Representation of arbitrary rational functions and polynomials by non-Foster resistor-capacitor-inductor networks
Year: 2026
Type: preprint
Abstract: The Bott-Duffin theorem shows that any arbitrary positive real rational function of finite order, representing a passive network, can be represented by a finite number of positive value resistors, capacitors and inductors. It is shown here that if the positivity restriction is lifted, any rational function or polynomial of any order may be represented by a network of (possibly negative) inductors, capacitors and resistors. When there are no repeated roots this is a sum of simple sub-circuits each of which contains no more than four components. When there are repeated roots a more complex circuit is required, here featuring iterated Wheatstone bridges of special form.
Source: arXiv (Cornell University)
Author: Mackay, Andrew
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211995259