A voltage rail limits a gain stage without changing the filter ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The ideal gain request is above the rail

Input 3 volts with gain 3 asks for 9 volts.

33=93\cdot 3=9
Gain requestThe gain contract computes the requested output.V3 VV8 V+-3 V+-8 Vgain

The rail limit is not a filter ratio

The upper rail is 8 volts, so the checked output clips to 8 volts.

Vout=8 VV_{\text{out}}=8\ V
Rail-limited outputClipping is checked separately from filter ratio.V3 VV8 V+-3 V+-8 Vgain