Synthesis of nonlinear multiport resistors: a PWL approach

This paper presents a method for the approximate synthesis of nonlinear multiport resistors. According to some fundamental circuit theory results, the general problem of synthesizing a multiport resistor with given constitutive equations corresponds to that of the synthesis of nonlinear controlled sources. Following this idea, in this paper, we focus on the design of nonlinear controlled sources using a piecewise-linear (PWL) approach. The constitutive equations are first approximated by resorting to canonical expressions for continuous PWL functions, and then implemented using a set of elementary building blocks. The proposed method is applied to the synthesis of the nonlinear resistive part of an equivalent circuit of the Hodgkin-Huxley nerve membrane model.