Ideal Feedback Contract

Rails Break the Linear Contract

saturation is piecewise

A rail-limited output stops satisfying the equal-input feedback condition. 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 feedback formula requests more than the rail

The linear request is 15 volts, above the high rail of 12 volts.

Vrequest=15 V>12 VV_{\text{request}} = 15\ \text{V} > 12\ \text{V}
Requested outputThe requested output is beyond the available rail.+-op amprails -12 V to 12 VVout 12 VclippedV+ 5 VV- 4 VI+ 0 AI- 0 AVin 5 VRg 3 ohmRf 6 ohmV+ != V-noninverting

The rail breaks the equal-input contract

The clipped output is 12 volts, and the feedback node is only 4 volts while the plus input is 5 volts.

V+=5 V≠V−=4 VV_+ = 5\ \text{V}\ne V_- = 4\ \text{V}
Clipped outputThe saturated state shows the broken equality.+-op amprails -12 V to 12 VVout 12 VclippedV+ 5 VV- 4 VI+ 0 AI- 0 AVin 5 VRg 3 ohmRf 6 ohmV+ != V-noninverting