RLC Impedance Calculator

Impedance (Z) is the complete AC equivalent of resistance — it describes the total opposition to sinusoidal current flow, incorporating both resistive (real) and reactive (imaginary) components. Expressed as a complex number Z = R + jX, the magnitude |Z| = √(R² + X²) gives the ratio of voltage amplitude to current amplitude, while the phase angle θ = arctan(X/R) gives the phase shift between voltage and current. This calculator computes the series RLC impedance at any specified frequency.

For a series RLC circuit, the net reactance is X = XL − XC = ωL − 1/(ωC), where ω = 2πf. The inductive reactance XL increases linearly with frequency; capacitive reactance XC decreases inversely with frequency. Their difference X passes through zero at the resonant frequency f₀ = 1/(2π√(LC)), where impedance is minimum and purely resistive (Z = R).

The phase angle θ indicates the nature of the load: θ > 0 means the circuit is inductive (current lags voltage by θ degrees); θ < 0 means the circuit is capacitive (current leads voltage); θ = 0 means purely resistive (in-phase current and voltage, maximum power transfer). Understanding phase angle is critical for power factor correction, filter phase response, and stability analysis in feedback amplifiers.

Admittance Y = 1/Z (in siemens) is the complex reciprocal of impedance, just as conductance G = 1/R is the reciprocal of resistance. Its magnitude |Y| = 1/|Z|. Admittance is more convenient for parallel circuit analysis — admittances add directly in parallel, as do their components: susceptance B = −X/|Z|² and conductance G = R/|Z|². This calculator provides |Y| for those working with admittance-based analysis or parallel circuit models.

At DC (f = 0 Hz): XL = 0 (inductor is a short circuit), XC = ∞ (capacitor is an open circuit) — no steady-state current flows through the capacitor. At very high frequencies: XL → ∞ (inductor blocks high-frequency current), XC → 0 (capacitor passes high-frequency current). These asymptotic behaviors define the roll-off characteristics of RLC filters.

Impedance matching is a critical concept in RF engineering: maximum power transfer occurs when source impedance equals the complex conjugate of load impedance (Z_load = Z_source*). An RLC matching network transforms one impedance to another for optimal power transfer between source and load — as in antenna-to-transmission line matching and amplifier interstage coupling networks.