Summing and Difference Networks

Weighted Summer Shows Resistor Weights

currents encode weights

Different input resistors give different exact current weights into the same node. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Different resistors make different current weights

The first branch contributes 1 ampere, and the lower-resistance second branch contributes 2 amperes.

Itotal=1 A+2 A=3 AI_{\text{total}} = 1\ \text{A} + 2\ \text{A} = 3\ \text{A}
Weighted currentsThe resistor values set the input weights.+-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

Feedback turns weighted current into voltage

The total current is 3 amperes through 2 ohms, again producing -6 volts.

Vout=−(3 A)⋅2 ohm=−6 VV_{\text{out}} = -\left(3\ \text{A}\right)\cdot 2\ \text{ohm} = -6\ \text{V}
Weighted summer outputThe same output can come from a different current/resistor pair.+-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