A Comparison of Distortion Analyses Based on Volterra Series and Steady State Algorithm

Abstract

The most accurate way for computing the distortion coe-cients is to flnd a steady state period of the signal, and then to determine spectrum by means of fast Fourier transform. In the paper, main features of a reliable and e-cient algorithm for determining the steady state are described. However, even such accelerated method often needs a time-consuming numerical integration over many periods of the faster signal. For this reason, an e-cient method for a fast estimation of the main distortion coe-cients is also presented which does not contain frequent imperfections in the algorithm implementations. The algorithm uses higher-order Volterra series in a simple multistep algorithm which is compatible with a typical structure of the frequency do- main part of software tools. Both methods are compared by analyses of the main intermodulation products of a low-voltage low-power CMOS RF four-quadrant multiplier. A natural and accurate method for determining intermodulation products is to flnd a steady state period, and then to compute the spectrum of that signal by means of fast Fourier transform. This algorithm has been implemented into our original software tool C.I.A. (Circuit Interactive Analyzer) with a possibility of the automatic determination of the unknown period of autonomous circuits. Basic theory of the steady state analysis is described in (1), some improvements especially for automating the procedure for the autonomous circuits are deflned in (2). As the implemented method for a numerical integration (which is necessary for the steady state algorithm) is accurate and very ∞exible (it is based on an e-cient recurrent form of Newton interpolation polynomial (4,5)), computed intermodulation products are available even for higher orders. However, the numerical integration must still be performed over many periods of the faster signal and therefore the analysis is time-consuming. For this reason, another method for a fast estimation of the main interpolation products has also been implemented based on Volterra series. A brief introduction to using the Volterra series is shown in (6), a more comprehensive analysis can be found in (7). A disadvantage of many of the implementations of the Volterra series consists in a creation of a new (relatively large and isolated) block of the program. In this paper, a simple modiflcation of the method is deflned, which is compatible with the frequency domain part of the program | the algorithm is built into and uses a relatively large part of the AC analysis. 2. GENERAL DESCRIPTION OF THE STEADY STATE ALGORITHM