Rail Ceiling Three-Row Scan - Electronic Circuits VI: Op-Amp Feedback and Exact Gain Networks Step by Step

Three rail rows show where the ideal op-amp gain formula stops being available. 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 formula asks for fifteen volts but the rail gives eight

The non-inverting gain asks for 15 volts. With only an 8 volt high rail, the output clips at 8 volts.

V_{\text{out}}=\min(15\ \text{V},8\ \text{V})=8\ \text{V}

A higher rail raises the clipped output

The requested output is still 15 volts, but the high rail is now 10 volts. The output follows that rail.

V_{\text{out}}=\min(15\ \text{V},10\ \text{V})=10\ \text{V}

Twelve volts is still a clipped row

Even at a 12 volt rail, the 15 volt request is unavailable. The output is 12 volts.

V_{\text{out}}=\min(15\ \text{V},12\ \text{V})=12\ \text{V}