Frequency impulse response of selected FM discriminator

Carden, F. F.

Davis, G. L.

Kelly, L. R.

Osborne, W. P.

English

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This paper reports the results of an investi-
gation of the frequency impulse response of sever-
al FM discriminators. Experimental data are pre-
sented which display an impulse immunity of the
phase-lock loop, as a result of rejection of a
class of "fast" impulses. The results of a com-
puter study for the phase-lock loop verify this.
Experimental results for the pulse
-averaging dis-
criminator are also presented.
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INTRODUCTION
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A STUDY OF THE IMMUNITY OF FM DISCRIMINATORS
TO 2tr FREQUENCY IMPULSES
Frank F. Carden
Associate Professor
George L. Davis
Research Assistant
Lawrence R. Kelly
Research Assistant
William P. Osborne
Research Assistant
Communications Research Group
Electrical Engineering Department
New Mexico State University
Las Cruces, New Mexico
ABSTRACT
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unmodulated carrier of amplitude Q and additive
noise n(t). The noise phasor oscillates randomly
about point Q. The impulse event occurs when the
noise phasor assumes values such as to cause the
resulting envelope. R, to make a complete cycle
about the origin, causing 0 to increment by 2,t.
Figure 2 displays the phase 0 during the event,
and figure 3 shows the frequency modulation pro-
duced. The weight of the impulse is approximately
2w. Rice [l] has investigated this noise term for
the case of the ideal FM discriminator. Although
this noise is not strictly impulsive, the approxi-
mation is valid for filter bandwidths much less
than 1 /6, the event duration. The approximation
of the event by a pulse is used in the experimen-
tal and theoretical work contained in this paper.
If the filter bandwidths are small compared to
1/6, the noise power in the output is proportional
to the number of events per unit time (1J. There-
fore, an FM discriminator which rejects some of
the impulses will display an enhanced threshold
characteristic over the ideal detector.
An ideal discriminator (whose output is 0)
would pass all the impulses, and the filter output
per event would approach the impulse response of
the filter. Therefore, this detector offers no
rejection capabilities.
The possibility of threshold extension in FM
systems has created interest in the mechanism of
this extension. The realization of threshold ex-
tension, using specific detectors and/or detector
adjuncts, requires a knowledge of the low signal
to noise behavior of these detectors. That be-
havior is the concern of this paper. Rice [1) has
studied the threshold region for the ideal detec-
tor by considering the noise to be the superposi-
tion of "click" noise impulses and a gaussian
noise component. The impulsive noise has a spec-
trum that is relatively flat across the bandwidth
of the post-detection filter, and is proportional
to the average number of click events per second.
This impulsive noise may be reduced by a detector
which rejects a fraction of the incoming impulses,
or by a detector adjunct which senses the impulse
	 The experimental results for the pulse aver-
and takes action to prevent its passage through
	 aging detector are shown in figures 4 through 6.
the remainder of the system. The phase-lock loop
	 The square pulse represents the input impulse, and
operates in the first mode, rejecting a class of
	 is superposed on the response curve. ,Although the
"fast" impulses.
	
