In the second part of my demonstration, based on the Superposition Theorem, R2 is connected back to V2 and V1 = 0, by connecting R1 to ground. The non-inverting input voltage V1n, can be written asĪnd, based on the non-inverting amplifier transfer function, Vout1 isīy replacing V1n in (4), the output voltage is If the current in the non-inverting input is zero, R1 and R2 make a voltage divider for V1. The Op Amp is considered an ideal component, so that the input bias currents are negligible. We will first make V2 = 0V, by connecting R2 to ground, as in Figure 3. We are only interested in Vout, so this should be simple. Then we do the same with V1 and then sum up the currents on each branch and the voltage levels on each node. Therefore, if we take out one source, V2, and replace it with a wire, we then can find the voltage in each node and the current in each branch of this circuit due to the remaining source V1. We will use the Superposition Theorem, which says that, the effect of all the sources in a circuit is equal with the sum of the effects of each source taken separately in the same circuit.

I like to derive the transfer function if I need it. If you followed this website, by now you probably figured that I am not a promoter of learning formulas by heart.

If the gain is not needed, this should come up from calculations, as in this article Solving the Summing Amplifier. Therefore, the amplifier in Figure 1 gives us more choices when designing a function with this circuit. It performs the analog summation between V1 and V2, with a gain of 1. In Figure 2, R4 is zero, while R3 is infinity (open connection). One can see that the summing amplifier in Figure 2 is a subset of my preferred schematic in Figure 1. Some authors prefer the following schematic,

Derive op amp offset voltage