APPENDIX B A General‐Purpose Nonlinear Approach to the Computation of Sideband Phase Noise in Free‐Running Microwave and RF Oscillators

Abstract

The harmonic balance method, used in calculating phase noise in nonlinear circuits, has some magic to it for most of us. Here is a look at our magic-lady (Figure B-1). The amplifier shown in Figure B-2 was the world's first validation of the Compact Software Harmonic Balance Simulator, being able to correctly calculate the noise and gain of this 10 GHz amplifier. It uses measured Spice parameters. The success of the harmonic balance method was written up amongst others in Communications Quarterly, shown in Figure B-3, covering both amplifiers and oscillators.We want to look at the contribution of active devices like field effect transistors (FETs) and BIPs as well as a novel algorithm for the computation of near-carrier noise in free-running microwave oscillators by the nonlinear harmonic-balance (HB) technique [1].The application of the HB methodology to nonlinear noise analysis is very effective, because frequency-domain analysis is well suited for describing the mechanism of noise generation in nonlinear circuits. This topic has received the interest of several research teams; however, until the first edition of this book, a rigorous treatment of noise analysis in autonomous circuits had not appeared in the technical literature.The usual approach, relying on a simple noise model of the active device and the frequency-conversion analysis, is not sufficient to describe the complex physical behavior of a noisy oscillator. Instead, we apply the following approach:• A complete bias-dependent noise model for bipolar transistors and FETs is developed.• The frequency-conversion approach is reviewed, and its limitations are pointed out.• It is shown how the analysis procedure can be extended to include the case of autonomous circuits.• The capabilities of the proposed algorithm are demonstrated by means of some application examples.