	 pulse amplitude in figure 6 is.502 'greater than in
.figure -5, maintaining an area of 2R, the output
has not changed significantly from figure 5 to
figure 6. The output is approaching the impulse
response of the filter used after the detector
21 B 1
The impulse event in FM systems is a random
phenomenon, which may be depicted as in figures
1, 2, and 3. Figure 1 is a phasor diagram of an
Im
2n
0
0
t
0
e
which for this case is
-apt
h(t) - ante	 t > o	 (1)
From these results, it is noted that the pulse-
averaging detector is operating as an ideal detec-
tor, followed by a low-pass filter with an h(t)
as in equation (1). All the input impulses are
passed.
Results for the phase -lock loop are shown in
figures 8 through 16. Figures 8 through 10 are
experimental data, and 11 through 16 are computer
solutions for the loop. Figures 14, 15, and 16
are phase error -time protraits corresponding to
figures 11, 12, and 13, respectively. The com-
puter data are hyperplane projections of the state
space solutions of the set
Y1 	0	 1	 Y1
Y2 	I 0
	 -2 &en COS Y1	Y2
0
,2 in Y1 + •0 W	 (2)
where Yl is the phase error, Y2 the frequency
error, and O i (t) the input phase.
The operation of the loop clearly shows its
non-linear properties as the pulse amplitude be-
comes larger (compared to wn). Figure 13 corre-
sponds to the experimental results of figure 10
for the came of no significant output. The para-
meters of interest in describing when the rejec-
tion takes place are um, & (loop parameters), and
Aw (the input pulse amplitude). Figure 13 depicts
the results when (Aw/wn) - 12.5, and & - .3. The
pulse is rejected and the phase error increments
by 2Tr, indicating that the loop has skipped a
cycle in the process. Figures 14 and 15 indicate
that, although phase lock has been broken, the
loop has not skipped a cycle and the pulse was not
rejected. For both of these cases (&Aj/wn) - 1.25
and £ - .3. Data presented in [2] indicate the
location of the first separatrix for a second
order phase-lock loop is
Aw
C " 2+ 32 f,
W
n	 Aw
That is, for a step size (normalized)	 > 2 +
32 ^, the loop will skip at least one • ele be-
fore relocking. Based on the data and 	 s re-
lationship, it appears that, if the input impulse
has an amplitude greater than 5(Aw c), the loop
will reject the impulse and skip a cycle during
the event.
SUMARY
The phase-lock exhibits a click noise im-
munity not displayed by the ideal, or the pulse-
averaging, FM discriminator to a class of "fast"
impulses. The pulse -averaging detector passes
the impulses as an ideal discriminator yielding
an output determined by the post -detection fil;.er
The phase-lock loop rejects(negligible response
to)those smiulses whose amplitude exceeds a mul-
tiple of i.a first separatrix location.
REFERENCES CITED
[1) Rice, S .O. "Noise in FM Receivers," Proc. Sym.
on Time Series Analysis, M. Rosenblatt,
Wiley, 1963.
(2) Carden, Lucky, Swinson. "The Quasi-Stationary
and Transient Behavior of Non-Linear Phase-
Lock Loops," SWIEEE, 1967 Record, Dallas.
This work was supported by NASA
grant /NGR-32-003-037
Figure 1. Impulse Event,
Phasor Diagram
Figure 2. Impulse Event
Phase vs Time
Figure 3. Impulse Event
Frequency Impulse
21 B 2
F _
le:
Detector. Experimental Results.
A	 --.
t^
Figure 7. Demodulated Output, Phase-lock Loop.
Experimental Results.
lo`
Figure S. Demodulated Output, Pulse Averaging
Detector. Experimental Results.
Figure S. Demodulated Output, Phase-lock-Loop.
Experimental Results.
Figure b. Demodulated Output, Pulse Averaging
Detector. Experimental Results.
Figure 9. Demodulated Output, Phase-lock Loop.
Experimental Results.
21 8 3
.44
0
Y1
0
N
r
1
.m
-.6
0
1
-1.
Tl 0
0
0
I v	 -.42 1 v
Figure 10. Demodulated Output, Phase -lock Loop.	 Figure 13. Phase Error vs Time, Phase-lock Loop.
Computer Simulation. 	 Computer Simulation.
1	 n	 1.01	 n
j v	 -•89 J v
Figure 11. Demodulated Output, Phase -lock Loop.	 Figure 14. Phase Error vs Time, Phase-lock Loop.
Computer Simulation.	 Computer Simulation.
N Y1
i
•O
-13
Figure 12. Demodulated output, Phase-lock Loop. 	
271
Computer Simulation. 	 Figure 15. Phase Error vs Time, Phase-lock Loop-
Computer Simulation.
2184


A study of the immunity of FM discriminators to 2 pi frequency impulses

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