Explain the operation of an op amp as an inverting summer.?

Question

Explain the operation of an op amp as an inverting summer.

Answer 1

The sum of the currents through each input resistor (from each voltage source), must equal the current through the negative feedback resistor This is assuming the offset and bias currents out of the negative input are negligible, AND, that the positive input of the op amp is connected to signal ground (may be through a resistor).

If the positive input is at signal ground potential, then the negative input must also be at ground potential, or the op amp will 'rail' at the output. The negative feedback current forces the voltage at the negative input to match the positive input (zero volts). This is why the negative input is called a 'virtual' ground. You can use this fact to make your calculations.

Since the voltage at the negative input is 0, you can easily calculate each current through each input resistor. It will be V/R. V1/R1, V2/R2, V3/R3... etc.
The current in the negative feedback resistor is the sum of all of those input currents: V1/R1+V2/R2+V3/R3...
The voltage across it is that sum * Rfb
But the voltage is across it is also -Vout-0, so the final function becomes:

Vout = -Rfb * (V1/R1+V2/R2+V3/R3...)

I hope I was clear.

.