Comparator Sense Margin Three-Row Scan - Electronic Circuits III: Comparators and Interfaces Step by Step

A comparator decision table needs low, equality, and high sense rows before the output rail claim is trusted. 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 comparator compares two voltmeter readings

The minus input is held fixed while the plus input is scanned. The equality row is included because this book defines a low-on-tie decision rule.

V_+>V_-\Rightarrow V_{\text{out}}=V_{\text{HIGH}}

Three sense rows show below, tie, and above

The table makes the output rail a consequence of the comparison. There is no analog middle output in this ideal comparator model.

\begin{array}{c|c|c|c}V_+&V_-&\text{state}&V_{\text{out}}\\4\ \text{V}&6\ \text{V}&\text{LOW}&0\ \text{V}\\6\ \text{V}&6\ \text{V}&\text{LOW}&0\ \text{V}\\8\ \text{V}&6\ \text{V}&\text{HIGH}&12\ \text{V}\\\end{array}

Equal inputs use the stated tie rule

In the boundary row, both inputs read 6 volts. The output is the 0 volt low rail.

6\ \text{V}=6\ \text{V}\Rightarrow V_{\text{out}}=0\ \text{V}

Decision rows must be read before downstream loading

This scan stops at the ideal output rail. Output resistance, load current, hysteresis, and noise are separate budgets in later rows.

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