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Unformatted text preview: EE 350 PROBLEM SET 2 DUE: 11 SEP 2007 Reading assignment: Lathi Sections 2.1 and 2.2, Background Section B.1 Recitation #2 will be held this week. Problem 5: (16 points) A system with two series capacitors has as an input the independent current source f ( t ) as shown in Figure 1. At time t = −∞ the voltage across the capacitors C 1 and C 2 are v 1 ( −∞ ) = α and v 2 ( −∞ ) = β , respectively. The output of the system is the voltage y ( t ) across the series capacitor combination. v (t) 2 v (t) 1 f(t) + − + − + − y(t) Figure 1: Capacitor circuit with input current f ( t ) and output voltage y ( t ). The initial capacitor voltages are α and β . 1. (4 points) Find an expression for the response y ( t ) of the circuit for t ≥ −∞ in terms of the initial conditions α and β , and the input f ( t ). 2. (2 points) Does the decomposition property hold for this system? If so, find an expression for the zeroinput response y zi ( t ) and the zerostate response y zs ( t ) for t ≥ −∞ . If not, explain why. 3. (3 points) Determine whether or not the system is zeroinput linear by checking to see if the superpo sition property holds with respect to the initial conditions. 4. (3 points) Determine whether or not the system is zerostate linear by checking to see if the superpo sition property holds with respect to the input. 5. (1 point) Based upon your results in parts 2 through 4, is the system linear? 6. (3 points) Using the inputoutput relationship in part 1, determine whether or not the circuit is • timeinvariant or time varying • causal or noncausal • instantaneous (memoryless) or dynamic Remember that these properties are determined using the zerostate response of the system. Problem 6: (16 points) From the standpoint of analysis and design, a mathematical representation of the inputoutput description of a system is more useful than a schematic representation of an electrical system. The relationship between the input f ( t ) and zerostate response y ( t ) are shown below for two different systems. Determine if each system is • zerostate linear or nonlinear • timeinvariant or time varying • causal or noncausal • instantaneous (memoryless) or dynamic Justify your answers....
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This note was uploaded on 07/23/2008 for the course EE 350 taught by Professor Schiano,jeffreyldas,arnab during the Fall '07 term at Pennsylvania State University, University Park.
 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB

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