LC Resonant Frequency Calculator

What Is an LC Circuit? An LC circuit (also called a tank circuit or resonant circuit) consists of an inductor (L) and a capacitor (C) connected together. When given an initial charge, energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor, the way a pendulum swings energy between kinetic and potential forms.

The Resonance Formula At the resonant frequency f, the inductive reactance (XL = 2πfL) exactly equals the capacitive reactance (XC = 1/2πfC). Setting these equal and solving for f gives the fundamental formula: f = 1 / (2π√(LC)). The angular frequency ω = 2πf = 1/√(LC) radians per second.

Why Resonance Matters At resonance a parallel LC tank presents its maximum impedance, and a series LC presents its minimum. Whether that gives you a band-pass or a band-stop depends on where you put it. A parallel tank sitting as the collector load of an RF amplifier passes only its resonant frequency, while the same tank placed in series with the signal path blocks that one frequency and lets everything else through. A series LC does the mirror image. This selectivity is what makes radio tuning possible. By varying the capacitance of a variable capacitor, the resonant frequency shifts to match a different radio station’s carrier frequency.

Radio Frequency Ranges AM radio broadcasts from 535 kHz to 1,705 kHz. FM radio uses 87.5 MHz to 108 MHz. These different bands require very different L and C values. An AM radio tuner might use 250 μH inductance with a variable capacitor swinging from about 35 to 353 pF, which is what it takes to cover the band end to end: 353 pF lands on 536 kHz and 35 pF on 1.70 MHz. An FM tuner needs far smaller parts: roughly 0.1 μH (100 nH) paired with 22 to 33 pF. Plug 0.1 μH and 25 pF into the calculator and you land at about 100 MHz, right in the middle of the FM band. That inductor is often just a few turns of stiff wire with no former at all, and you tune it by squeezing the turns together.

Worked example: a 455 kHz IF transformer Every superheterodyne AM radio converts the incoming station down to a fixed 455 kHz intermediate frequency, and the filter that does the work is an LC tank. Say you have a 680 μH coil and want to know what capacitor pairs with it:

C = 1 / ((2πf)² × L) = 1 / ((2π × 455,000)² × 0.00068)

(2π × 455,000) = 2.859 × 10⁶, squared = 8.174 × 10¹². Multiply by 0.00068 and you get 5.558 × 10⁹, so C = 1.80 × 10⁻¹⁰ F, or 180 pF. That is a stock value, which is not a coincidence: the coils were designed around the capacitors people could buy.

Crystal Oscillators For applications requiring extremely precise frequency stability (clocks, GPS receivers, microprocessors), quartz crystal oscillators replace the LC tank circuit. A quartz crystal acts like a very high-Q LC circuit with exceptional stability. The crystal in a typical computer runs at tens to hundreds of MHz and drifts only a few parts per million per year.

Wavelength Connection Every frequency corresponds to a wavelength: λ = c/f, where c is the speed of light (299,792,458 m/s). At 100 MHz (FM radio), the wavelength is about 3 meters. At 2.4 GHz (Wi-Fi), the wavelength is about 12.5 cm, which is why Wi-Fi antennas are measured in centimeters.