Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2004 Problem Set 2 Issued 2 11 04 Due 2 18 04 Exercise 2 1 In each circuit shown below three light bulbs are driven by a single source In two of the circuits the source is a voltage source and in the other it is a current source Assume that one of the three light bulbs burns out and becomes an open circuit Do the other two light bulbs 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 network shown below that can be used to solve for the three unknown node voltages in the network Express these equations in the form e1 G e2 S e3 where G is a 3 3 matrix of conductance terms and S is a 3 1 vector of terms involving the sources You need not solve the set of equations for the node voltages e2 R3 R1 e1 R2 I e3 R4 V R5 Problem 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 shown below B Find the node voltage e in Network 1 by superposition That is determine e due to each source alone and then add the two results The use of parallel series resistor simplifications and or voltage current division should make this analysis easier Compare your answer to that found in Part A C Find v0 in Network 2 as a function of v1 v2 and v3 assuming i0 0 Also find the Thevenin equivalent of the network as viewed from its i0 v0 port What application might make use of this network Network 2 Network 1 R R1 e R2 2R R 2R R 2R 2R 2R V1 R3 v3 V2 i0 v2 v0 v1 Problem 2 2 Two networks N1 and N2 are described in terms of their i v relations and connected together through a single resistor as shown below A Find the Thevenin and Norton equivalents of N1 and N2 B Find the currents i1 and i2 that result from the interconnection of N1 and N2 Network 2 i1 i2 N1 v1 v V2 R v2 N2 I2 I1 V1 i Network 1 Problem 2 3 Find the Thevenin and Norton equivalents of the following networks and graph their i v relations as viewed at their ports i i R2 i v R1 R2 I Network A v V v R2 R1 I V R1 Network C Network B Problem 2 4 This problem studies the network shown below The network contains a 2 for v 0 and i 0 for v 0 where nonlinear resistor having the terminal relation iN vN N N N 2 is a constant with units A V Assume that and iS are both positive A Analyze the network graphically to determine iN and vN in terms of iS and the network parameters To do so note that the current source and linear resistor together constrain the relation between iN and vN and that the nonlinear resistor also constrains this relation State the two constraints and on a single graph sketch both constraints and identify the solution for iN and vN Within what voltage range will vN lie B Analytically solve for vN in terms of iS Check that this solution is consistent with the graphical solution from Part A C Now let iS IS is and let vN VN vn where IS and VN are a constant large signal current and voltage respectively which together form an operating point and is and vn are a varying small signal current and voltage Using the solution from Part B determine VN in terms of IS Then linearize the solution from Part B around the operating point to determine vn in terms of is and IS iN iS R Nonlinear Resistor vN
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