Resonant Frequency Calculator

In an ideal LC circuit, energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor. Resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC). The governing equation relating resonant frequency (f) to inductance (L) and capacitance (C) is derived from setting XL equal to XC, which yields the standard Thomson formula: f = 1 / (2 * pi * sqrt(L * C)). From this core frequency, angular frequency can be found using omega = 2 * pi * f, while individual reactances are calculated as XL = omega * L and XC = 1 / (omega * C).

Let us calculate the resonant frequency for an LC circuit with an inductance (L) of 1 millihenry (1 mH or 0.001 H) and a capacitance (C) of 220 picofarads (220 pF or 220 x 10^-12 F). First, multiply inductance and capacitance: 0.001 * 220 x 10^-12 = 2.2 x 10^-13. Next, take the square root of this product, which gives approximately 4.6904 x 10^-7. Multiply this result by 2 * pi (approx 6.28318), yielding 2.947 x 10^-6. Finally, divide 1 by this product to find the resonant frequency: f = 1 / 2.947 x 10^-6, which results in approximately 339,325 Hz or 339.3 kHz.

When working with resonant circuits, always convert your units into standard SI units before calculating—use farads for capacitance, henries for inductance, and hertz for frequency. Pay close attention to parasitic resistance in real-world components, as ideal calculations assume zero resistance, whereas physical inductors and capacitors introduce damping that can slightly broaden your tuning bandwidth.