Tank Circuit Resonance Calculator
Calculate the resonant frequency of a tank circuit using inductance (L) and capacitance (C). Perfect for RF filters, oscillators, tuning circuits, antennas, and resonant power applications.
What the tank circuit resonance calculator does
The tank circuit resonance calculator gives the resonant frequency of a parallel inductor-capacitor circuit, the “tank” used in oscillators, RF filters and tuned amplifiers. Enter the inductance in henries and the capacitance in farads and press Calculate. The result is the resonant frequency in hertz and the angular frequency in radians per second.
The formula
f0 = 1 / (2π √(L × C))
At this frequency the inductive reactance 2πfL equals the capacitive reactance 1 / (2πfC). In a parallel tank the two currents cancel, the circuit presents its maximum impedance to the outside, and energy sloshes back and forth between the magnetic field of the coil and the electric field of the capacitor, which is where the name comes from.
Worked examples
| L | C | Enter L | Enter C | f0 | Use |
|---|---|---|---|---|---|
| 1 mH | 1 µF | 0.001 | 0.000001 | 5.03 kHz | Audio / default values |
| 220 µH | 470 pF | 2.2e-4 | 4.7e-10 | 495 kHz | AM radio IF region |
| 1 µH | 100 pF | 1e-6 | 1e-10 | 15.9 MHz | Shortwave |
| 100 nH | 27 pF | 1e-7 | 2.7e-11 | 96.9 MHz | FM broadcast |
| 10 nH | 1 pF | 1e-8 | 1e-12 | 1.59 GHz | GPS / mobile bands |
Parallel versus series LC
The resonant frequency is the same for both arrangements, so this tool and the LC resonant frequency calculator give identical numbers. The difference is in impedance. A series LC has minimum impedance at resonance and is used as a pass filter or trap in series with a signal. A parallel tank has maximum impedance at resonance, so as a collector or drain load it gives a tuned amplifier high gain at one frequency, and in an oscillator it sets the frequency at which feedback is strongest.
Quality factor and bandwidth
A real tank has loss, mostly in the coil’s wire resistance. The quality factor Q describes how sharp the resonance is:
- Parallel tank with parallel loss resistance Rp: Q = Rp / (2πf0L)
- Series loss r in the coil: Q = 2πf0L / r
- Bandwidth between −3 dB points: BW = f0 / Q
A 96.9 MHz tank with a Q of 50 passes a band about 1.9 MHz wide, enough to select one FM station. Air-core coils reach Q of 100 to 300; ferrite cores and small chip inductors are often 20 to 60.
Tuning the tank
Because frequency depends on the square root of LC, halving C raises f0 by only 41%. A variable capacitor covering 30 to 300 pF therefore tunes across a 3.16:1 frequency range, which is why the old AM band (530 to 1,700 kHz) fits one capacitor. Varactor diodes do the same job electronically; their capacitance falls as reverse voltage rises. Rearranging the formula, the capacitance needed for a target frequency is C = 1 / (4π²f0²L). For 100 nH at 96.9 MHz that is 27 pF, as in the table.
Parasitics that shift the frequency
- Stray capacitance. PCB pads and the coil’s own turns add a few picofarads, which is a large fraction of a 27 pF tank. Design with a smaller nominal C and trim.
- Lead inductance. A 10 mm lead adds roughly 10 nH, doubling a 10 nH tank’s inductance.
- Loading. Whatever connects to the tank, a transistor or an antenna, adds capacitance and lowers Q.
- Temperature. Ferrite cores and some ceramic capacitors drift by hundreds of ppm per °C; C0G/NP0 capacitors and air cores are stable.
Common mistakes
- Entering microhenries or picofarads without the exponent. 100 pF is 1e-10 F; 100 µH is 1e-4 H.
- Expecting a change in L to change f0 proportionally. It is a square-root relationship.
- Ignoring Q. A tank with Q below about 10 barely resonates and gives little selectivity.
- Forgetting self-resonance. Every inductor has a self-resonant frequency above which it behaves as a capacitor; check the datasheet for RF work.
Related tools
The inductive reactance and capacitive reactance calculators give the individual reactances at any frequency, which must be equal at resonance. The impedance converter and frequency converter handle unit changes, and the RC time constant calculator covers the non-resonant RC case.
External references
Frequently asked questions
Why is it called a tank?
Because it stores energy, alternately in the coil and the capacitor, like a tank storing fluid that flows back and forth.
Does resistance change the resonant frequency?
Very slightly. For Q above about 10 the shift is under 0.5% and is ignored in practice.
What is the impedance of a tank at resonance?
Ideally infinite; in practice Rp = Q × 2πf0L. A 100 nH coil with Q = 50 at 96.9 MHz presents about 3 kΩ.
Can I get a lower frequency with a bigger capacitor instead of a bigger coil?
Yes, and it is usually cheaper, but a very low L/C ratio reduces the tank’s impedance and Q. Designers keep the ratio moderate.
How do I make the tank tunable?
Use a variable or varactor capacitor for C, or a slug-tuned coil for L. Capacitor tuning is more common because it is easier to control precisely.