.1 Spectral-domain Analysis

1 Nonlinear circuit design methods This chapter presents the most commonly used design techniques for analysing nonlinear circuits , in particular, transistor oscillators. There are several approaches to analyse and design nonlinear circuits, depending on their main specifications. This means an analysis both in the time domain to determine transient circuit behaviour and in the frequency domain to improve power and spectral performances when parasitic effects such as instability and spurious emission must be eliminated or minimized. Using the time-domain technique, it is relatively easy to describe a nonlinear circuit with differential equations, which can be solved analytically in explicit form for only a few simple cases. Under an assumption of slowly varying amplitude and phase, it is possible to obtain separate truncated first-order differential equations for the amplitude and phase of the oscillation process from the original second-order nonlinear differential equation. However, generally it is required to use numerical methods. The time-domain analysis is limited to its inability to operate with the circuit immittance (impedance or admittance) parameters as well as the fact that it can be practically applied only for circuits with lumped parameters or ideal transmission lines. The frequency-domain analysis is less ambiguous because a relatively complex circuit can often be reduced to one or more sets of immittances at each harmonic component. For example, using a quasilinear approach, the nonlinear circuit parameters averaged by fundamental component allow one to apply a linear circuit analysis. Advanced modern CAD simulators incorporate both time-domain and frequency-domain methods as well as optimization techniques to provide all necessary design cycles. This chapter also includes a brief introduction of simulator tools based on the Ansoft Serenade circuit simulator. In addition, some practical equations, such as the Taylor and Fourier series expansions, Bessel functions, trigonometric identities and the concept of the conduction angle, which simplify the circuit design procedure, are given. The best way to understand the oscillator electrical behaviour and the fastest way to calculate its basic electrical characteristics such as output power, efficiency, phase noise, or harmonic suppression, is to use a spectral-domain analysis. Generally, such an analysis is based on the determination of the output response of the nonlinear active device when the multiharmonic