# Transfer Function, Impulse Response and Steady State Analysis

Please refer to the attached file.

1. What is the response function of the circuit in the s-domain?

2. What are the poles? Is than an impulse response stable circuit?

3. What are the poles? Is than an impulse response stable circuit?

4. What is the natural response of the circuit?

5. Is the circuit impulse stable?

6. Is the circuit impulse stable? What is the neutral response?

7. Consider a series RLC circuit. The initial voltage across the capacitor is 2 V and the initial current flowing in the circuit is zero amps. Find the voltage across the capacitor in the s domain and determine if the circuit is stable.

8. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with , connected in series to the load. What is the impedance of the load? Use phasor transform methods to obtain your answer.

9. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source connected in series to the load. What is the current flowing through the load? Use phasor transform methods to obtain your answer.

10. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source connected in series with the load. What is the average power delivered to the load?

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#### Solution Summary

Complete calculations for the circuit problems are formatted and included in the attached Word document.

Transfer Functions and Steady State Analysis

Please help in understanding how to solve the following problems.

1. The impulse response for a circuit is h(t) = e^-t, t >= 0. What is the response function of the circuit in the s-domain if the input is f(t) = cos(2t)?

2. The transfer function for a circuit is H(s) = 1/[(s+2)(s+5)]. What are the poles? Is this an impulse response stable circuit?

3. The transfer function for a circuit is H(s) = 1/[(s-2)(s+5)]. What are the poles? Is this an impulse response stable circuit?

4. Suppose that H(s) = (s+4) / [(s+4)^2 + 49]. What is the natural response of the circuit?

5. If H(s) = (s+4) / [(s+4)^2 + 49], is the circuit impulse stable?

6. If H(s) = (s-4) / [(s-4)^2 + 49], is the circuit impulse stable? What is the natural response?

7. Consider a series RLC circuit with R = 2 Ohm, C = 1/2 F, and L = 4 H. The initial voltage across the capacitor is 2 V and the initial current flowing in the circuit is zero amps. Find the voltage across the capacitor in the s domain and determine if the circuit is stable.

8. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with v(t) = 100 cos(50t), connected in series to the load. What is the impedance of the load? Use phasor transform methods to obtain your answer.

9. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with v(t) = 100 cos(50t), connected in series to the load. What is the current flowing through the load? Use phasor transform methods to obtain your answer.

10. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with v(t) = 100 cos(50t), connected in series with the load. What is the average power delivered to the load?

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