RLC Resonant Frequency Calculator (Series and Parallel)

What is resonance?

Inductive reactance rises with frequency and capacitive reactance falls. At the frequency where they are equal they cancel, and the circuit behaves like a pure resistance. That frequency is the resonant frequency:

f0 = 1 / (2π × √(L × C))

It depends only on L and C, not on the resistance.

Series and parallel circuits

• Series RLC: at resonance the impedance drops to its minimum (R) and the current peaks. The voltage across the inductor and the capacitor rises to Q times the source voltage.
• Parallel RLC: at resonance the impedance rises to its maximum (R) and the current drawn from the source is at its minimum. A current Q times the source current circulates between L and C.

Quality factor and bandwidth

Q tells how sharply selective the circuit is. For a series circuit Q = (1 / R) × √(L / C), for a parallel circuit Q = R × √(C / L). The bandwidth is B = f0 / Q, the gap between the two frequencies where the power falls to half.

Example

Take R = 2 Ω, L = 1 mH and C = 0.4 µF in series. ω0 = 1 / √(0.001 × 0.0000004) = 50,000 rad/s, so f0 = 7958 Hz. Since √(L / C) = 50 Ω, Q = 50 / 2 = 25 and the bandwidth is 7958 / 25 = 318 Hz. The half power frequencies are 7800 Hz and 8118 Hz.

Choosing L or C

When the target frequency and one component are known, the other follows from L = 1 / ((2π f0)² × C) or C = 1 / ((2π f0)² × L). The tool has a tab for each.

Limits

Components are treated as ideal. The winding resistance and stray capacitance of a real inductor and the losses of a capacitor shift the result. In a parallel circuit with the winding resistance in series with the inductor, resonance falls slightly lower. At high frequencies lead lengths matter as well.