Environmental Engineering Reference
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Newton-Raphson iterations for To reduce the cost
of computation, the piecewise harmonic balance method [133, 135] and
substitution methods [136] were proposed to accelerate the computation
by partitioning a nonlinear circuit into linear and nonlinear sub-circuits.
The linear sub-circuit can be solved efficiently in the frequency domain
while the nonlinear sub-circuit is solved using conventional harmonic
balance approach. The solutions of both circuits are matched at the
boundary of the two sub-circuits. Because the size of the nonlinear sub-
circuit is usually much smaller, a significant reduction in computation is
achieved.
As compared with harmonic balance methods that derive distortion
from solving determining equations numerically using Newton-Raphson
iterations, Volterra series based approaches [137, 138, 43] compute dis-
tortion in the frequency domain directly and are computationally effi-
cient. They have been applied for distortion analysis of nonlinear time-
invariant circuits and ideal switched capacitor networks [86, 139]. To
investigate the distortion of nonlinear switched current networks, non-
linear switched capacitor networks with parasitics and non-idealities, and
general switched nonlinear circuits, it becomes indispensable to include
other types of elements, such as resistors, inductors, controlled sources,
and current sources in both the modeling of the nonlinear elements of
these circuits and the analysis of these circuits.
This chapter is concerned with distortion analysis of multi-phase pe-
riodically switched nonlinear circuits in the frequency domain. The ap-
proach presented in the chapter is based upon time-varying Volterra
functional series, Schetzen's multi-linear theory [140], and time-varying
network functions and multi-frequency transfer functions of nonlinear
periodically time-varying systems introduced in Chapter 3. The chapter
is organized as follows: Section 1 reviews the basics of the frequency
domain characteristics of nonlinear circuits. Section 2 investigates the
representation of the network variables of periodically switched nonlinear
circuits using Volterra functional series. It also develops an algorithm for
frequency analysis of periodically switched nonlinear circuits. In Section
3, the harmonic distortion of periodically switched nonlinear circuits is
derived whereas the intermodulation distortion of these circuits is ob-
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