LC Resonance Calculator
Find ideal resonant frequency from inductance and capacitance, then examine equal reactances, period, angular frequency, characteristic impedance, a series-RLC Q and half-power bandwidth, plus a component-tolerance frequency window.
Lumped, linear starting model. Parasitics, component loss, loading, coupling, temperature, bias, layout, and distributed transmission behavior can shift or suppress the measured resonance.
Resonance result
Tuning trace
f₀ = 1 ÷ (2π√(0.010000 H × 0.000001000 F)) = 1,591.549 Hz At f₀: XL = XC = 100.000 Ω Series R = 5.000 Ω gives Q = 20.000 and bandwidth = 79.577 Hz
Resonance is the equality of opposite reactances
Magnetic storage
An inductor stores energy in a magnetic field. Its reactance XL = 2πfL increases with frequency. In a series circuit its impedance contribution is positive imaginary, and its current tends to lag voltage.
Electric storage
A capacitor stores energy in an electric field. Its reactance magnitude XC = 1/(2πfC) decreases with frequency. Its complex impedance contribution is negative imaginary, opposing the inductor’s contribution.
Reactive balance
At ideal resonance, XL and XC are equal in magnitude. Their series reactances cancel, leaving resistance to set current. Energy continues to exchange between the capacitor’s electric field and inductor’s magnetic field.
The U.S. Department of Energy electrical fundamentals handbook defines resonance as the condition where inductive and capacitive reactance are equal and gives this frequency relationship. In a series RLC circuit at resonance, net reactance is zero and impedance is resistive. A practical response still depends on resistance, source impedance, load, component losses, and topology.
Worked example: 10 mH and 1 µF
The default inductor is 0.010 H and the capacitor is 0.000001 F. Their product is 10⁻⁸, its square root is 0.0001, and dividing one by 2π times that value gives 1,591.549 Hz, or approximately 1.59155 kHz.
The corresponding angular frequency is exactly 10,000 rad/s for these nominal values. Inductive reactance is ωL = 100 ohms. Capacitive reactance is 1/(ωC), also 100 ohms. The characteristic impedance √(L/C) therefore matches the equal resonance reactance.
With 5 ohms total series resistance, the simple series Q is ω₀L/R = 20. The exact half-power bandwidth for this constant-R series model is R/(2πL), approximately 79.577 Hz. The two half-power frequencies are about 1,552.258 Hz and 1,631.835 Hz; their difference equals the calculated bandwidth, and their geometric mean is the resonant frequency.
With ±10 percent L and ±5 percent C, the ideal worst-case arithmetic corner range is approximately 1.48091 to 1.72122 kHz. This combines both low-value corners for the high frequency and both high-value corners for the low frequency. It is not a statistical production distribution and excludes temperature, aging, voltage coefficient, bias, and parasitics.
Series half-power window
At the half-power points of a constant-resistance series RLC circuit, the magnitude of net reactance equals R and current magnitude is 1/√2 of its resonance value for a constant-voltage ideal source. Power in R is half its resonance maximum. This is the electrical basis for the familiar −3 dB bandwidth description.
When Q is high, the response is narrow and sensitive to small component shifts. When Q is low, the response is broad and the notion of a sharply defined peak becomes less useful. Coupling and load resistance can deliberately lower loaded Q even when the individual inductor and capacitor are high quality.
Series and parallel resonance are not interchangeable
Series RLC
At resonance, series reactances cancel and the ideal branch impedance reaches its minimum, equal to total series resistance. Branch current is maximum for a fixed source voltage. Component voltages can greatly exceed source voltage in a high-Q circuit, so voltage ratings still matter.
Parallel RLC
Ideal inductor and capacitor branch susceptances cancel at resonance. Input impedance can reach a maximum and source current a minimum, but results depend strongly on how losses are represented. Converting series coil loss to an equivalent parallel model is frequency dependent.
