Optimal frequency sweep method in multi-rate circuit simulation

TL;DR

This paper introduces an optimal frequency sweep method for multi-rate circuit simulation, effectively decoupling different time scales and improving efficiency in simulating RF circuits with complex signals.

Contribution

A novel optimal frequency sweep method based on MPDEs and a smoothness condition, enabling more efficient multi-rate circuit simulations.

Findings

Method successfully tested on a Phase Locked Loop with frequency modulation.

Requires minimal additional computational effort.

Provides a more efficient simulation approach for multi-rate RF circuits.

Abstract

Purpose -- RF circuits often possess a multi-rate behavior. Slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit. Frequency modulated signals pose a particular challenge. Design/methodology/approach -- The ordinary circuit differential equations (ODEs) are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. For an efficient simulation we need an optimal choice of a frequency dependent parameter. This is achieved by an additional smoothness condition. Finding -- By incorporating the smoothness condition into the discretization, we obtain a nonlinear system of equations complemented by a minimization constraint. This problem is solved by a modified Newton method, which needs only little extra computational effort. The method is tested on a Phase Locked Loop with a frequency modulated input signal. Originality/value -- A new optimal frequency sweep method was introduced, which will permit a very efficient simulation of multi-rate circuits.