Correspondence between phasor transforms and frequency response function in RLC circuits

TL;DR

This paper establishes a theoretical link between phasor transforms and frequency response functions in RLC circuits, deriving precise expressions for resonance and anti-resonance frequencies considering damping effects.

Contribution

It demonstrates the correspondence between phasor analysis and FRF of RLC circuits and provides accurate formulas for key resonance parameters.

Findings

Derived expressions for resonance and anti-resonance frequencies.

Showed the equivalence between phasor transforms and FRF in RLC analysis.

Accounted for damping effects in impedance calculations.

Abstract

The analysis of RLC circuits is usually made by considering phasor transforms of sinusoidal signals (characterized by constant amplitude, period and phase) that allow the calculation of the AC steady state of RLC circuits by solving simple algebraic equations. In this paper I try to show that phasor representation of RLC circuits is analogue to consider the frequency response function (commonly designated by FRF) of the total impedance of the circuit. In this way I derive accurate expressions for the resonance and anti-resonance frequencies and their corresponding values of impedances of the parallel and series RLC circuits respectively, notwithstanding the presence of damping effects.