EE 350 Problem Set 1 Cover Sheet Fall 2014Last Name (Print):First Name (Print):ID number (Last 4 digits):Sectio n:Submission deadl ines:• Turn in the written solutions by 4:00 pm on Tuesday September 9 i n the homework slot outside 121 EE East.Problem Weight Score1 202 203 204 205 20Total 100The solution submitted for grading represents my own analysis of the problem, and not that of another student.Signature:Neatly print the name(s) of the students you coll ab orated with on this assignment.Reading assignment:• Lathi Chapter 1 and Background, Sections B.2 and B.3• Priemer Chapters 1 and 2Problems 1 through 4 review EE 21 0 material. Problem 5 introduces MATLAB com mands for constructing andlabeling plots.Problem 1:(20 points)Consider the RL circuit in Figure 1. You may assume that the switch has been closed long enough for the voltagesand currents to reach steady-state values. At time t = 0 the switch is opened.Figure 1: The switch in the RL circuit is opened at ti me t = 0.1. (6 points) Find the voltage v(0−) and the current i(0−) just befo re the switch is opened.2. (6 points) Find the voltage v(0+) and the current i(0+) immediately after the switch is opened.3. (2 points) Find the voltage v(∞) and the current i(∞) after the switch has been opened for a very long ti me.Justify your answer in one or two sentences.4. (6 points) Find a differential equation that describes the response of the voltage v(t) fo r t ≥ 0.Problem 2:(20 points)Consider the RC circuit in Figure 2. You may assume that the switch has been opened long enough for the voltagesand currents to reach steady-state values. At time t = 0 the switch is closed.Figure 2: The switch in the RC circuit is closed at time t = 0.1. (6 points) Find the voltage v(0−) and the current i(0−) just befo re the switch is closed.2. (6 points) Find the voltage v(0+) and the current i(0+) immediately after the switch is closed.3. (2 points) Find the voltage v(∞) and the current i(∞) after the switch has been closed for a very long time.Justify your answer in one or two sentences.4. (6 points) Find a differential equation that describes the response of the current i(t) for t ≥ 0.Problem 3: (20 points)Consider the RL C circuit in Figure 3. You may assume that the switch has been closed long enough for the voltagesand currents to reach steady-state values. At time t = 0 the switch is opened.Figure 3: The switch in the RLC circuit is opened at ti me t = 0 .1. (10 points) Determine the initial conditions(a) (3 points) i(0+)(b) (7 points)didtt=0+2. (1 point) What is the final value of i(t)? Justify your answer in one or two sentences.3. (9 points) Obtain a second-order differential equation in the current i(t) for t ≥ 0.Problem 4: (20 points)The input to the RC circuit in Figure 4 is the voltage source f(t) and the o utput is the voltage y(t).Figure 4: An RC circuit with input voltage f(t) and output voltage y(t).1. (10 points) Suppose that the input voltage f(t) is a sinusoid with phasor representation˜F . Show that thephasor representation˜Y of the output voltage y(t) has the form˜Y =Kωτ + 1˜Fby representing the parameters K and τ in terms o f R1, R2, a nd C.2. (10 points) Suppose that the parameters R1, R2, and C are chosen so that K = 1/2 and ωoτ = 1. Given theinputf(t) = 10 cos(ωot + 60◦),find an expression for the sinusoidal steady-state response y(t) in terms of the cosine function and the parameterωo.Problem 5: (20 points)MATLAB is an important tool that is widely used in industry to anal yze dynamic systems. Each problem set willcontain an exercise that introduces various features of MATLAB. You can access MATLAB in the EE computerlaboratory in 304 Hammond. When using MATLAB, you can learn about a specific MATLAB f unction by typinghelp followed by the MATLAB function name. Typing help by itself will display a long list of topics for which helpis available.Start MATLAB and set the Current Folder to your working directory. Select New Script under the File tab and savethe following MATLAB m-file as go.m in your directory. Execute the m-file by typing go at the command prompt,alternatively, press F5 when the cursor is positioned in the MATLAB editor window containing the file go.m.% Example m-file% Plot the sinc(x) function, w here sin c(t) = sin(t) / tt = linspace(-20 ,20,200); % generate a time vectory1 = sin(t) ./ t;figure(1)clfplot(t,y1,’-k’)xlabel(’Time (sec)’)ylabel(’Amplitude’)% Now plot an exponentiall y weighted sinusoidy2 = exp(-abs(t/4)) .* cos(t);hold onplot(t,y2,’--r’)title(’EE 350 Proble m Set 1 Problem 5 E xample’)xlabel(’Time (sec)’)ylabel(’Amplitude’)legend(’sinc(t) = sin(t)/t’, ’e^{-|t|/3} cos(t)’ )1. (2 points) Three of the lines in the m-file end with a semicolon. What is the function of the semicolon inMATLAB?2. (2 points) What are the dim ensions of the vectors t, y1, and y2 generated by the example m-file? {Hint: Usethe MATLAB command whos or size.}3. (2 points) Why must we use the op erator . * in calculating the signals y1 and y2?4. (2 points) What happens if the command ho ld on is removed from the m-file?5. (2 points) What do the com mands figure(1) and clf accomplish?6. (10 points) Type help subp lot at the MATLAB command line to learn about the function subp lot. Addcode to the example m-file so it that plots the sinusoidsy = 2e−t/2sin(2π t)x = 2e−t/2cos(2π t)in the upper subplot of figure 2, and in the lower subplot of figure 2, plots y versus x for 0 ≤ t ≤ 4. Use a timevector that contains 300 uniformly spaced points. For the upper subplot, show y as a sol id black curve and xas a dashdot blue curve using a single plot command line. Label the two curves in the upper subplot usingthe legend command. For the lower subplot, use a solid magenta curve and follow the plot command by thecommand line axis equal. Why benefit does the command axis equal provide?To receive credit• Turn in figures 1 and 2 along with a copy of your m-file.• Include your name and section at the top of the m-file as comment lines.• Use the MATLAB command gtext to place your name and section number within each figure.• Make sure that you appropriately label the x and y axes; no credit is given for MATLAB plots whose axesare unlabeled.• Use the legen d command to distinguish multiple curves in a single plot.• Add an appropriate title to each
View Full Document
Unlocking...