RLC Circuit Simulator — Frequency Response

Set R, L and C and watch the frequency response of a series RLC circuit: resonant frequency, quality factor Q and −3 dB bandwidth, with the output taken across the resistor.

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How to use this tool

Set the resistance R, inductance L and capacitance C. The tool plots gain versus frequency, marks the resonant frequency f₀, the quality factor Q and the bandwidth, and updates live as you drag the sliders.

H(jω) = R / (R + j(ωL − 1/ωC))
f₀
Q
BW

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What is a series RLC circuit?

A series RLC circuit is a resistor, inductor and capacitor in series driven by an AC source. Because inductive reactance rises with frequency and capacitive reactance falls, the total impedance is frequency-dependent, so the circuit behaves as a frequency-selective filter. With the output taken across the resistor it is a band-pass filter that peaks at resonance.

Resonance, Q factor and bandwidth

Resonance occurs at f₀ = 1 / (2π√(LC)), where the inductive and capacitive reactances cancel, the impedance is purely resistive and the current is maximum. The quality factor Q = (1/R)√(L/C) sets how sharp the peak is, and the −3 dB bandwidth is Δf = f₀ / Q = R / (2πL). A high-Q circuit is a narrow, selective filter; a low-Q circuit is broad and heavily damped.

How to use the simulator

Drag the R, L and C sliders and read the response curve: the peak marks f₀, its sharpness is Q, and the width between the half-power points is the bandwidth. Increasing R lowers Q and flattens the peak; increasing L or C moves f₀ down.

Note: the model is an ideal linear series RLC with lumped, frequency-independent components and no parasitic resistance in the inductor or capacitor. Real components add ESR and self-resonance that broaden and shift the response at high frequency.

Frequently asked questions

What is the resonant frequency of an RLC circuit?

f0 = 1 / (2*pi*sqrt(L*C)). At the resonant frequency the inductive and capacitive reactances cancel, the impedance is purely resistive and, in a series circuit, the current is at its maximum.

What is the Q factor of a series RLC circuit?

Q = (1/R)*sqrt(L/C), which also equals 2*pi*f0*L/R. A higher Q means a sharper, narrower resonance peak and a more frequency-selective filter.

What is the bandwidth of an RLC circuit?

The -3 dB (half-power) bandwidth is delta_f = f0 / Q = R / (2*pi*L). It is the width of the frequency band, centered on resonance, where the output stays within 3 dB of its peak.

Is this a series or parallel RLC circuit?

Series. The three components share the same current and the output is taken across the resistor, giving a band-pass response that peaks at the resonant frequency.