Rails Break the Linear Contract - Electronic Circuits V & VI: Front-End Conditioning and Op-Amp Feedback Step by Step

This rails-break-linear-contract lesson shows the boundary where the ideal feedback rule stops applying: a 15 V requested output clips at the 12 V rail. Once clipped, the plus and minus inputs no longer match, so the circuit is in a saturated piecewise state rather than the linear op-amp contract. Real devices add rail headroom, output-current limits, recovery time, finite gain, offset, slew-rate limits, tolerances, and measurement uncertainty.

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.

V_{\text{request}} = 15\ \text{V} > 12\ \text{V}

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\ \text{V}\ne V_- = 4\ \text{V}