LC resonant frequency calculator
At resonance the inductive and capacitive reactances cancel and the circuit presents pure resistance.
microhenry
picofarad
ohm
Resonant frequency
1.591 549 4MHz
- Resonant frequency
- 1 591 549.4 Hz
- Reactance at resonance
- 1000 ohm
- Q factor
- 200.000
- Bandwidth
- 7957.75 Hz
- Free-space wavelength
- 188.365
Show the working
- Inductance = 100
- Capacitance = 100
- Series resistance = 5
- l_h = 100 * 1e-6 = 0.0001
- c_f = 100 * 1e-12 = 1e-10
- Resonant frequency = 1 / (2 * pi * sqrt(0.0001 * 1e-10)) = 1 591 550
- Resonant frequency = 1 591 550 / 1e6 = 1.591 55
- Reactance at resonance = 2 * pi * 1 591 550 * 0.0001 = 1000
- Q factor = 1000 / 5 = 200
- Bandwidth = 200 > 0 ? 1 591 550 / 200 : 0 = 7957.75
- Free-space wavelength = 1 591 550 > 0 ? c / 1 591 550 : 0 = 188.365
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- f = 1 / (2 pi sqrt(L C))
- Q = XL / R
- bandwidth = f / Q