Feedback Gain Cross Scans

Summing Current Three-Row Scan

branch currents become output

The inverting summer is a current ledger followed by feedback conversion. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Equal branch currents make a two-ampere total

The two input branches each contribute 1 ampere. Total current 2 amperes through the feedback resistor gives -4 volts.

Itotal=1 A+1 A=2 A,Vout=−(2 A)⋅2 ohm=−4 VI_{\text{total}}=1\ \text{A}+1\ \text{A}=2\ \text{A},\quad V_{\text{out}}=-\left(2\ \text{A}\right)\cdot2\ \text{ohm}=-4\ \text{V}
Summing current scan rowThe virtual node adds input currents before feedback.+-op amprails -12 V to 12 VVout -4 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 1 AR2 4 ohmI2 1 ARf 2 ohmIf 2 AV+ = V-summing

A lower input resistor contributes more current

The first branch contributes 1 ampere and the second contributes 2 amperes. The output is -6 volts.

Itotal=1 A+2 A=3 A,Vout=−(3 A)⋅2 ohm=−6 VI_{\text{total}}=1\ \text{A}+2\ \text{A}=3\ \text{A},\quad V_{\text{out}}=-\left(3\ \text{A}\right)\cdot2\ \text{ohm}=-6\ \text{V}
Summing current scan rowCurrent weights come from voltage divided by input resistance.+-op amprails -12 V to 12 VVout -6 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 1 AR2 3 ohmI2 2 ARf 2 ohmIf 3 AV+ = V-summing

Raising both branch currents raises the output magnitude

Both branches now contribute 2 amperes. The total is 4 amperes, and the output is -8 volts.

Itotal=2 A+2 A=4 A,Vout=−(4 A)⋅2 ohm=−8 VI_{\text{total}}=2\ \text{A}+2\ \text{A}=4\ \text{A},\quad V_{\text{out}}=-\left(4\ \text{A}\right)\cdot2\ \text{ohm}=-8\ \text{V}
Summing current scan rowThree rows show the summer as current addition plus feedback conversion.+-op amprails -12 V to 12 VVout -8 VV+ 0 VV- 0 VI+ 0 AI- 0 ARin 2 ohmIin 2 AR2 3 ohmI2 2 ARf 2 ohmIf 4 AV+ = V-summing