Design around tolerance, temperature, bias, and parasitics
| Effect | Likely frequency influence | Design response |
|---|---|---|
| Initial L and C tolerance | Higher product LC lowers f₀; lower product raises f₀. | Use worst-case corners, Monte Carlo distributions when justified, bins, trimming, or calibration. |
| Temperature coefficient | Component values and loss vary as the circuit warms or ambient changes. | Use specified coefficients over the full environment and include self-heating. |
| DC bias and AC amplitude | Magnetic permeability and ceramic capacitance may change with electrical stress. | Use bias curves and test levels matching the actual operating point. |
| Layout parasitics | Trace inductance and pad, winding, probe, and device capacitance alter effective L and C. | Model the physical layout, shorten critical connections, and de-embed fixtures when measuring. |
| Source and load coupling | External resistance changes loaded Q and may shift the observed peak. | Include source impedance, termination, coupling coefficient, and instrument loading. |
| Self-resonance and distributed behavior | Lumped elements cease to behave as ideal L or C near their own resonances. | Stay within characterized frequency ranges and use impedance data or electromagnetic models. |
The tolerance interval is deterministic: it assumes every part can sit simultaneously at the arithmetic limit. Real production yield depends on distributions, correlations, supplier process, lot, temperature, aging, and measurement uncertainty. Do not label the corner range as a confidence interval without statistical evidence. Preserve instrument calibration status, fixture configuration, and test amplitude whenever resonance measurements are compared across prototypes or production lots.
A practical resonator workflow
- Choose topology and function. Define whether the circuit is a filter, tank, trap, oscillator network, impedance match, sensor, or energy-transfer stage.
- Establish target frequency and bandwidth. Include tuning range, adjacent signals, settling time, transient response, and regulatory or system constraints.
- Select initial L and C. Use values with appropriate voltage, current, saturation, loss, dielectric, temperature, and package ratings.
- Assemble the loss model. Include ESR, inductor winding and core loss, source impedance, load, switches, traces, and measurement fixture.
- Run corners. Evaluate tolerance, temperature, voltage coefficient, DC bias, aging, and parasitics across the real environment.
- Simulate and measure. Sweep impedance or transfer response with calibrated equipment and avoid probe loading that moves the result.
- Document loaded Q. Distinguish component Q, unloaded resonator Q, external Q, and loaded Q so bandwidth claims remain reproducible.
Frequently asked questions
Does resistance change the ideal LC resonant frequency?
The basic 1/(2π√LC) balance frequency does not contain R. In real networks, damping, topology, source and load coupling, and the measured output quantity can shift the frequency of an observed peak or natural response. Use the appropriate full transfer function.
Why are XL and XC equal at resonance?
Substituting ω₀ = 1/√LC into ωL and 1/(ωC) gives the same magnitude √(L/C). Their complex signs are opposite, so they cancel in series and their ideal susceptances cancel in parallel.
Can component voltage exceed source voltage?
Yes. In a high-Q series resonator, inductor and capacitor voltages can be much larger than the source while opposing each other in phase. Check peak current, voltage magnification, dielectric rating, insulation, core saturation, and transient conditions.
What does Q mean here?
This calculator reports the simple series value Q = ω₀L/R, with R treated as constant total series resistance. A measured component or loaded-circuit Q can differ because loss and coupling are frequency dependent and distributed among several elements.
Is the tolerance range a probability interval?
No. It is a worst-case arithmetic corner using the entered symmetric limits. It does not assume a distribution or yield percentage. Statistical limits require component process data, correlations, environmental variables, and a justified analysis method.
Why is the measured resonance lower than calculated?
Uncounted parallel capacitance, higher actual component values, fixture loading, temperature, bias, and layout can lower resonance. Confirm calibrated L and C at the operating point, de-embed the fixture, and include device and board parasitics.
References
- U.S. Department of Energy, Electrical Science, Volume 3: Resonance
- National Bureau of Standards, Standard Radio Wavemeter
- National Institute of Standards and Technology, Time and Frequency from A to Z: Resonance Frequency
Educational lumped-element estimate only. Verify topology, losses, component ratings, parasitics, coupling, environmental corners, stability, measurement loading, and qualified electrical or RF design.