= Amplifier clipping
\b[Amplifier clipping] occurs when an <electronic amplifier> cannot follow the output amplitude predicted by its small-signal <voltage gain>. Its finite <amplifier output range> truncates the waveform. For a deliberately simple, instantaneous model with positive gain $G$ and fixed lower and upper output limits,
$$
v_o(t)=\operatorname{clip}(Gv_i(t))
=\min\!\bigl(V_{\rm hi},\max(V_{\rm lo},Gv_i(t))\bigr).
$$
Here $v_i$ and $v_o$ are input and output <electric potential differences>. The flat portions express a <nonlinearity>: doubling an already excessive input need not change the output. Real output limits depend on the supply, load and output stage. They need not equal the supply rails. Texas Instruments' example <integrating amplifier> uses separate supply and output-range design goals and explains how unrestricted DC integration eventually reaches saturation.<Integrator Circuit by Pete Semig>[p1, Design Goals and Design Description]{ref}
<Amplifier clipping> can corrupt an area measurement even when the waveform still looks easy to integrate. Suppose $G=10$, $V_{\rm lo}=-2\,\mathrm V$, $V_{\rm hi}=2\,\mathrm V$, and a rectangular input is $0.4\,\mathrm V$ for $1\,\mathrm{ms}$ and zero otherwise. Its true area is $0.4\,\mathrm{V\,ms}$, but the ideal unclipped output of $4\,\mathrm V$ is reduced to $2\,\mathrm V$. Dividing the <clipped waveform area> by the gain gives
$$
\widehat A_i=\frac1G\int v_o(t)\,dt
=0.2\,\mathrm{V\,ms},
$$
\b[50% below the true input area]. Any rectangular input at or above $0.2\,\mathrm V$ with the same duration produces this same clipped plateau in the stipulated model. Subsequent <integration> cannot recover which of those input amplitudes was present.
A useful bench experiment feeds a repeatable pulse into an <electronic amplifier> and records both input and output on an <oscilloscope>. Increase the input amplitude while holding the gain, pulse duration and load fixed. The output first scales with the input, then ceases to do so near its limits. Reducing the gain tests whether an apparent input plateau is actually a receiver limit. Comparing measured areas before and after that change reveals the <clipped waveform area> bias directly.
The instantaneous clipping formula does not describe the internal dynamics of a saturated <integrating amplifier>. Once its feedback assumptions fail, recovery can take additional time. The ACF2101's historical datasheet explicitly distinguishes output overload from ordinary reset and describes extra recovery delay; the relevant behavior must be characterized for the actual circuit.<ACF2101 Low Noise, Dual Switched Integrator datasheet>[p10, Output Overload]{ref} An <integrator reset> establishes a new starting state, while a suitable input range prevents information being lost before that reset.
\Image[/amplifier-clipping-and-integrator-reset.png]
{title=Ideal pulse clipping loses area, while a finite reset leaves an exponentially decreasing residual; the separate dashed level illustrates a stipulated charge-injection pedestal.}
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