Work out the resonant frequency of an inductor-capacitor (LC) tank circuit, or solve for the inductance or capacitance needed to hit a frequency. Add a resistance to get Q factor and bandwidth.
| Target frequency | Capacitance needed with this L |
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An inductor stores energy in its magnetic field and a capacitor in its electric field. Connected together, energy swings back and forth between them at one natural frequency: the resonant frequency.
Doubling the capacitance or the inductance lowers the frequency by a factor of the square root of 2 (about 0.707), which is why tuning capacitors often have a 10:1 range to cover about a 3:1 frequency range.
XL = 2*pi*f*L and XC = 1/(2*pi*f*C), equal at resonance.
Z0 = sqrt(L/C), the characteristic impedance.
Higher Q means a sharper, narrower resonance peak.
f = 1 / (2 * pi * sqrt(L * C)), with L in henries, C in farads and f in hertz.
Rearrange the formula: C = 1 / ((2 * pi * f)^2 * L). Choose the "Find C" mode and enter the inductance and target frequency.
The inductive reactance 2*pi*f*L equals the capacitive reactance 1/(2*pi*f*C). In a series circuit the impedance drops to just the resistance; in a parallel tank it rises to a maximum.
For a resistance in series, Q = (1/R) * sqrt(L/C). For a resistance in parallel with the tank, Q = R * sqrt(C/L). Bandwidth is f / Q.
Yes. Stray capacitance and inductance shift real circuits slightly, especially above a few MHz, so treat the result as a design starting point.
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