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Journal ArticleDOI

Essential Nonlinearity of Phase-Sensitive Detector Characteristics

01 Jun 1969-IEEE Transactions on Instrumentation and Measurement (IEEE)-Vol. 18, Iss: 2, pp 81-87

Abstract: The effect of essential nonlinearity of phase-sensitive detector characteristics is studied and determined theoretically in detail, assuming that the input signal is a sine wave in the presence of additive narrow-band Gaussian noise. Minimum, maximum, and limiting values of nonlinearities of detector characteristics as functions of the input signal-to-noise ratio and the phase angle between the input signal and the reference wave are determined by means of computer-aided analysis. A set of curves that can be used to evaluate in detail the essential nonlinearities of detector performance and characteristics over a wide range of operating conditions and significant parameters is presented. Particular emphasis is placed on the determination of optimum detector operating conditions for minimum essential nonlinearities in wide-band Fourier-transform high-resolution nuclear magnetic-resonance and electron-spin-resonance spectrometers.
Topics: Phase detector characteristic (65%), Phase detector (62%), Detector (62%), Sine wave (55%), Amplitude modulation (52%)

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Lawrence Berkeley National Laboratory
Recent Work
Title
ESSENTIAL NONLINEARITY OF PHASE-SENSITIVE DETECTOR CHARACTERISTICS
Permalink
https://escholarship.org/uc/item/76v9f3w7
Author
Leskovar, Branko.
Publication Date
1968-08-01
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University of California

':
~
University of California
Ernest
O.
Radiation
.,
,
Lawrence
Laboratory
R.
UCRL-1830 1 Rev
.~.'
ESSENTIAL
N0NLINEARITY
OF
PHASE-SENSITIVE DETECTOR CHARACTERISTICS
....
I.'
~
,.,
"
..
Branko Leskovar
August 1968
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This document was prepared as an account
of
work sponsored
by
the United States
Government. While this document is believed
to
contain correct information, neither the
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of
the University of
California, nor any
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United States Government or any agency thereof, or the Regents
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the University
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the United States Government or any agency thereof or the Regents
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University
of
California.

For 6th Allerton Conference
on
Circuit
and
System Theory, Urbana, Illinois, Oct.
2--4,1968
( Proceedings)
UNIVERSITY
OF
CALIFORNIA
Lawrence Radiation Laboratory
Berkeley, California
AEC Contract No. W-7405-eng-48
UCRL-18301
Rev
Preprint
ESSENTIAL
NONLINEARITY
OF
PHASE-SENSITIVE DETECTOR CHARACTERISTICS
Branko Leskovar
August 1968

-1-
UCRL-18301
Rev
I
ESSENTIAL NONLINEARITY OF PHASE-SENSITIVE DETECTOR CHARACTERISTICS
BRANKO LESKOVAR
Lawrence Radiation Laboratory, University
of
California
Berkeley, California
ABSTRACT
The effect
of
essential nonlinearity
of
detector
characteristics
in
a phase-sensitive
detection.
system
is
studied and determined theoretically
in
detail over a wide dynamic range
of
optimum
and nonoptimllm operating conditions, assuming
that
the
input
signal
is
in
the
narrow-band Gauss-
ian noise. Minimum, maximum, and limiting values
of
nonlinearities
of
detector
characteristics
are determined by means
of
computer-aided analysis.
J.
INTRODUCTION
In
many cases
of
practical interest,
there
is
concern
about
the
nonlinear behavior
of
phase-
sensitive system characteristics over a wide dynamic range
of
operating conditions. For example,
in
wide-band Fourier-transform high resolution nuclear-magnetic-resonance and electron-spin-
resonance
spectrometry,
total system nonlinearity
is
of
prime importance. System nonlinearity
is
determined
by
the
essential nonlinearity
of
the
phase-sensitive
detector
used. Essential nonlineari-
ties result from
the
inherent
detector
behavior
in
detection arnplitude
or
phase
of
the
input
signal
in
the
presence
of
noise. They
do
not
involve nonlinearities resulting from
the
nonlinearity
of
the
characteristics
of
the
electronic
components
used.
I n previous work [1] essential non linearity analysis
of
detector
characteristics was presented
for
particular operating conditions. Based on this,
further
effort
has been
expanded
by
means
of
computer-aided analysis
to
include a very wide dynamic range
of
optimum
and
nonoptimum
operating conditions.
According
to
Fig. 1,
the
normalized form
of
the
phase-sensitive characteristics used lor deter-
mination
of
detector
nonlinearities as a function
of
the
input
signal-to-noise ratio x = V
slV
0'
and
the
reference wave-to-input noise ratio p.= V elV 0 is given by
~
(1r
)12
{ }
Vo
=
TId
"2
u[v(x)l-y[t(x)],
(1
)
INPUT
SIGNAL
Vs
AND
NOISE
NARROW
BAND
Vu
PHASE-SENSITIVE
Va
OUTPUT
FILTER
~
DETECTOR
OUTPUT
SIGNAL
MEASUREMENT
SYSTEM
-
Vc
REFERENCE
WAVE
PHASE
SHIFTER
XBL
687-1177
Fig. 1. Phase-sensitive detector.

