Term Project - The Step Response of RLC Circuits

The team project pertains to Chapter 9 in the text book. You should submit a single report and Multisim/ LTSpice file. The report should be submitted as a Word document and include the following items.

1. Title page - The title page should include the title of the project, names and date.

2. Introduction - The introduction should include the background and theory of the project.

3. Questions - This section includes calculations and answers to all questions.

4. Simulation Results - This section includes the circuits built in Multisim/LTSpice and simulation results.

5. Discussion - This is the section where the results are explained.

6. Conclusion - This section includes one or two sentences that summarize the conclusions from the results.

Series RLC Circuits

The initial energy stored in the circuit in Figure 1 is zero. The dc voltage source, 5V, is applied to the circuit at t = 0. The value of the inductor is 25 mH and the capacitor is 25nF.

a) Finding the Overdamped Step Response When the value of R is 2.5 k?, find the expression for V_c(t) when t > 0.

b) Finding the Critically Damped Step Response When the value of R is 2 k?, findthe expression for V_c(t) when t > 0.

c) Finding the Underdamped Step Response When the value of R is 1.5 k?, find the expression for V_c(t) when t > 0.

d) Comparing the Three Step Response Conditions

(i)  Build the circuits in Multisim/LTSpice and measure V_c(t) from part a) to part c). Plot the above three step responses on a single graph, over a range from 0 to 200 µs.

(ii) Use the plot of (i) to find the time required for V_c to reach 90% of its final values.

(iii) On the basis of the circuits obtained in (ii), which response reaches 90% of the final value of the output in the shortest time?

(iv) Which response ensures that the final value of the current is never exceeded?