Weighted Summer Shows Resistor Weights - Electronic Circuits V & VI: Front-End Conditioning and Op-Amp Feedback Step by Step

Different input resistors set different virtual-ground currents, so each branch enters the summing node with its own weight set by resistance. The 2 ohm and 3 ohm input branches carry 1 A and 2 A for 3 A total, and the 2 ohm feedback yields -6 V exactly for the ideal op-amp model; real summers add input bias and offset, finite open-loop gain and bandwidth, resistor tolerance, rail limits, source impedance, loading, and measurement uncertainty.

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.

I_{\text{total}} = 1\ \text{A} + 2\ \text{A} = 3\ \text{A}

Feedback turns weighted current into voltage

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

V_{\text{out}} = -\left(3\ \text{A}\right)\cdot 2\ \text{ohm} = -6\ \text{V}