Resonant phenomena in bridge circuits: duality, amplitude, and phase resonance

Abstract

This paper presents a theoretical investigation of the frequency characteristics of alternating current (AC) bridge circuits, considered as two-terminal networks. The study focuses on the manifestation of resonant phenomena - particularly amplitude and phase resonance — and the role of structural dualities inherent in bridge configurations. Despite extensive prior research on bridge applications, the frequency behaviour of such circuits remains insufficiently characterized. The proposed analysis provides a unified mathematical framework for describing impedance and admittance properties of bridge circuits and establishes the conditions for the occurrence of resonance. The obtained results extend the potential applications of bridge circuits to analog signal processing, specifically in the design of frequency-selective filters.