Beyond a simple filter: transient and steady state analysis of first-order resistor-resistor-capacitor circuits

Abstract

This paper presents a quantitative analysis of a first-order resistor-resistor-capacitor (RRC) circuit, detailing its transient, steady state, and frequency-domain behaviors through computational modeling. The study confirms that the circuit's time constant (τ) governs its dynamic response, with the capacitor charging to 63.2% of its final voltage in one τ. The key finding is the circuit's fundamental distinction from a simple resistor-capacitor (RC) filter: under a 100 V step excitation, the RRC topology stabilizes with a non-zero steady-state current of 0.35 A, following a controlled transient inrush of 1.0 A. Frequency analysis further characterizes the circuit as a stable low-pass filter with a predictable -20 dB/decade roll-off. This work elucidates a critical engineering trade-off, demonstrating that the RRC's components dually define its transient speed and its final steady state operating point, providing a quantitative framework for advanced power management and signal conditioning applications.