Explore resonance sharpness using inductance, capacitance, and resistance. Choose units, solve missing values instantly here. See Q, bandwidth, damping ratio, and energy loss clearly.
The quality factor Q describes how underdamped a resonant circuit is. A higher Q indicates a sharper resonance peak and a narrower bandwidth.
ω₀ = 1 / √(LC)f₀ = ω₀ / (2π)Q = ω₀L / R = (1/R) √(L/C)Q = R / (ω₀L) = R √(C/L)Q = f₀ / BW and Q = ω₀ / Δωζ = 1 / (2Q) (underdamped when Q > 1/2)τ ≈ 2Q / ω₀Tip: Use effective resistance values (losses) for realistic Q results.
| Case | Type | L | C | R | Computed f₀ | Computed Q | Approx BW |
|---|---|---|---|---|---|---|---|
| 1 | Series | 10 mH | 100 nF | 5 Ω | ≈ 159.15 Hz | ≈ 2.00 | ≈ 79.6 Hz |
| 2 | Parallel | 1 mH | 1 µF | 2 kΩ | ≈ 159.15 Hz | ≈ 12.57 | ≈ 12.7 Hz |
| 3 | Frequency | — | — | — | 10 kHz | 40 | 250 Hz |
Example values are illustrative. Real-world losses shift Q and bandwidth.
The quality factor, Q, is a compact measure of resonance sharpness. In practical terms, it describes how strongly a circuit stores energy compared with how quickly it loses energy. High-Q networks produce narrow peaks that are useful for selective filters and stable oscillators.
In a series RLC, resistance directly damps current at resonance, so Q increases when R is reduced. In a parallel RLC, the resistance provides an alternate loss path, so Q increases when the parallel resistance rises. This calculator lets you compare both connections using consistent units.
Resonance is set mainly by L and C through f₀ = 1/(2π√(LC)). Doubling inductance lowers f₀ by √2, while doubling capacitance lowers it by the same factor. Keeping f₀ fixed while increasing L usually reduces required C, which can change loss mechanisms at higher frequencies.
The classic relationship Q = f₀/BW connects resonance sharpness to the -3 dB bandwidth. A 10 kHz resonator with BW of 250 Hz has Q = 40. Narrow bandwidth improves selectivity, but can also slow transient response and increase sensitivity to tolerances.
Damping ratio ζ = 1/(2Q) provides another view of the same physics. Lower ζ means oscillations decay more slowly. The ring-down time constant τ ≈ 2Q/ω₀ helps estimate how long energy persists after excitation, important in pulsed sensing and switching designs.
Effective resistance is rarely just a resistor. Inductors include winding resistance and core loss, capacitors include ESR and dielectric loss, and wiring adds parasitics. Use measured f₀ and bandwidth when possible, because it captures total loss without needing a detailed model.
Power inductors may show Q from single digits to a few tens at their operating frequency, while air-core inductors and RF capacitors can achieve much higher Q. Audio bandpass filters often target Q from 0.5 to 10, while narrow RF filters may exceed 50 depending on technology.
Start with component inputs for a first estimate, then confirm with the frequency method using measured f₀ and BW. Compare series versus parallel results when translating designs between topologies. Export CSV or PDF outputs to document tuning steps, test data, and final acceptance limits.
A higher Q produces a narrower passband and stronger selectivity near resonance. It can also increase sensitivity to component tolerances and temperature drift, so stability considerations matter.
Use the effective series resistance that represents total loss at the operating frequency. This can include winding resistance, capacitor ESR, and any intentional series damping resistor.
Parasitic capacitance, inductor core loss, ESR, and layout resistance change the true loss. Measuring f₀ and bandwidth captures these effects, which often lowers Q compared with ideal calculations.
In many filter measurements, bandwidth refers to the -3 dB (half-power) points around the peak. If you use a different definition, your computed Q will not match standard comparisons.
Use it when you have test data: resonant frequency and measured bandwidth. It is ideal for prototypes and troubleshooting because it avoids assumptions about component loss models.
Yes. Q below 0.5 corresponds to heavy damping where the response is not strongly resonant. The circuit behaves more like a broad, gently varying network than a sharp resonator.
Reduce loss: choose lower-ESR capacitors, higher-Q inductors, thicker traces, and shorter connections. Avoid saturating cores and keep components within frequency and current ratings.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.