current · voltage · capacitance · feedback
To move the voltage across a capacitor we have to supply current: I = C·dV/dt. Ask for a small, slow signal and the amplifier follows it exactly. Ask for a swing that is too large and too fast and it runs into its current limit — and something less obvious breaks: it stops holding the DC level steady, and stray currents we would never normally notice show up as slow drift. The controls below push it there on demand.
The amplifier can source or sink current only up to ±I_max. Wherever the trace hits the dashed limit and flattens it is marked in yellow — there it is delivering every bit of current it has, with none left over to correct anything.
Following the target needs a peak current of I = C·A·2πf — it grows with both amplitude and frequency. Below the mark the amplifier can supply it. Past the mark the demand exceeds I_max and the voltage simply cannot keep up.
Peak voltage of the target signal.
How fast the target voltage swings.
Most current the amplifier can source or sink.
Real output stages source and sink slightly unequal current.
Leakage, bias, or rectified interference at the output node — normally negligible.
A simplified but faithful model: a capacitor driven by a current-limited amplifier under feedback. Real hardware adds detail, but the two effects shown — the DC level drifting, and quiet stray currents becoming visible — are exactly what saturation does once it starves the feedback loop of current.