Gain Still Has Rails - Electronic Circuits VI: Op-Amp Feedback and Exact Gain Networks Step by Step

Closed-loop gain is checked first, then rails clip unavailable output. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Closed-loop gain gives a requested output first

Gain 3 times 5 volts requests 15 volts.

3\cdot 5\ \text{V} = 15\ \text{V}

The rail decides what output is available

The available output clips to 12 volts, leaving the feedback node at 4 volts instead of 5 volts.

V_{\text{out}} = 12\ \text{V}\qquad V_- = 4\ \text{V}