Sensor Comparator Load Chain Scan - Electronic Circuits III: Comparators and Interfaces Step by Step

A sensor divider, comparator tie rule, and loaded output stage form one exact interface chain. 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 whole chain is a sequence of exact decisions

The sensor divider sets a sense voltage. The comparator compares that value with a 6 volt reference. The output rail then drives a resistive load through a source resistance.

V_{\text{sense}}\rightarrow\text{comparator rail}\rightarrow V_L

Three sensor rows include tie, low, and high cases

The corrected scan keeps the divider convention explicit: a larger bottom resistor raises the sensed node; a larger top resistor lowers it.

\begin{array}{c|c|c|c|c}V_{\text{sense}}&V_{\text{ref}}&V_{\text{rail}}&V_L&I_L\\6\ \text{V}&6\ \text{V}&0\ \text{V}&0\ \text{V}&0\ \text{A}\\3\ \text{V}&6\ \text{V}&0\ \text{V}&0\ \text{V}&0\ \text{A}\\9\ \text{V}&6\ \text{V}&12\ \text{V}&8\ \text{V}&2\ \text{A}\\\end{array}

Comparator equality selects low in this book

For the rendered row, sense and reference are both 6 volts. The comparator therefore selects the 0 volt rail, and the load current is 0 amperes.

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

A high sensor row still loses voltage in the output stage

The high row senses 9 volts, so the rail is 12 volts. The output source resistance still leaves only 8 volts at the load.

4\ \text{V}+8\ \text{V}=12\ \text{V}

The high-row output power budget is still closed

Only the high rail row carries output power. The zero-rail rows stay at zero current, while the high row closes useful and lost power through the same output stage.

\begin{array}{c|c|c|c}V_{R_s}&V_L&P_L&P_{R_s}\\0\ \text{V}&0\ \text{V}&0\ \text{W}&0\ \text{W}\\0\ \text{V}&0\ \text{V}&0\ \text{W}&0\ \text{W}\\4\ \text{V}&8\ \text{V}&16\ \text{W}&8\ \text{W}\\\end{array}