alternate "proof" consists in showing X = A sin (^oT-* ~^Sin ft )
satisfies the differential equation solved by the analog loop.
: A
^ C6l>o -*- Aa3 Cos pif-
41
543-1-65-40
Sine* -^ <■<-{ and --j-^i£.c\ , th« a«cond tern may be neglected, Thua
4f (-S) - Acc,(cAA^^s.>.e^)
Siailarly we can ahow
^[zT^fel] a -As.nUi--, ^5,nH)=-X Cvf").
The approximation employed here is exactly the aame as used in showing
a conventional modulator produces FH as defined above. One makes a
binomial expansion approxiaation on /c - \jC -t^C ,
(See Seely "Electron Tube Circuits" page 377, or Tempn, or numerous
other references.)
42
eJyifco ^55083
(\
GENERAL. DYIMAIVIK
GIIIIIIIID
CIOIMVAIR