D *2.69 To obtain a high-gain, high-input-resistance difference amplifier, the circuit in Fig. P2.69 employs positive feedback, in addition to the negative feedback provided by the resistor R connected from the output to the negative input of the op amp. Specifically, a voltage divider (R5, R6) connected across the output feeds a fraction β of the output, that is, a voltage βvO, back to the positive-input terminal of the op amp through a resistor R. Assume that R5 and R6 are much smaller than R so that the current through R is much lower than the current in the voltage divider, with the result that β R6|(R5 +R6). Show that the differential gain is given by A d ≡ v O v Id = 1 1−β (Hint: Use superposition.) Design the circuit to obtain a differential gain of 10 V/V and differential input resistance of 2 M. Select values for R, R5, and R 6, such that (R5 +R6) ≤ R/100.