Sensor Gain Three-Row Scan - Electronic Circuits IX & X: Feedback Control and Sampled Conversion Step by Step

Sensor gain changes how strongly the output is reported back to the comparator, so a larger sensor gain can reduce the output needed to balance the same target. With a 12 V target the sensor gains 1, 2, and 3 close at outputs 6, 4, and 3 V exactly for the ideal proportional loop; real sensors add calibration error, offset, noise, bandwidth limits, delay, loading, temperature drift, and voltage measurement uncertainty.

Holding target and forward gain fixed isolates sensor gain as a source factor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Sensor gain one measures output directly

Target 12 volts and sensor gain 1 close at output 6 volts.

y={12\over 2}=6\ \text{V}

Sensor gain two lowers the output

Sensor gain 2 makes output 4 volts read as measured feedback 8 volts.

y={12\over 3}=4\ \text{V},\quad m=8\ \text{V}

Sensor gain three lowers the output again

Sensor gain 3 gives output 3 volts and measured feedback 9 volts.

y={12\over 4}=3\ \text{V},\quad m=9\ \text{V}