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I E E E TRANSACTIONS
ON
COMMUNIChTION
TECHNOLOGY
DECEMBER
S65
1967
Concise Papers
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Experimental Verification of a Model of the
Oscillating Limiter
ENRICO BOZZONI
AND
UMBERTO MENGALI
REFERENCE : Bozzoni, E., and Mengali, U. : EXPERIMENTAL
VERIFICATION OF A MODEL OF THE OSCILLATING LIMITER,' University of Pisa, Pisa,Italy. Rec'd 3/6/67; revised 5/23/67.
Paper 19TP67-968, approved by the IEEE Communication Theory
Committee for publication without oral presentation. IEEE TRANS.
ON COMMUNICATION TECHNOLOGY, 15-6, December 1967,
pp. 865-867.
ABSTRACT: Work done to verify the results of an analysis of the
oscillating limiter published previously is reported upon in this paper.
To this purpose experiments were made with an oscillating limiter,
the characteristics of which are given, to check the nonlinear
distortion produced on the baseband signals. The baseband equivalent circuit and nonlocking behavior of the oscillating limiter
were also tested. Finally, anetwork for compensating the linear
distortion produced in the message modulation by the oscillating
limiter is shown, as well as experimental results.
further stage is added to keep constant the level of the output of the
limiter.
Figure 2 shows the amplitude of the voltage at the output of the
bandpass filter (when the feedback loop is open) vs. the amplitude
of the voltage at the input
of the limiter.
Figure 3 illustrates the modulation suppressing properties of the
limiter. The ordinates are the ratio between the amplitude modulation index of the inputof the limiter and the ratioof rms value of the
envelope to thatof the carrier at the output
of the filter; the abscissa
is the modulation frequency.
The filter is a simple double tuned amplifier. The amplitude and
phase characteristics of the cascaded limiter and filter are given in
Figs. 4 and 5.
The center frequency is f~ = 30 MHz, the bandwidth a t - 3 dB
is 520 kHz, and themean group delayis 1.3 MS.
TRANSFER
FUNCTION
OF THE BASEBAND
EQUIVALENT
CIRCUITOF
THE OSCILLATING
LIMITER
With reference to the block diagram of Fig. 1, let
e t r ( t ) = Etr cos [wet
- $.(t)l
Efb COS [mol
- dt)]
and
KEYWORDS: Detection, Distortion, Experimental Data, Feedback, Filters, Frequency Modulation, Phase Modulation.
INTRODUCTION
In arecentpaper[']
the performance of the oscillating limiter
driven by exponentiallymodulated signals has been investigated.
This investigation led tothestudy
of anequation relating the
message modulation of the signal applied to the oscillating limiter
to that of the signal at its output. This equation
is a finite nonlinear differential and, assuch,inherently
shows that the action
of the oscillating limiter may give rise to nonlinear distortion in the
message modulation. The conditionsunder
which thisequation
may be substituted witha linear one have been determined.
Finally, the distortion affecting the message modulation at the
oscillating limiter's output, when the aforementioned conditions
are not fulfilled, has been given throngh graphs.
In the following, the results of an experimental verification of the
major conclusions reached in the preceding paper are reported and,
furthermore,anetworkcapable
of compensating the linear distortions will be shown.
efb(t) =
be the voltage a t the input and output of the oscillating limiter,
where $ ( t ) and ~ ( t are
) the instantaneous phase fluctuations due to
the modulation and wo is the angular frequency of oscillation of the
circuit when it is not driven by external signals.
Subject to the conditions that
1)limiter is ideal
2) amplitude response of filter is flat over band B occupied by
first spectral zone of signal a t output of limiter
3) filter's group delay7 is constant in B,
the characteristic eqostion of the baseband equivalent is[']
sin [ ~ ( t ) $(t
- T)] + K
sin [ ~ ( t ) ~ ( -t
T)]
=
0
(I)
in which K = Efb/Eif.
There arecnses in which (1) may be linearized in the form
d t ) - $(t -
7)
+ K[dO- d t -
T)] =
0.
(2)
When (2) holds, the effect of the oscillating limiter on the message
is taken into account through the transfer function
DESCRIPTION O F OSCILLATINGLIMITER
EMPLOYED
FORi\lEASUREMENTS
Figrlre 1 is a block diagram of the oscillating limiter. The limiter
itself is realized with three cascaded st,ages.
