An efficient transient analysis algorithm for mildly nonlinear circuits

Abstract

This paper presents a new and efficient transient analysis method for mildly nonlinear circuits. The method is based on Volterra series representation of nonlinear circuits. It characterizes nonlinear circuits using a set of linear circuits called Volterra circuits. The input of the first-order Volterra circuit is identical to that of the nonlinear circuit, whereas that of higher order Volterra circuits is obtained from the response of lower order Volterra circuits. Fourier series interpolation is employed to approximate the input of higher order Volterra circuits. These circuits are analyzed using the sampled-data simulation of linear circuits for computational efficiency and the response of nonlinear circuits is obtained at equally spaced intervals of time. The accuracy of the method is controlled by the order of Volterra and interpolating Fourier series. Various sources contributing to the error are analyzed. The method has been implemented in a computer program. Numerical results on example circuits demonstrate that the accuracy of the method is comparable to that of linear multistep predictor-corrector algorithms, but with greatly improved speed.

Nonlinear Transient and Distortion Analysis via Frequency Domain Volterra Series

“…Examples are the linear centric method for nonlinear distortion analysis [3] and the sampled-data simulation method using Volterra functional series [13]. Volterra functional series can represent a weakly nonlinear function in terms of a number of linear functions called Volterra kernels.…”

An efficient algorithm for transient and distortion analysis of mildly nonlinear analog circuits

“…D is the position vector for input w(t) and i non (v(t)) represents the second and higher-order currents generated by the nonlinear devices. By substituting Volterra functional series of v(t) and i(t) into the equation, we will obtain a set of linear differential equations [4,6]:…”

“…Examples are linear centric method for nonlinear distortion analysis [5] and sampled-data simulation method using Volterra functional series [6]. Volterra functional series can represent a weakly nonlinear function in terms of a number of linear functions called Volterra kernels.…”

“…From circuit theory's perspective, it leads to a set of linear circuits, called Volterra circuits, whose responses can adequately approximate the response of the original nonlinear circuit. In [6], a sampled-data simulation method is used where the simulation errors are dependent on sampling intervals and sampling window sizes. As a result, the runtime is dependent on the accuracy requirements.…”

“…Our method is also based on the Volterra functional series. But instead of solving the Volterra circuits in time domain as done by traditional methods like SPICE3 or by the sampled-data method [6], we solve the Volterra circuits in frequency domain by using a graph-based symbolic analysis method [7,8]. Once frequency domain responses are obtained, transient responses can be obtained by fast numerical inverse Laplace transformation [1].…”