RLC resonance PUBLIC

A square wave into a resistor, inductor, and capacitor can produce ringing and narrowband amplification

At low frequencies, L1 looks like a short circuit, and C1 looks like an open circuit, so V(in) and V(out) are closely linked by R1. At high frequencies, L1 looks like an open circuit and C1 looks like a short circuit, so V(out) approaches zero. But in the middle range of frequencies, something interesting happens.

In fact, for a narrow range of frequencies around 1MHz, this circuit actually produces a tremendous amount of voltage amplification!

A few things to try in CircuitLab

This circuit highlights several cool features of CircuitLab simulations that you can quickly try. Load this circuit with the "Open in editor" button above, and then click the "Simulate" tab to get started.

Time

We've configured V1 to put a square wave into the input, and if we plot the output, we can see a tremendous amount of ringing in the output. Try changing R1 and seeing how it affects the shape of the ringing! Also adjust L1 and or C1 to tune the exact frequency of the resonance.

Bode

Run the frequency domain analysis to see a sharp peak of about +36dB around 1MHz. That means that a signal around 1 MHz will get amplified by a factor of about 63x (10^(36/20) = 63)! That's a lot of gain, all from a passive circuit. That's why this kind of inductor/capacitor combination is often found in radio equipment, as it can select a narrow band of frequencies and amplify them without amplifying the rest of the spectrum.