The first consist,s of an amplifier whose gain is automatically
cont,rolled witha time constant of the order of one second, and
which serves the purpose of maintaining the level needed for the
best, performance of t>hefollowing stage.
The latter is a modu1at)iou sxppressitg circuit in which the envelope of the voltage at the plateof a pentode is detected, amplified,
and fed to the suppressor of the same tube with the appropriate
phase.
Since this circuit gives rise to a variat,ion of the level of the carrier
at, it,s output when the depth of modulation at its input varies, a
1 T h e work reported in this paper was carried
o u t a s a p a r t of the research
by theConsiglioNazionale
programonsatellitecommunicationsestablished
delle Ricerche (Italian National Research Council).
Figure 6 shows the graphs of IW(0)I for some values of K together
with experimentally obtained values.
As may be seen, the agreement is excellent in the whole range of
frequencies in which the hypotheses 2) and 3) are satisfied.
NONLINEAR
DISTORTION
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When the conditions under which (1) is linearizable do not occur,
the oscillating limiter gives rise to non!inear distortion in the message modulation.
The amountof such distortion has been c a l ~ u l a t e d ~ ~ la function
as
of the frequency modulation index m, of the ratio N between the
period of the modulating sinusoid and the group delay T, and of the
value of K.
I n Figs. 7 and 8 some analytical results are compared with the
corresponding experimental ones.
866
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IEEE TRANSACTIONS ON COMMUNICATION TECHNOLOGY
DECEMBER
1967
Fig. 1 . Block diagram of csci1l:tting limiter.
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Fig. 2. Amplitude Etb of voltage a t outpui, of bandpass limiter vs.
amplitude Eif of voltage at input (no feedback).
Fig. 7.
K-3
Fig. 8.
Fig. 3.
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Continuous line gives calculated total distortion, dots experimental results.
el
511
Continuous line gives calculated total distortion, dots experimental results.
Modulation suppressing characteristics of bandpass limiter.
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Fig. 9.
Fig. 4.
Calculated waveform of dppldt for continuous wave excitation with frequency 39 KHz off center, K = 4.
Amplitude response of bandpass limit,er. Markers are 0.5
MHz apart.
Fig. 11).
Fig. 5 . Phase characteristic of bandpass limiter.
Oscillogram of dppldt obtainedin conditions of Fig. 9.
Time base 20 &3/div.
CONCISE PAPERS
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867
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The Quatrix-A Proposed Electrooptical Position or
Angle Sensor
BURTON J. ASKOWITH
REFERENCE : Askowith, B. J. : THE QUATRIX-A PROPOSED
ELECTROOPTICAL POSITION OR ANGLE SENSOR, Martin
Marietta Corp., Orlando, Fla. Recd. 3/22/67;revised
8/30/67.
Paper 19TP67-975, approved by theIEEEData
Communication
and Telegraph Systems Committeefor publication without oral
presentation. IEEE TRANS. ON COMMUNICATION TECHNOLOGY, 15-6, December 1967, pp. 867-868.
Fig. 11. Block diagram of compensating network.
Fig. 12. [ W ( n ) M
. ( n )1 obtainedexperimentally for some values of K .
For comparison, the corresponding gra,phs of IW(n)I are also drawn.
NONLOCKING BEHAVIOR
It has been
that when the exciting signa' e l l has aconstant
, oscillating limiter will or will not lock according
frequency w / ~ T the
to whether
Klsin (w -
oo)7\
5
I.
KEYWORDS: Coding, Data Display, Data Storage, DataTransmission Systems,Detection, Digital Signals, Optical Communica(4) tions, Telephone Systems, Television Systems.
Equation (I) has been used to determine the waveform of d q /
dt when the sign > applies in (4).
I n Fig. 9 is shown the waveform of dpp/dt pertaining to a case
studied in Boszoni and Mengali;['I Fig. 10 shows the oscillogram of
&/dt obtained experimentally.
COMPENSATION FOR LINE.411 DISTORTION
Under the conditions necessary for (3) to hold, the oscillating
limiter originates linear distortion in the message modulation. When
the waveform of the message must be preserved, it is therefore indispensable that compensation be supplied. This may be realized
most easily a t baseband by means of acircuithavingatransfer
function of the form
M ( n ) = C(1
+ K - Ke-jn')
(5)
in which C is an arbitrary real constant.
