Mathematically the voltage gain offered by the circuit is given as Where,
However, it is to be noted that ideal Op-Amps have infinite input impedance due to which the currents flowing into its input terminals are zero i.e. I1 = I2 = 0. Thus, Ii = -If. Further, as the non-inverting terminal is grounded (V2 = 0), one gets V1 = 0 due to the fact that the voltages at the inverting and the non-inverting terminals of an ideal Op-Amp are equal. Hence,
Substitution V1 and If in equation of Vo yields This indicates that the voltage gain of the inverting amplifier is decided by the ratio of the feedback resistor to the input resistor; with the minus sign indicating the phase-reversal. Further, it is to be noted that the input impedance of the inverting amplifier is nothing but Ri. Inverting amplifiers exhibit excellent linear characteristics which make them ideal to be used as DC amplifiers. Moreover they are often used to convert input current to output voltage in the form of Transresistance or Transimpedance Amplifiers. Further these can also be used in audio mixers when used in the form of Summing Amplifiers.