Electric circuit, Bode plots

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Electric Circuit Problems:

1. Given the circuit shown below in Fig. 1.1, where the output signal is the capacitor voltage, v(t):

a. Identify the frequency-domain system (or transfer) function.

b. Create a Bode Plot, Magnitude and Phase, for the system function.

c. Mathematically show what this circuit will do to an input signal, vs(t) = 100 cos(ωt); for ω = 0, 10, 103 and 105 rad/s.

Fig. 1.1

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2. Given the circuit shown below in Fig. 2.1, where the output signal is the voltage across the inductor and the 2ohms resistor, v(t):

a. Identify the frequency-domain transfer function.

b. Create a Bode Plot, Magnitude and Phase, for the system function.

c. Mathematically show what this circuit will do to an input signal, vs(t) = 100 cos(ωt); for ω = 0, 10, 103 and 105 rad/s.

Fig. 2.1

Shown in Fig. 3.1 is an op-amp circuit.

3. Given the circuit shown below in Fig. 3.1, where the output signal is the op amp output voltage, vo(t). Let R1 = R2 = R3 = 3 k ohms and C = 1/9 μF:

a. Identify the frequency-domain system (or transfer) function.

b. Create a Bode Plot, Magnitude and Phase, for the system function.

c. Mathematically show what this circuit will do to an input signal, v(t) = 100 cos(ωt); for ω = 0, 10, 103 and 105 rad/s.

Fig. 3.1