A system having a transfer function of the type
[1/(1
+ K ) ] (1 + K
- Ke-jnr)
(6)
is shown, as a block diagram, in Fig. 11.
The circuit originating the delay T has been realized with an allpass network built around a phase splitter.L31
Figure 12 provides the comparison of the calculated amplitude
characteristic of W ( 0 )with that of M ( 0 ) . W ( 0 ) obtained experimentally for some values of K .
It is worthwhile noticing that the value of M . W begins to depart
appreciably from unity a t frequencies near the half of the bandwidth B f of the bandpassfilter.
CONCLUSION
Excellent compliance of the experimentalresults
with those
obtained on the basis of the models advanced in Bozzoni and Mengalir'l is shown. Also shown is a circuit that compensates for the
linear distortionoriginatedin
the message modulation bythe
oscillating limiter.
REFERENCES
E. Rozzoni and U. Mengali "A general analysis of the performance of the
oscillatinglimiterwithnoiseless'signals,"
I E E E Trans.CommunicationTechnologg. vol. COM-14, pp:, 578-588 October 1966.
121 E. J. Raghdady,
Theory 'of feedbackaround the limiter," 1967 I R E
Nat'l Conu. Rec.. vol. 5, pt. 8. pp. 176-202.
Ial R. W . Calfee. "An active netxvyk equivalent to the
constant-resistance
lattice with delay circurt applications, I E E E Trans. Circuit Theory, vol. CT-10,
pp. 532-533, December 1963.
111
ABSTRACT: This technique, called puatriz (for quasi-matrix),
has potential application in numerous communication anddatahandling areas,sinceit
provides high-density matrix-photocell
capability at much lower cost. The method uses a few photographically-produced precision coding masks fitted over an equal number
( N ) of photocells. Thus, ten ( N ) typical high-detectivity photocells
and ten coding masks will produce 21° (2N) binary combinations,
behaving like a 32 by 32 matrix photodetector and using only 10
preamps. Twenty larger cells and preamps promise a million element
matrix. Limitations are discussed.
INTRODUCTION
The quatrix is a novel method of angle sensing devised by t,he
author. I t provides many of the advantages of a high-density photoelectric matrix detector withoutmany of the disadvantages, suchas
excessive multicell and preamp cost. Its use as a densely packed discrete angle detector has been demonstrated and proved to be basically feasible.
POTENTIAL
APPLICATIONS
AND CONCEPT
DESCRIPTION
Possible applications include: random-scan television, satellite
tracking, high-density switchboards, optical-communication monitoring in space (laser beams), visual presentation, character
reading,
infraredtracking,
analog-to-digital conversion, computerrandom
read-in, read-out, data storage and display techniques, and many
others.
The
quatrix
technique employs a high-quality
camera-type
objective of medium focal length (typically 3 inches or more) to
collect incident light from a source, distant or near, at any angle
within the field of view of an on-axis photocell set in the focal plane
behind the lens. This central on-axis cone is intercepted by several
partially aluminized mirrors or beam splitters (Fig. 1) arranged to
reflect or split,-off approximately equal-intensity convergent cones,
each incident onthe geometric center of a photocell of the same type
and configuration as the on-axis photocell. Thus, for a total of N
photocells, there are N - 1 beam splitters. The photosensors are
preferably, although notnecessarily, of the flatphotocathode variety,
and should be large enough in diamet,er to subtend a substantial
angular field of view (five or ten degrees or more). Flat photoconductors, photodiodes, and head-on photomultipliers are good
examples. By using two such systems side-by-side or stacked (as in
Fig. 2 ) , 2N photocells may be employed. Stacking permits use of
only three mirrors with 20 cells, as in Fig. 2.
Over each photocathode area is placed a thin, square matrix-like
mask (Fig. 3), each mask different for each photocell, and each
divided up into alternate lands and seas or opaque and transmissive
portions. Thus, one mask [Fig. 3(a), (l)] consists of one opaque
and one transmissive vertical column or broad slit; a second [Fig.
3(a), ( 2 ) ] consists of four columns, twoopaque and twotransmissive; a third [Fig. 3(a), (3)], of eight dternate columns. Similarly,
an equal number of masks [Fig. 3(b), (1)-(3)] consists of two, four,
eight, etc., alternate horizontal rows making up the square area of