Inverting Amplifier Gain Analysis

This is a constant gain amplifier with negative feedback where the input signal is applied to the inverting terminal of the opamp.  The resultant output is inverted.

As per Kirchoff’s Current Law,

I + If = Ii

Opamp input current is Zero i.e Ii = 0

I + If = 0

If Vi is the voltage at the inverting input terminal,

(Vs - Vi)/Ri + (Vo - Vi)/Rf = 0

Opamp input voltages are always equal, ∴ Vi = 0, because non inverting input terminal is connected to ground.

Vs/Ri + Vo/Rf = 0

Vo/Vi = -Rf/Ri

∴ The gain of inverting amplifier is A = -Rf/Ri