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Dynamic RC Low-Pass Filter

Analog

A first-order shunt-capacitor filter. The cutoff and the $|H(j\omega)|$ magnitude are derived live; the output wire fades its opacity and stretches its dash pattern to visualise physical damping, and both channels drive the oscilloscope.

6 components · 6 connections · frequency-domain transfer function

the aha
A capacitor is a bucket. Slow signals fill it; fast ones wiggle away before it can respond.

why it works

The capacitor needs time to charge through

R

, and that time sets a verdict. Below the cutoff

f_c = \frac{1}{2\pi RC}

the bucket keeps up and the output follows the input. Above it, the signal reverses before the bucket fills, so the amplitude collapses as

|H(j\omega)| = \frac{1}{\sqrt{1 + (f/f_c)^2}}

. At

f = f_c

exactly, the output has dropped to

\frac{1}{\sqrt 2} \approx 0.707

of the input — the famous −3 dB point, the frequency where the filter says "this is where I start giving up."

governing model

f_c = \dfrac{1}{2\pi RC} \;\cdot\; |H(j\omega)| = \dfrac{1}{\sqrt{1 + (f/f_c)^2}}

structural inventory

input source node
series resistor $R$
shunt capacitor $C$
reference ground

boundaries

$R: 100\ \Omega$ – $1\ \mathrm{M\Omega}$
$C: 1\ \mathrm{nF}$ – $10\ \mathrm{\mu F}$
sweep $10\ \mathrm{Hz}$ – $100\ \mathrm{kHz}$

fault relay capacitor branch open

Sweep the frequency slider past the cutoff.

Watch the output trace fade and its dash-pattern stretch as $f$ climbs past $f_c$ — the fading is the attenuation, drawn in real physical proportion.
Halve C and watch the cutoff move.

Smaller bucket, faster response: $f_c$ doubles. The filter now passes signals it used to block — you moved the verdict by changing one component.
Open the capacitor branch.

With nowhere to dump charge, there is no pole at all — the filter stops filtering and the output tracks the input at every frequency.

causal signal trace paused

Apply $V_{in}$ The source establishes the stimulus and the return reference.

t_{stage} = 0.00 s

step 1 / 4 Apply Vᵢₙ

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