Created by Created June 14, 2013 Last modified June 14, 2013 Tags

### Summary

Why does does a rail-less opamp connected as feedback amplifier with a negative open loop gain (i.e. as an inverting amplifier) still invert even when the open loop gain is positive?

### Description

Why does does a rail-less opamp connected as feedback amplifier with a negative open loop gain (i.e. as an inverting amplifier) still invert even when the open loop gain is positive?

These sums describe the output voltage of an ideal opamp with an open loop gain of Avol.

They show that for ABS(Avol) > (1+R2/R1), the closed loop gain of the opamp in this configuration is always negative.

As Avol approaches (1+R2/R1), the closed loop gain explodes.

For Avol < (1+R2/R1) the closed loop gain goes positive.

V(out) = V(fb)*Avol

So

V(fb) = V(out)/Avol

The ideal gain block, V2, draws no input current therefore,

I(R1) = I(R2)

Hence

(V(in)-V(fb))/R1 = (V(fb)-V(out))/R2

and so

(V(out)-V(fb))/(Vin)-V(fb)) = -R2/R1

substitute for V(fb)

(V(in)-V(out)/Avol)/R1 = (V(out)/Avol-V(out))/R2

(V(in)-V(out)/Avol)R2/R1 = V(out)(1/Avol-1)

V(in)R2/R1 = V(out)/Avol - V(out) + R2/R1V(out)/Avol

V(in)R2/R1 = V(out)(1/Avol - 1 + R2/R1/Avol)

V(out)/V(in) = R2/R1/(1/Avol - 1 + R2/R1/Avol)

V(out)/V(in) = R2/R1/((1+R2/R1)/Avol - 1)

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