Question

The op amp in the circuit shown below is ideal. The adjustable resistor has a maximum value of 100 k Ohm , and alpha is restricted to the range of 0.2 a 1.0. Calculate the range of v0 if vg = 40mV. If alpha is not restricted, at what value of alpha will the op amp saturate?

Answer 1

Let v_Delta be the voltage from the potentiometer contact to ground. Use Kirchhoff's current;aw to write the below equations 0 - v_g/2000 + 0 - v_Delta/50000 = 0 - v_g/2000 + - v_Delta/50000 = 0 - 25 v_g/50000 = 0 - 25 v_g - v_Delta = 0 - 25 v_g = v_Delta - 25 v_g = v_Delta v_Delta = - 25 (40 times 10^- 3) v_Delta = - 1 V Apply Kirchhoff's current law at node v_Delta v_Delta/alpha R_Delta + v_Delta - 0/50000 + v_Delta - v_0/(1 - alpha) R_Delta = 0) = v_0/(1 - alpha) R_Delta v_Delta (1/alpha + R_Delta/50000 + 1/(1 - alpha)) = v_0/(1 - alpha) v_Delta (1/alpha + 2 + 1/(1 - alpha)) = v_0/(1 - alpha) By further simplification v_0 = v_Delta ((1 - alpha)/alpha + 2 (1 - alpha) + 1) (1) Substitute alpha = 0.2 in the equation (1), v_0 = v_Delta ((1 - alpha)/alpha + 2 (1 - alpha) + 1) = (- 1) ((1 - 0.2)/0.2 + 2 (1 - 0.2) + 1)