Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits & ElectronicsSpring 2004Problem Set #2Issued 2/11/04 – Due 2/18/04Exercise 2.1: In each circuit shown below, three light bulbs are driven by a single source. Intwo of the circuits the source is a voltage source, and in the other it is a current source. Assumethat one of the three light bulbs burns out and becomes an open circuit. Do the other two lightbulbs get brighter, get dimmer, or exhibit no change in intensity? Why?Exercise 2.2: Using the node method, develop a set of simultaneous equations for the networkshown below that can be used to solve for the three unknown node voltages in the network. Expressthese equations in the formGe1e2e3= Swhere G is a 3 × 3 matrix of conductance terms and S is a 3 × 1 vector of terms involving thesources. You need not solve the set of equations for the node voltages.e1VR1R2R4R5R3Ie2e3Problem 2.1: This problem focuses on the use of superposition to analyze linear networks.(A) Write and solve a node equation that determines the node voltage e in Network #1 shownbelow.(B) Find the node voltage e in Network #1 by superposition. That is, determine e due to eachsource alone, and then add the two results. The use of parallel/series resistor simplificationsand/or voltage/current division should make this analysis easier. Compare your answer tothat found in Part (A).(C) Find v0in Network #2 as a function of v1, v2and v3assuming i0= 0. Also, find the Theveninequivalent of the network as viewed from its i0-v0port. What application might make use ofthis network.V1V2R1R3R22Rv3v2v12R 2R2R2RRR R+_v0i0Network #1Network #2eProblem 2.2: Two networks, N1 and N2, are described in terms of their i-v relations, andconnected together through a single resistor, as shown below.(A) Find the Thevenin and Norton equivalents of N1 and N2.(B) Find the currents i1and i2that result from the interconnection of N1 and N2.N1 N2+_v2+_v1Ri1i2iv-V1I1V2-I2Network #1Network #2Problem 2.3: Find the Thevenin and Norton equivalents of the following networks, and graphtheir i-v relations as viewed at their ports.V+_vR1R2iI+_vR1R2iVIR1R2+_viNetwork (A) Network (B)Network (C)Problem 2.4: This problem studies the network shown below. The network contains anonlinear resistor having the terminal relation iN= αv2Nfor vN≥ 0andiN=0forvN≤ 0, whereα is a constant with units A/V2. Assume that α and iSare both positive.(A) Analyze the network graphically to determine iNand vNin terms of iSand the networkparameters. To do so, note that the current source and linear resistor together constrain therelation between iNand vN, and that the nonlinear resistor also constrains this relation. Statethe two constraints, and on a single graph sketch both constraints and identify the solutionfor iNand vN. Within what voltage range will vNlie?(B) Analytically solve for vNin terms of iS. Check that this solution is consistent with the graphicalsolution from Part (A).(C) Now let iS= IS+ isand let vN= VN+ vn, where ISand VNare a constant large-signal currentand voltage, respectively, which together form an operating point, and isand vnare a varyingsmall-signal current and voltage. Using the solution from Part (B), determine VNin terms ofIS. Then, linearize the solution from Part (B) around the operating point to determine vninterms of isand
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