RC OP AMP Circuit Design , An upgrade to one of your company’s robotics products requires a proportional plus integral compensator that implements the input-output relationship vOðtÞ ¼ vSðtÞ þ 50 Zt o

vSðxÞdx The input voltage vS(t) comes from an OP AMP, and the output voltage vO(t) drives a 10-kV resistive load. Two competing designs are shown in Figure P6–63. As the project engineer, you are responsible for recommending one of these designs for production. Which design would you recommend and why?

(Your mentor, a wise senior engineer, suggests that you first check that both designs implement the required signal processing function.)

Use MATLAB to solve problem.

(a) Use the capacitor’s i-v characteristic to find the current i(t) for t 0.

(b) Use the inductor’s i-v characteristic and i(t) to find vL(t)
for t 0.

(c) Use vC(t), vL(t), and KVL to find the voltage v(t) delivered to the rest of the circuit.

(d) The v(t) found in

(c) should be proportional to the i(t)
found in (a). If so, what is the equivalent resistance looking into the rest of the circuit?

(e) On the same axes, plot vC(t), vL(t), and v(t). Use a different color for each waveform. Use the plots to verify KVL for the circuit.

Transcribed Image Text:

+ vs(t) 10 w 10 20 1 F ww www + vo(t) 10 10 50 w Design #1 0.4 F + vs(t) + Design #2 + vo(t) FIGURE P6-63