Design the circuit shown in Figure DP 10-1 to produce the specified output voltage vo(t)

Chapter 10, Problem DP10-1

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QUESTION:

Design the circuit shown in Figure DP 10-1 to produce the specified output voltage \(v_0(t)=8 \cos \left(1000 t+104^{\circ}\right) \mathrm{V}\) when provided with the input voltage \(v_{\mathrm{i}}(t)=2.5 \cos (1000 t) \mathrm{V}\).

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QUESTION:

Design the circuit shown in Figure DP 10-1 to produce the specified output voltage \(v_0(t)=8 \cos \left(1000 t+104^{\circ}\right) \mathrm{V}\) when provided with the input voltage \(v_{\mathrm{i}}(t)=2.5 \cos (1000 t) \mathrm{V}\).

ANSWER:

Step 1 of 4

Considered voltages    and   can be expressed as phasors:

The reactance   can be determined as follows:

 = 1000 rad/s

Assume that operational amplifier is ideal, which means:

The equivalent circuit diagram is shown on Figure below.

                                               

 

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