Series and parallel RLC resonance — resonant frequency, quality factor, bandwidth, half-power frequencies, and dynamic impedance. Live plots of |Z|, phase, and current versus frequency. Edit L, C, R, or switch topology; the curves re-draw instantly.
ω0 = 1/√(LC), f0 = 1/(2π√LC)
Q = ω0L/R = 1/(ω0RC) = (1/R)√(L/C)
BW = f0/Q = R/(2πL)
f1,2 = f0/2 ± √((f0/2)² + (BW/2)²)
or f1 ≈ f0 − BW/2, f2 ≈ f0 + BW/2 (high Q)
Z = R + j(ωL − 1/(ωC)). At f0: Z = R (purely resistive, minimum for series).
ω0 = (1/√(LC)) · √(1 − R²C/L)
High-Q approximation: ω0 ≈ 1/√(LC)
Q = (1/R)√(L/C) = ω0RC = Rp/X0
BW = f0/Q = 1/(2πRC)
At f0, |Z| = Rp = L/(RC) = Q·ω0L (maximum for parallel).
Z = 1 / (1/R + jωC + 1/(jωL)). At f0: purely resistive, maximum.