Threshold Margin Scan - Electronic Circuits II & III: Decision Networks and Interfaces Step by Step

This threshold model uses a strict greater-than rule, so equality stays open and only an above-threshold control voltage closes the load path. The 5 V boundary and 3 A load row are exact training cases; real interfaces need hysteresis, noise margin, input offset, propagation delay, source loading, and measurement uncertainty.

A controlled switch needs below, equality, and above-threshold rows before a margin 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 switch helper uses a strict greater-than threshold

This ideal interface closes only when control voltage is greater than threshold. Equality is still open, so the boundary row must be shown instead of assumed.

V_c>V_{\text{th}}\Rightarrow\text{closed}

Three control rows expose the boundary

The source and load stay fixed. Only the control voltage changes, so the current column is a checked consequence of the strict comparison.

\begin{array}{c|c|c|c}V_c&V_{\text{th}}&\text{state}&I_L\\1\ \text{V}&5\ \text{V}&\text{open}&0\ \text{A}\\5\ \text{V}&5\ \text{V}&\text{open}&0\ \text{A}\\9\ \text{V}&5\ \text{V}&\text{closed}&3\ \text{A}\\\end{array}

Equality does not close this model

For the rendered boundary row, control and threshold are both 5 volts. The switch is open and load current is 0 amperes.

5\ \text{V}=5\ \text{V}\Rightarrow I_L=0\ \text{A}

Only the above-threshold row carries load current

The high control row is 9 volts, so the closed load path gives 3 amperes from a 12 volt source and 4 ohm load.

12\ \text{V}/4\ \text{ohm}=3\ \text{A}

The margin audit avoids a fuzzy threshold story

The lesson claims only this ideal static rule. It does not add device gain, hysteresis, noise margin, or timing delay.

V_c=V_{\text{th}}\Rightarrow\text{open},\quad V_c>V_{\text{th}}\Rightarrow\text{closed}