About this calculator
An inductor and a capacitor together will exchange energy back and forth at one particular frequency — the resonant frequency, where their opposing reactances cancel exactly. That effect is behind tuned radio circuits, oscillator tanks, notch filters and switching-supply snubbers.
This calculator solves for whichever of frequency, inductance or capacitance you are missing, and adds the characteristic impedance, Q factor and bandwidth that describe how sharp the resonance is.
How it works
Inductive reactance rises with frequency (XL = 2πfL) while capacitive reactance falls (XC = 1/2πfC). Setting them equal and solving for f gives the resonant frequency f₀ = 1 / (2π√(LC)). Note that only the product LC matters — swapping a larger inductor for a proportionally smaller capacitor lands on the same frequency.
What does change is the characteristic impedance Z₀ = √(L/C), which sets how much voltage the tank develops for a given circulating current, and therefore how it interacts with the circuit around it.
At resonance the two reactances cancel, so a series LC looks like a short circuit — only the resistance remains. A parallel tank does the opposite and looks like an open circuit. That is why series LC makes a notch filter and parallel LC makes a bandpass.
Losses determine how sharp the peak is. Q is the ratio of energy stored to energy lost per cycle, and bandwidth follows directly as BW = f₀ / Q. A high-Q tank is selective but rings; a low-Q one is broad and well damped.
Worked example
Building a tank circuit for a 455 kHz IF stage, using a 100 µH inductor.
- C = 1 / ((2π × 455000)² × 100e-6)
- (2π × 455000)² = 8.174e12
- C = 1 / (8.174e12 × 1e-4) = 1.223e-9 = 1.22 nF
- Z₀ = √(100e-6 / 1.223e-9) = √81766 = 286 Ω
- With a 10 kΩ parallel load: Q = 10000 / 286 = 35
- BW = 455 kHz / 35 = 13 kHz
1.22 nF alongside the 100 µH inductor resonates at 455 kHz with a 13 kHz passband — about right for an AM IF stage, which needs roughly 10 kHz to pass the audio sidebands.
Practical notes
- Only the LC product sets frequency, but the L/C ratio sets impedance. Choose the ratio to suit the circuit the tank connects to, then the product to hit the frequency.
- Above a few megahertz the layout becomes part of the circuit. An inch of wire is roughly 20 nH, and a pair of adjacent pads a few picofarads — enough to shift a VHF tank noticeably.
- Real inductors have series resistance and their own self-resonance from winding capacitance. Above that self-resonant frequency an inductor behaves as a capacitor.
- Q above about 100 is hard to achieve with ordinary components. Core losses, winding resistance and dielectric losses all conspire to damp the tank below the ideal figure.
- Series resonance produces voltages across L and C that are Q times the applied voltage. In a high-Q series circuit that can be hundreds of volts from a small drive — check component ratings.
- For crystal-accurate frequencies, use a crystal. An LC tank drifts with temperature and component tolerance and is typically good to a few percent, not a few parts per million.
Frequently asked questions
How do I calculate LC resonant frequency?
Use f₀ = 1 / (2π√(LC)), with L in henries and C in farads. 100 µH with 100 nF resonates at about 50.3 kHz.
What is the difference between series and parallel resonance?
Both resonate at the same frequency, but series LC presents minimum impedance there (a short, limited only by resistance) while parallel LC presents maximum impedance (an open). Series makes notches, parallel makes bandpass peaks.
What is the Q factor?
A measure of how lightly damped the resonance is — energy stored divided by energy lost per cycle. High Q gives a narrow, sharp peak; low Q gives a broad, gentle one. Bandwidth is simply f₀ divided by Q.
How do I choose between a big inductor and a big capacitor?
The product sets the frequency, so many combinations work. Pick the ratio for the impedance you want — Z₀ = √(L/C) — and to keep both parts practical. Very large inductors are bulky and lossy; very small capacitors get swamped by stray capacitance.
Why does my circuit resonate at a different frequency than calculated?
Stray capacitance and lead inductance add to your intended values, and inductors in particular carry substantial tolerance. Ferrite cores also vary batch to batch. A few percent off is normal; a long way off suggests the layout is contributing more than the components.