Op-Amps having negative feedback

same input.

– The noninverting input is grounded.

– For finding the gain, let’s assume there is infinite impedance at the input (i.e. between the inverting and non-inverting inputs).

– Infinite input impedance implies zero current at the inverting input.

– If there is zero current through the input impedance, there is NO voltage drop between the inverting and noninverting inputs.

– Thus, the voltage at the inverting input is zero!

- The zero at the inverting input is referred to as virtual ground.

– Since there is no current at the inverting input, the current through R_i and the current through R_f are equal:

I_in = I_f.

– The voltage across R_i equals V_in because of virtual ground on the other side of the resistor. Therefore we have that

I_in = V_in/R_i.

– Also, the voltage across R_f equals –V_out, because of virtual ground. Therefore:

I_f = -V_out/R_f

– Since I_f = I_in, we get that:

-V_out/R_f = V_in/R_i

– Or, rearranging,

V_out/V_in = -R_f/R_i

– So,

A_cl(I) = -R_f/R_i

– Thus, the closed loop gain is independent of the op-amp’s internal open-loop gain.

– The negative feedback stabilizes the voltage gain.

– The negative sign indicates inversion.

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