Conversion matrix extraction by commercial CAD software for the stability design of autonomous circuits

Abstract

In this article a method to extract the conversion matrix of a nonlinear circuit by commercial CAD simulators is proposed. As an example, the conversion matrix, computed from a harmonic balance simulation, is used to control the stability of oscillators under large-signal conditions. This allows the suppression of possible spurious frequencies or the intentional generation of spurious signals (e.g. at subharmonic frequency). V C 2010Wiley Periodicals, Inc. Int J RF and Microwave CAE 20: 313-320, 2010.

Transient‐based conversion matrix approach for nonlinear stability analysis

“…If this is the case, the passive matching networks are modified or designed for stability. The conversion matrix can be obtained by means of a simple and straightforward procedure and is defined as an N ‐ports linear and frequency‐converting network, as in a mixer [7]. The ports refer to a physical port (gate or drain of the transistor for instance) and also to a sideband frequency.…”

“…Considering the same parameters at all the mixed frequencies, the conversion matrix can be obtained [6] that allows having a fully, time varying, linear description of the nonlinear characteristics of the analysed circuit. As stated in [7], the conversion matrix can be reduced to a two‐port network and the stability can be checked with traditional methods. In addition, tracing stability circles, suitable regions of the Smith Chart are identified that correspond to loads giving stable or unstable behaviour.…”

Systematic Synthesis and Design of Ultralow Threshold 2:1 Parametric Frequency Dividers

“…In contrast, the detection of sub-harmonic oscillations through conventional Harmonic-Balance (HB) algorithms shows severe limitations due to the absence of sub-harmonic frequencies among those used to find the steady-state solution of timevarying circuits. Consequently, alternative approaches were developed to detect the onset of sub-harmonic oscillations, in PFDs, through perturbation methods [12], [27] or through the iterative determination of the conversion matrix [28], [29] associated to any adopted variable reactance. Unfortunately, all the previously developed approaches require the adoption of a fine sweep of an input parameter, such as the excitation frequency (f pump ), the input voltage (V 1 shown in Fig.…”