Nonlinear Transient and Distortion Analysis via Frequency Domain Volterra Series

Abstract

This paper presents a novel approach for transient and distortion analyses for time-invariant and periodically time-varying mildly nonlinear analog circuits. Our method is based on a frequency domain Volterra series representation of nonlinear circuits. It computes the nonlinear responses using a nonlinear current method that recursively solves a series of linear Volterra circuits to obtain linear and higher-order responses of a nonlinear circuit. Unlike existing approaches, where Volterra circuits are solved mainly in the time domain, the new method solves the linear Volterra circuits directly in the frequency domain via an efficient graph-based technique, which can derive transfer functions for any large linear network efficiently. As a result, both frequency domain characteristics, like harmonic and intermodulation distortion, and time domain waveforms can be computed efficiently. The new algorithm takes advantage of identical Volterra circuits for second-and higherorder responses, which results in significant savings in driving the transfer functions. Experimental results for two circuits-a low-noise amplifier and a switching mixer-are obtained and compared with SPICE3 to validate the effectiveness of this method.

Perturbation-Based Fourier Series Analysis of Transistor Amplifier

“…Putting the input voltage v i (t) = A cos(ωt) = Ae jωt /2+Ae −jωt /2 in U and using (3) to (9), it is clear that u(t) has a Fourier series given by T and * denotes complex conjugate. Now from (9), the zeroth-order state vector is given by…”

“…The latter one is simulation-based. Although the Volterra series method [2,4,5,9] is a powerful method for analyzing nonlinear circuit dynamics in weakly nonlinear circuits, yet the application of this method requires rigorous calculations of the kernels for higher order series. In this paper, we present a perturbation-based Fourier series model for multi-variable state equations, arising from nonlinear circuits, by considering the nonlinear effect to be weak.…”

Determination of the analytical parametric relationship for output spectrum of Volterra systems based on its parametric characteristics

“…For clarity of illustration, consider a much simpler case of c 2 = 0, i.e., C 30 = c 1 (more complicated cases can be referred to [23]). When N = 21, it can be obtained from (14) that CE(Y ( jω)) = [1 c 1 c 2 1 c 3 1 · · · c 10 1 ], and consequently…”

Soft Fault Feature Extraction in Nonlinear Analog Circuit Fault Diagnosis

“…The adaptive Volterra filter is studied deeply [4,27], which is a type of intelligent Volterra model. The Volterra model is studied in the frequency domain in reference [31]. The nonlinear system is decomposed into parallel-cascade wiener systems [18].…”