Calculator
Formula used
The ideal (lossless) resonance angular frequency is:
ω0 = 1 / √(LC) and f0 = ω0 / (2π)
When resistance is included, the oscillation exists only if the response is underdamped. The damped angular frequency is:
- Series: ωd = √(1/(LC) − (R/(2L))²)
- Parallel: ωd = √(1/(LC) − (1/(2RC))²)
Quality factor (Q) and bandwidth (approx.) are computed as:
- Series: Q = (1/R) √(L/C)
- Parallel: Q = R √(C/L)
- Bandwidth: BW ≈ f0 / Q
How to use this calculator
- Select whether your circuit is series or parallel.
- Enter R, L, and C with suitable units.
- Click Calculate to view results above the form.
- If a resonance peak is not expected, check the status note.
- Use CSV or PDF buttons to save a shareable summary.
Example data table
| Type | R | L | C | Ideal f0 | Approx. Q | BW |
|---|---|---|---|---|---|---|
| Series | 25 Ω | 10 mH | 0.47 µF | ≈ 2.32 kHz | ≈ 9.23 | ≈ 251 Hz |
| Parallel | 5 kΩ | 100 µH | 1 nF | ≈ 503 kHz | ≈ 15.81 | ≈ 31.8 kHz |
| Series | 2 Ω | 1 H | 100 µF | ≈ 15.9 Hz | ≈ 50.0 | ≈ 0.318 Hz |
These examples show typical magnitudes. Real circuits may include parasitics that shift resonance and lower Q.
1) What resonance means in an RLC network
An RLC circuit resonates when energy repeatedly exchanges between the inductor’s magnetic field and the capacitor’s electric field. Near resonance, inductive and capacitive reactances oppose each other, so the remaining response is mainly set by resistance and damping. The sharper the resonance peak, the higher the selectivity for frequency-sensitive designs.
2) Ideal resonance frequency and scaling laws
The ideal resonance is set by f0 = 1/(2π√(LC)). Doubling L lowers the resonance by about 29%, while doubling C lowers it by the same proportion because frequency scales with 1/√(LC). For example, L = 10 mH and C = 0.47 µF gives an ideal resonance near 2.32 kHz, matching the example table.
3) Series versus parallel interpretation
In a series RLC, resonance is often observed as a minimum impedance and a maximum current at f0. In a parallel RLC, resonance typically appears as a maximum impedance and a minimum supply current at f0. This calculator lets you switch modes because the damping model and the Q definition change with topology, even when L and C are identical.
4) Damping, underdamped checks, and real peaks
Resistance limits how “oscillatory” the system behaves. The calculator reports whether the circuit is underdamped, meaning the damped resonance frequency is real and a clear peak is expected. For series networks the damping term depends on R/(2L); for parallel it depends on 1/(2RC). When damping is strong, resonance broadens or disappears.
5) Quality factor and bandwidth as usable metrics
Q indicates how narrow and strong the resonance is. Higher Q means lower loss and tighter selectivity. Bandwidth is estimated with BW ≈ f0/Q, a common engineering approximation for moderate-to-high Q circuits. If your design targets a 3 dB bandwidth of 200 Hz at 2 kHz, a Q near 10 is a practical starting point.
6) Typical component data that shifts resonance
Real parts introduce tolerance and loss. Film capacitors may be ±5% with low dissipation, while electrolytics can be ±20% with higher ESR. Inductors often range from ±5% to ±20%, and their DC resistance acts like added series R. These variations can move f0 by several percent because the frequency depends on the square root of L and C.
7) Parasitics and layout at higher frequencies
At higher frequencies, stray capacitance and lead inductance can dominate. A few picofarads of parasitic capacitance can noticeably detune circuits using small C values, while wiring inductance can alter resonance in fast layouts. Keep leads short, use ground planes, and consider component self-resonant frequency when working in the hundreds of kilohertz or above.
8) How to use the calculator output in design reviews
Use the ideal f0 for a first pass, then compare it with the damped resonance and the status note. If Q is too low, reduce loss by lowering effective resistance or selecting higher-Q inductors and capacitors. Export CSV for documentation, or PDF for quick sharing with teammates and lab reports.
1) Why does the calculator show both ideal and damped resonance?
Ideal resonance assumes no loss. Damped resonance accounts for resistance and only exists when the response is underdamped. Comparing them helps you see whether losses meaningfully shift the expected peak.
2) Which R value should I enter for a real inductor?
Use the inductor’s effective series resistance at your operating frequency, not only the DC resistance. Winding resistance, core loss, and skin effect can increase the effective R and reduce Q.
3) My circuit resonates lower than predicted. What is a common cause?
Stray capacitance is a frequent reason, especially with small capacitors. Probe capacitance, wiring, and PCB pads add to C, lowering f0. Inductor value drift and saturation can also reduce resonance frequency.
4) How reliable is the bandwidth estimate?
BW ≈ f0/Q is a standard approximation that works best for moderate-to-high Q. With strong losses or unusual loading, measured bandwidth can differ. Treat it as a design estimate and validate with measurement or simulation.
5) What Q range is considered “high” in practice?
It depends on frequency and parts. Audio-frequency filters may achieve Q of 5–50, while RF coils can exceed 100 in optimized designs. If Q is below about 2, resonance will look broad and weak.
6) Can I use this for driven response peaks, not just natural oscillation?
Yes. The ideal f0 and Q-based bandwidth are widely used for driven frequency response planning. Loading from sources and measurement equipment can change the effective R, so your observed peak may shift.
7) Why are series and parallel Q formulas different?
They reflect how losses appear relative to the reactive elements. In series networks, R directly dissipates current, so Q falls with higher R. In parallel networks, resistance represents a leakage path, so Q rises with higher R.