Comparator Output Rule - Electronic Circuits II & III: Decision Networks and Interfaces Step by Step

A comparator-output-rule scan drives an ideal open-loop comparator from exact input voltages, checking that the greater plus input selects the high rail and the lower plus input selects the low rail row by row. The arithmetic is exact only for the stated input voltages, output voltages, rails, and rows in the ideal comparator model. Real comparators add input offset, hysteresis, noise, finite response time, reference tolerance, probe/calibration limits, finite precision, and measurement uncertainty.

An ideal open-loop comparator chooses a rail from exact input voltages and a stated rule. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Greater plus input selects the high rail

The plus input is 8 volts and the minus input is 6 volts, so the ideal comparator output is 12 volts.

8\ \text{V} > 6\ \text{V}\Rightarrow V_{\text{out}} = 12\ \text{V}

Lower plus input selects the low rail

When the plus input is 4 volts and the minus input is 6 volts, the output is 0 volts. Linear op-amp gain and feedback are deferred.

4\ \text{V} < 6\ \text{V}