Assume ideal operational amplifiers in the circuit of Figure P5.50.

a. Show that the leftmost operational amplifier works as a subtracting amplifier. Namely, v₁ = v_o - v_in.

b. Draw a block diagram of the system, with the subtracting amplifier represented with a summing junction, and the circuit of the rightmost operational amplifier with a transfer function in the forward path. Keep R as a variable.

c. Obtain the system’s closed-loop transfer function.

d. For a unit step input, obtain the value of R that will result in a settling time T_s = 1 msec.

e. Using the value of R calculated in Part d, make a sketch of the resulting unit step response.

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0.1 F 10 k R 10 k No Vin M. + 10 k 10 k FIGURE P5.50