How do you derive the gain of a non-inverting amplifier from basic principles?

Question

I know the gain is 1+(R2/R1), but the full derivation isn't written in my notes and I need it for a piece of coursework, please help!

Answer 1

Look at the inverting and non-inverting terminals on the op-amp. In 'normal' operation, the voltages (v1, v2) have to be the same. Since the inverting input is fed from the output ov the op-amp through a simple divider circuit, the voltage seen at the non-inverting input is
Vo*(R1/(R1+R2)) so
Vi = Vo*(R1/(R1+R2)) and
Vo = Vi*((R1+R2)/R1)= Vi(1+R2/R1)

HTH ☺

Doug

Answer 2

confident, your question is obscure. The income of an inverting configuration is -Rf/Ri. The income of a non inverting configuration is (Rf+Ri)/Ri. it extremely is undemanding to coach that it extremely is the case by assuming an appropriate amplifier. The bandwidth would be on the factor of GBWP divided by the closed loop income.