RLC Resonance Calculator (Series Resonant Frequency, Q and Bandwidth)
Enter the resistance, inductance and capacitance of a series RLC circuit. You get the resonant frequency f0, the quality factor Q and the bandwidth. The test frequency gives the impedance and phase at that point.
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Formula
- Resonant frequency:
f0 = 1 / (2π × √(L × C)) - Quality factor (series):
Q = (1 / R) × √(L / C) - Bandwidth:
BW = f0 / Q = R / (2π × L) - Reactances at frequency f:
XL = 2π f LandXC = 1 / (2π f C) - Impedance:
Z = √(R² + (XL − XC)²) - Phase angle:
atan2(XL − XC, R), negative when the circuit is capacitive
Resistance, inductance, capacitance and test frequency must all be above zero (R = 0 would make Q infinite).
Worked example
R = 10 Ω, L = 10 mH, C = 1 µF:
f0 = 1 / (2π × 0.0001) = 1591.5 HzQ = 0.1 × √(0.01 / 0.000001) = 0.1 × 100 = 10BW = 1591.5 / 10 = 159.15 Hz- At 1 kHz:
XL = 62.83 Ω,XC = 159.15 Ω,X = −96.32 Ω,Z = √(100 + 9278.2) = 96.84 Ω, phase−84.07°.
Frequently asked questions
What is the resonant frequency of a series RLC circuit?
f0 = 1 / (2π × √(L × C)). For 10 mH and 1 µF, √(0.01 × 0.000001) = 0.0001, so f0 = 1 / (2π × 0.0001) = 1591.5 Hz. At f0 the inductive and capacitive reactances are equal and cancel.
How is the Q factor calculated?
For a series circuit Q = (1 / R) × √(L / C). With R = 10 Ω, L = 10 mH and C = 1 µF: √(10,000) = 100, so Q = 100 / 10 = 10. A higher Q means a sharper, more selective resonance.
How do I find the bandwidth?
Bandwidth is the width between the half-power points: BW = f0 / Q = R / (2π × L). Here that is 1591.5 / 10 = 159.15 Hz. More resistance widens the bandwidth and lowers Q.
What is the impedance at resonance?
The impedance is at its minimum and equals R, because XL − XC = 0 and the phase angle is 0. Away from resonance Z = √(R² + (XL − XC)²). At 1 kHz for the example circuit, XL = 62.83 Ω and XC = 159.15 Ω, so Z = 96.84 Ω with a phase of −84.07 degrees (capacitive).
Can I use this for safety or final design sign-off?
No. This calculator is for learning and design checks, not safety certification. At resonance the voltage across L or C can be Q times the source voltage, so a high-Q circuit can exceed component ratings. Real parts also have tolerance and loss that this ideal model ignores.