EP 214 Assignment 6

Engineering Physics 214 Assignment 6 This assignment is worth 45 marks. Due: Tuesday February 27, 2024 at 10:00am For this assignment you will need to use the files Assignment6Template.m, Inhomogeneous- RLCTemplate.m, UnitStep.m and UnitImpulse.m that can be found on Canvas along with this assignment. InhomogeneousRLCTemplate.m is an incomplete version of the function that you will need to complete this assignment. Assignment6Template.m is an incomplete version of the script file that you will need to create to complete this assignment. UnitStep.m and UnitImpulse.m contain functions that are helpful for constructing the input voltage and the unit impulse response. Questions 1 is to be done by hand. For question 2, submit your MATLAB function. For questions 3, 4, 5, and 6, submit your graphs, MATLAB files, and your documentation for question 6. All your graphs and written work should be combined into a single pdf file and your MATLAB code should be submitted as .m files. 1. (10 marks) For this question, and all remaining questions, consider a series RLC circuit that is not critically damped, has zero initial charge and current ( q (0) = 0, i (0) = 0), and an input voltage source v ( t ). Derive the unit impulse response for the charge on the capacitor h q ( t ), the unit impulse response for the current in the circuit h i ( t ), and the unit impulse response for the time derivative of the current h di dt ( t ). 2. (5 marks) Fill in the template MATLAB file InhomogeneousRLCTemplate.m to write a func- tion that calculates the capacitor charge q ( t ), current i ( t ), and the time derivative of the current di ( t ) dt using the built-in MATLAB convolution function and unit impulse responses from question 1. 3. (5 marks) For L = 10 mH and C = 1 μ F, choose values of R to make two graphs that clearly show the behaviour of the unit impulse response of the capacitor charge h q ( t ) for an underdamped case and an overdamped case. Make sure to include the R, L and C values on your graphs. 4. (5 marks) In Assignment6Template.m there is some code to make an input voltage source. Note that the input voltage is only non-zero between 5 ms and 15 ms . Write your own code to make a second input voltage source that is 5 V between these same two time values and zero elsewhere. Make a graph that shows the two different voltage sources. 5. (10 marks) Use the input voltage source provided in Assignment6Template.m, and the MAT- LAB function in that you wrote in question 2, to plot the voltage drop across each of the RLC components and the total voltage drop across all three components. Choose values of R to make a graph for an underdamped case and a second graph for an overdamped case. 6. (10 marks) For this question you will need to use the second input voltage source that you made in question 4. Use your code to design an RLC series circuit such that the maximum voltage drop across the capacitor is 6 . 00 V ± 0 . 01 V . Document your design procedure and include plots that show the voltage drop across all of the components. The documentation must include a discussion of the component values and why you chose them. Make sure to include the final R, L and C values.