= Square-wave response of an RC low-pass filter
{title2=$v_p=A\tanh[T/(4RC)]$}
For an equal-duty <square wave> alternating between $\pm A$ with period $T$, the steady periodic <capacitor> <voltage> has extrema $\pm v_p$. A positive half-period maps $-v_p$ to $A-(A+v_p)e^{-T/(2RC)}=v_p$, proving the title formula. The negative half-period is its sign-reversed copy. Short periods give a small nearly triangular output; long periods give input-like plateaux with exponential transitions.
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