Feedback Gain Cross Scans

Summing Current Three-Row Scan

branch currents become output

An inverting summer adds branch currents at the virtual node before the feedback resistor converts the total into an output voltage. The three rows are exact only for the declared branch currents, feedback resistor, and ideal op-amp assumptions; real summing amplifiers inherit resistor tolerance, source impedance, input bias and offset, finite gain-bandwidth, rail headroom, slew limits, loading, noise, temperature drift, and voltage/current measurement uncertainty.

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