Electronics
RC, RL and RLC Circuits
Put a resistor with something that stores energy and the circuit stops answering instantly. A capacitor and a resistor give one time constant and a lazy approach to the answer; add an inductor and the two stores start passing energy back and forth, so the circuit rings, and how fast the ringing dies is a knob you can turn. The same two poles decide the transient, the ringing and which frequencies get through.
slowfar past resonance
rings for agesrefuses to ring
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The poles panel is the same circuit seen from the Laplace side. Move R and watch the two poles travel; everything else on screen follows them.
What to observe
- Start on RC with a step. The capacitor does not jump, because jumping would need infinite current through R. It fills at a rate set by how much is still missing, which is what makes the curve an exponential, and after one τ = RC it has covered 63% of the gap. That mark is drawn on the scope.
- Now RL. The roles swap: the current is what refuses to jump, and the inductor briefly puts the whole source voltage across itself to stop it. Same shape, same kind of τ = L/R, but the quantity that has inertia is the current rather than the charge.
- Switch to RLC and drop R low. Now there are two stores and they argue: the capacitor dumps into the inductor, the inductor refuses to stop and overcharges the capacitor the other way, and the whole thing rings. Watch the energy panel, where the two bars trade back and forth while the total slowly leaks away through R.
- Raise R and watch the ringing die sooner. Keep going and atζ = 1 it stops ringing at all: the fastest approach that never overshoots, which is why critically damped is what you want a door closer or a car suspension to be. Past that it is overdamped and just sluggish.
- Switch the side panel to Poles and do it again. Underdamped, they sit as acomplex pair, their distance from the origin is ω₀ and their height is the frequency you can hear in the ringing. At ζ = 1 they collide on the real axis and then split apart along it. Every shape the scope draws is already written there.
- Switch the source to Sine and sweep the frequency. Slow, and the output follows the input; fast, and it cannot keep up. The Bodepanel is that whole experiment done at once, and the point where it has fallen by 3 dB is the same 1/τ the step response showed you. One circuit, one number, two apparently unrelated measurements.
- With RLC underdamped, put the drive right on f₀. The output climbs well past the input: at resonance the reactances cancel and only R is left to limit anything, so the capacitor voltage overshoots the source by roughly Q. Turn R down to make Q large and watch how long it takes the amplitude to build.
Shortcuts: space run/pause · s step · r reset · f fullscreen