RLC Circuit Resonance Calculator
Calculate resonant frequency, Q factor, bandwidth, and cutoff frequencies for RLC series circuits.
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RLC Series Circuit
Impedance vs Frequency (series RLC)
How does RLC circuit resonance work?
An RLC series circuit contains a resistor (R), inductor (L), and capacitor (C) in series. At the resonant frequency f₀ = 1/(2π√(LC)), the inductive reactance XL equals the capacitive reactance XC, and they cancel each other. The impedance drops to its minimum value R, and the circuit passes maximum current.
The quality factor Q = (1/R)×√(L/C) measures how sharp the resonance peak is. A high Q means a narrow bandwidth and strong frequency selectivity — the circuit strongly amplifies signals near f₀ while rejecting others. A low Q gives a broad, gentle response useful for wideband applications.
The bandwidth BW = f₀/Q defines the range of frequencies where the circuit response is within 3 dB of the peak. The lower and upper cutoff frequencies f₁ and f₂ mark the edges of this passband. RLC circuits are fundamental building blocks in radio receivers, audio crossovers, and power factor correction.
Resonant Frequency (f₀)
f₀ = 1 / (2π√(LC))Quality Factor (Q)
Q = (1/R) × √(L/C)Bandwidth (BW)
BW = f₀ / QKey Points
- At resonance: XL = XC, impedance is minimum (Z = R)
- Higher Q = narrower bandwidth = sharper selectivity
- Bandwidth BW = f₀/Q = R/(2πL) for series RLC
- Cutoff frequencies: f₁ = f₀ − BW/2, f₂ = f₀ + BW/2
Applications
- Bandpass and bandstop filter design
- Radio frequency tuning and receivers
- Power factor correction circuits
- Audio crossover networks