9
OSCILLATIONS
IN
NONLINEAR SAMPLEDDATA
SYSTEMS
9.0
INTRODUCTION
All the material of the preceding chapters has been concerned with systems
which process signals
continuously
around the loop.
This chapter takes
under consideration the describing function analysis of nonlinear systems
which at some point process
discrete samples
of signals.
It should not come
as a surprise that the analysis of nonlinear sampleddata systems is more
complicated, or at least more laborious, than the corresponding analysis of
nonlinear continuousdata systems.
The treatment in this chapter considers
just bias and singlesinusoid signals present at the input to the nonlinear part
of the system.
Even in the simplest case of a single sinusoid, the presence of
another periodic process in the systemthe
sampling operationgives
rise
to complications of the same kind as are encountered in the study of continu
ous systems with two sinusoidal components at the nonlinearity input.
These
complications are significant when the frequencies of the two periodic
processes are rationally related, and this is the case of first importance in the
study of nonlinear sampleddata systems.
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OSCILLATIONS IN NONLINEAR SAMPLEDDATA SYSTEMS
Sampleddata systems have come into practical importance for a variety
of reasons.
The earliest of these had primarily to do with economy in the
design and use of equipment.
Many problems in impedance matching or
powerlevel matching can be avoided if critical components are isolated
disconnectedmost
of the time, and the connection made only briefly at
periodic intervals to read out a sample of the signal.
The possibility of time
sharing one component among several systems also gives rise to a sampled
form of signal processing.
A major increase in interest in sampleddata
systems was caused by the development of radar systems during the 1940s.
Most radars provide information only in the form of periodic samples either
because of a periodic scanning process or because of pulsed transmission of
the microwave energy.
A more recent surge of interest has been due to the
increasing utilization of digital computers as controllers in feedback systems.
In some areas of application, especially aerospace guidance and control, the
use of discretedata processors is often a practical necessity. Thus many
system engineers find themselves concerned almost exclusively with the
design of sampleddata systems.
And as with continuous systems, these
systems may be designed with, or otherwise may suffer from, a number of
important nonlinear effects.
THE EFFECTS OF SAMPLING
In this chapter, as in most of the preceding material, attention is centered on
systems which can be reduced to singleloop configurations having a single
nonlinear part separated from the linear part.
The linear part in this case
may include any number of continuous linear elements and discrete, or
pulsed, linear elements.
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 Spring '04
 EricFeron
 Signal Processing, Nonlinear system, limit cycle, fundamental component, R SYSTEMS

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