Sensitivity Analysis of Resonant Circuits

TL;DR

This paper presents a method using first-order perturbation theory to analyze how small changes in RLC circuit parameters affect the system's poles, providing a statistical approach for sensitivity prediction.

Contribution

It introduces a sensitivity analysis framework based on eigenvector derivatives, linking circuit parameter variations to system response changes, with applications to probabilistic predictions.

Findings

Sensitivity matrix relates parameter changes to pole shifts.

Method enables efficient statistical sensitivity predictions.

Monte Carlo simulations validate the approach.

Abstract

We use first-order perturbation theory to provide a local linear relation between the circuit parameters and the poles of an RLC network. The sensitivity matrix, which defines this relationship, is obtained from the systems eigenvectors and the derivative of its eigenvalues. In general, the sensitivity matrix is related to the equilibrium fluctuations of the system. In particular, it may be used as the basis for a statistical model to efficiently predict the sensitivity of the circuit response to small component variations. The method is illustrated with a calculation of conditional probabilities by Monte Carlo Simulation.