NETWORK FUNCTIONS OF TIME-VARYING CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 33

Chapter 3
NETWORK FUNCTIONS OF
TIME-VARYING CIRCUITS
This chapter examines mathematical tools that are fundamentally im-
portant to the analysis of mixed-mode switching circuits. In Section
1, the time-varying network function of linear time-varying systems is
introduced and its usefulness in characterization of linear time-varying
systems is investigated. The aliasing transfer functions for characterizing
linear periodically time-varying systems are also introduced. We show
that although the input to a linear periodically time-varying systems is
a single tone, the response of the system has an infinite number of tones
located at the baseband and sideband frequencies. This characteristic of
linear periodically time-varying systems differs fundamentally from that
of linear time-invariant systems. In Section 2, Volterra functional series
for characterizing nonlinear time-invariant and time-varying systems is
introduced first. We then introduce multi-frequency time-varying net-
work functions and multi-frequency network functions to characterize
the behavior of nonlinear time-varying systems in both the time and
frequency domains. Section 3 derives the frequency response of non-
linear time-varying systems. Section 4 presents the frequency domain
response of a special class of nonlinear time-varying systems, nonlinear
periodically time-varying systems, to both single-tone inputs for har-
monic distortion and multi-tone inputs for intermodulation. The chap-
ter concludes in Section 5. A proof of the periodicity of the time-varying