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ps2 - EE 350 PROBLEM SET 2 DUE 11 SEP 2007 Reading...

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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 zero-input response y zi ( t ) and the zero-state response y zs ( t ) for t ≥ −∞ . If not, explain why. 3. (3 points) Determine whether or not the system is zero-input 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 zero-state 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 input-output relationship in part 1, determine whether or not the circuit is time-invariant or time varying causal or noncausal instantaneous (memoryless) or dynamic Remember that these properties are determined using the zero-state response of the system.
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Problem 6: (16 points) From the standpoint of analysis and design, a mathematical representation of the input-output description of a system is more useful than a schematic representation of an electrical system. The relationship between the input f ( t ) and zero-state response y ( t ) are shown below for two different systems. Determine if each system is zero-state linear or nonlinear time-invariant or time varying causal or noncausal instantaneous (memoryless) or dynamic Justify your answers.
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