# How to derive the transfer function of the Inverting Summing Amplifier?

I know that the transfer function of an inverting summing amplifier gives this, by using the Superposition principle: (for example with 2 input voltages)

$U_{ out }=-(\frac { R_{ 1 } }{ R_{ f } } U_{ in1 }+\frac { R_{ 2 } }{ R_{ f } } U_{ in2 })$

However, I don't exactly know how to derive this from the transfer function definition:

$H = U_{out}/U_{in} = G(U_{+}-U_{-})/U_{in}$

This is not explained in any book or on the Web. Can anyone explain this?

Thanks a lot!

• U+ is zero and U- can be found using again superposition. That`s all. But you have to realize that there are TWO transfer functions because you have two input voltages, unless you define Uin as the sum of both input signals.
– LvW
Commented Oct 25, 2015 at 16:35
• I know that U+ is 0. Commented Oct 25, 2015 at 16:37
• So, I need to transfer functions and then sum them? Like: H1 = Uout/Uin1 and H2 = Uout/Uin2 ? Commented Oct 25, 2015 at 16:38
• Ok! I got it! I did it by having 2 transfer functions! Would you like to post it as an answer so that I accept it? Commented Oct 25, 2015 at 16:52
• I think it is OK so. Congratulations.
– LvW
Commented Oct 25, 2015 at 19:25