6.01, Fall Semester, 2007—Assignment 8, Issued: Tuesday, Oct. 23rd 1MASSACHVSETTS INSTITVTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.01—Introduction to EECS IFall Semester, 2007Assignment 8, Issued: Tuesday, Oct. 23rdTo do this week...in Tuesday software lab1. Start writing code and test cases for the numbered questions in the software lab. Paste allyour code, including your test cases, into the b ox provided in the “Software Lab” (Part 8.1)problem on the on-line Tutor. This will not be graded....before the start of lab on Thursday1. Read the lecture notes.2. Do the on-line Tutor problems for week 8 that are due on Thursday (Part 8.2).3. Read through the entire description of Thursday’s lab....in Thursday robot lab1. Answer the numbered questions in the robot lab and demonstrate them to your LA.2. Do the nanoquiz; it will be based on the material in the lecture notes and the on-line Tutorproblems due on Thursday....before the start of lecture next Tuesday1. Do the lab writeup, providing written answers (including code and test cases) for everynumb e red question in this handout.6.01, Fall Semester, 2007—Assignment 8, Issued: Tuesday, Oct. 23rd 2On Athena machines make sure you do:athrun 6.01 updateso that you can get the Desktop/6.01/lab8 directory which has the files mentioned in thishandout.• You need the files resolveConstraints.py, circuitConstraints.py, genKCL.py(your code) or genKCL.pyc (ours), circuitt.py, circuitLine.py, genGrid.py,and thntest.py for the software lab, and may find them helpful for the circuit designlab.During software lab, if you are using your own laptop, download the files from the courseWeb site (on the Calendar page). Be sure you have numpy installed.6.01, Fall Semester, 2007—Assignment 8, Issued: Tuesday, Oct. 23rd 3VsR2R1R3R4VthRthFigure 1: Simple Circuit and its Thevenin EquivalentThevenin EquivalentsLast week you learned to use resolveConstraints to analyze circuits. You also wrote a classderived from ConstraintSet to automatically generate KCL constraints for circuits with two-terminal elements, though your program had to assume that the constitutive equations for theelements were written in a very particular form.For this software lab, you will be writing a program that computes the Thevenin equivalent re-sistance and Thevenin equivalent voltage source given an arbitrary circuit of resistors and voltagesources, and a specification of the terminals of your Thevenin equivalent.Your method should take three arguments. The first argument should be an instance of constraintSetKCL,one which includes only the constitutive relation constraints, but for which the KCL equations havenot been set, nor has a ground node been defined. The second two arguments are the two nodevoltage names that will be the terminals of your Thevenin equivalent. Your program should returnthe Thevenin equivalent resistance, Rthand the Thevenin equivalent voltage source, Vth. You mayfind that you will need of copy of the constraintSetKCL instance, if so, you should import themodule copy and use copy.deepcopy to make sure you ac tually generate a completely seperatecopy of the instance. Also, constraintSet has a method translate which you will find useful.The file thntest.py is an example of how to compute Thevenin equivalents.If you do not have a copy of your genKCL.py module, you can download a compiled version fromthe course web page.In order to test your method for computing Thevenin equivalents, demonstrate that you can com-pute the correct Thevenin equivalents for the circuits in figure 1 and figure 2. In each of the figures,the pair of open circles are used to indicate the terminals for the Thevenin equivalent. Note thatfor these two examples, the circuits only differ in that different circuit nodes are the terminals forthe Thevenin equivalent. Therefore, the two Thevenin equivalents are modeling how the circuitwill respond to changes across two different pairs of terminals. For your test examples, you canassume Vs= 5V, and R1= R2= R3= R4= 1KΩ, where 1KΩ means 1000 ohms.6.01, Fall Semester, 2007—Assignment 8, Issued: Tuesday, Oct. 23rd 4VsR2R3R1R4VthRthFigure 2: Simple Circuit and its Thevenin Equivalent for different terminalsQuestion 1. Describe how you implemented your program for computing Thevenin Equivalents.Question 2. Demonstrate that your program works correctly for the circuits in figure 1 and 2.Question 3. Explain why the Thevenin equivalent voltages and resistances are different for thetwo test cases, even though the original circuits are identical.As you recall from last week, the programs genGrid.py and circuitLine.py can be used togenerate the circuit in figure 3. Modify the genGrid.py and circuitLine.py files, and use yourprogram for computing Thevenin equivalents to answer questions about the Thevenin equivalentfor a part of the resistor line shown in figure 4.6.01, Fall Semester, 2007—Assignment 8, Issued: Tuesday, Oct. 23rd 5V1_0V0_1V2_1V1_1V0_2V2_2V1_2V0_4V2_4V1_4V1_5vL1vT1vB1vR1vB2vT2vB4vT4Figure 3: Resistor Line circuit generated by circuitLine.py.V1_0V0_1V2_1V1_1V0_2V2_2V1_2V0_4V2_4V1_4vL1vT1vB1vB2vT2vB4vT4VthRthFigure 4: Unterminated resistor line and its Thevenin equivalent.6.01, Fall Semester, 2007—Assignment 8, Issued: Tuesday, Oct. 23rd 6Question 4. Modify genGrid.py and circuitLine.py to eliminate the right hand voltagesource and associated resistor, so that you can generate the unterminated four-column re-sistor line in the left-hand circuit of figure 4.Question 5. Suppose all the resistors in your unterminated line are one ohm, and the top andbottom voltage sources are all zero. How does the Thevenin equivalent resistor and voltagesource for the unterminated line vary as you vary the left-hand voltage source? Can youexplain why?Question 6. Modify the grid generator so that you can use different values for the vertical andhorizontal resistors, if you did not do so last we ek.Question 7. Use your modified version of the grid generator, and modify circuitLine.py sothat the horizontal resistors in your unterminated line are one ohm, the vertical resistorsare all 10,000 ohms, and the top and bottom voltage sources are all zero. Now how does theThevenin equivalent resistor and voltage source for the unterminated line vary as you varythe left-hand voltage source? Can you explain why?Question 8. Use your modified version of the grid generator, and modify circuitLine.py sothat the horizontal
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