Three input-voltage rows contrast non-inverting proportional gain with inverting gain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One volt through gain three gives three volts

The feedback divider fixes gain 3. A 1 volt input gives 3 volts without inversion.

Vout=31 V=3 VV_{\text{out}}=3\cdot1\ \text{V}=3\ \text{V}
One-volt non-inverting source rowThe output follows the input sign.+-op amprails -12 V to 12 VVout 3 VV+ 1 VV- 1 VI+ 0 AI- 0 AVin 1 VRg 2 ohmRf 4 ohmV+ = V-noninverting

Two input volts make six output volts

Only the source input changes to 2 volts. Gain 3 makes 6 volts.

Vout=32 V=6 VV_{\text{out}}=3\cdot2\ \text{V}=6\ \text{V}
Two-volt non-inverting source rowThe divider ratio stays fixed.+-op amprails -12 V to 12 VVout 6 VV+ 2 VV- 2 VI+ 0 AI- 0 AVin 2 VRg 2 ohmRf 4 ohmV+ = V-noninverting

Three input volts close the proportional scan

The third source row is 3 volts, and the output is 9 volts. The sign is not flipped.

Vout=33 V=9 VV_{\text{out}}=3\cdot3\ \text{V}=9\ \text{V}
Three-volt non-inverting source rowThree source rows separate gain from input size.+-op amprails -12 V to 12 VVout 9 VV+ 3 VV- 3 VI+ 0 AI- 0 AVin 3 VRg 2 ohmRf 4 ohmV+ = V-noninverting