Noise in Linear and Nonlinear Circuits

Before exploring the subject of nonlinear noise, it is necessary to examine some basics of nonlinear circuit analysis. We must examine methods for performing large-signal analyses of nonlinear circuits, as we must know the large-signal waveforms that affect noise sources that depend upon them. We must also develop methods for treating the noise, which is a small perturbation of the large signals. We examine two methods for large-signal analysis, harmonic-balance analysis and time-domain (or transient) analysis.
Central to the treatment of nonlinear noise is the concept of the conversion matrix. Conversion matrices describe the response of a circuit, pumped by a large excitation, to small voltage or current deviations. This is precisely the situation when small-signal noise exists in a mixer, frequency multiplier, or oscillator. The idea of a conversion matrix has existed for many years, having been especially useful in the theory of mixers. The purpose of this section is to provide only the necessary basics; a more complete treatment of these topics can be found elsewhere in the literature [6.1].
Harmonic-balance analysis is the dominant method for large-signal analysis of microwave circuits. Harmonic-balance analysis is a hybrid method, using elements of both time-domain and frequency-domain analysis. Pure time-domain methods, which predate harmonic balance, do not easily handle circuit elements that are described in the frequency domain. Unfortunately, many linear elements in microwave circuits must be described in the frequency domain, and harmonic balance handles these in a completely natural...