The convergence of Volterra series describing lowpass OTA-capacitor (OTA-C) filters

TLDR: In this article, the region of convergence of Volterra series describing continuous-time lowpass filters based on OTA-C integrators has been considered for low frequency signals.

Abstract: The region of convergence of Volterra series describing continuous-time lowpass filters based on OTA-C integrators has been considered. Firstly the filter containing one OTA-C integrator has been studied. In this case for low frequency signals the Volterra series is an ordinary power series with an appointed radius of convergence. In a more general case when the circuits containing more than one nonlinear element for continuous and bounded input signals, one can only determine sufficient conditions for which the Volterra series is convergent. In particular, simple conditions of convergence for lowpass second-order OTA-C filters are presented. Using known numerical methods for computing the solution of the nonlinear equation, the size of the region of convergence can be determined more exactly. The method developed here is applied to determine the amplitude of an input harmonic signal for typical values of parameters.