Citations
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01 Apr 1973
TL;DR: A literature search was conducted in an effort to collect and compile as many references on the phase-locked loop as possible, and a comprehensive listing of approximately 800 references covering the past two decades of work reported throughout the world are presented.
Abstract: A literature search was conducted in an effort to collect and compile as many references on the phase-locked loop as possible. Although not all inclusive, a comprehensive listing of approximately 800 references covering the past two decades of work reported throughout the world are presented. The compilation is given in two parts: first by categories, and then alphabetically by authors.

77 citations


Journal ArticleDOI
TL;DR: A new generalized analysis is presented of operating characteristics of phase-sensitive detector circuits, assuming that the input signal and the reference wave are in the presence of independent, stationary, and additive Gaussian noise.
Abstract: A new generalized analysis is presented of operating characteristics of phase-sensitive detector circuits, assuming that the input signal and the reference wave are in the presence of independent, stationary, and additive Gaussian noise The generalized criteria are determined for the detector optimum operating conditions and for minimization of the detector characteristic essential nonlinearities by means of computer-aided analysis, using high-density discrete value calculations The results of the analysis are given in normalized form and can be directly applied to evaluate in detail the detector-circuit performance and characteristic essential nonlinearities over a wide dynamic range of operating conditions Furthermore, particular emphasis is laid on the determination of optimum detector-circuit operating conditions in contemporary instrumentation systems

4 citations


Journal ArticleDOI
TL;DR: Two generalized criteria for minimums and maximums of essential nonlinearity of a phase-sensitive detection system are presented.
Abstract: Two generalized criteria for minimums and maximums of essential nonlinearity of a phase-sensitive detection system are presented. Minimums and maximums are calculated and plotted by a digital computer over a wide dynamic range of operating conditions, assuming that the input signal is in the narrow-band Gaussian noise.

3 citations


Cites background or methods from "Essential Nonlinearity of Phase-Sen..."

  • ...Recent investigations [1], [2] have shown that in the instrumentation of experimental research the total nonlinearity of a phase-sensitive detection system is of prime importance....

    [...]

  • ...Q previous work [2] for a number of discrete values of the input signal-to-noise ratio X = V IV • and the reference wave-to-noise s a· ratio J....

    [...]

  • ...Based on reference [2], careful investigations show that a generalized criterion for NBMIN is given by...

    [...]

  • ...Va is the rms value of the input narrow-band noise e and Vc is the amplitude of the reference wave e Johnson (3) has pointed out a possibility of the existence of additional nonlinearity minimums and maximums which can be larger or smaller in value than those calculated in [2], due to the relatively complicated formulas expressing conditions for NBM1Nand NCMAX as well as to the NBMIN and NCMAX calculations made by a relatively small number of discrete values of Vs ' Yc t Va' and ~ (~is the phase angle between the input signal and the reference wave)....

    [...]

  • ...According to [2], normalized forms of the detector characteristics as a function of W, with lA....

    [...]


Journal ArticleDOI
01 Feb 1990
Abstract: The behaviour of a first-order phase-locked loop is critically examined under conditions where it is tracking a carrier corrupted by discontinuous (square-wave) amplitude modulation. The transient response of the system is first derived for the simple case of a PLL without time delay, and a comparison is made with a series of practical results obtained from a first-order loop. The agreement between the predicted response and that observed in practice is found to be extremely good. The theoretical behaviour of the loop is further analysed for the case of a system incorporating time delay. It is shown that such delay is detrimental to the tracking performance of the loop, when it is necessary to track a carrier modulated in the manner outlined above.

2 citations


References
More filters


Journal ArticleDOI
Abstract: The essential nonlinearity characteristics of a phase-sensitive detector are studied theoretically, assuming that the input signal is a sine wave in the presence of additive narrow-band Gaussian noise. Three interesting cases of the nonlinearity of the phase-sensitive detector characteristics are analyzed by means of the expression which has been derived for the output signal-to-input noise ratio as a function of the input signal-to-noise ratio, the reference wave-to-noise ratio, and the phase angle between the input signal and reference wave. In the first case, the detector nonlinearity NA as a function of the input signal-to-noise ratio is determined. In the second and third cases, the detector nonlinearities NB and NC as a function of the phase angle between the input signal and the reference wave are obtained. The results are presented as closed-form analytical expressions. Several interesting cases are plotted as a function of the significant parameters. Besides being important in themselves, the results are of a general interest because they may be used to estimate essential nonlinearities in some other more complicated cases.

4 citations