Challenge_27 - ) ( 1 = ) ( /-t u e RC t h RC t If RC=1...

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EEL 3135: Dr. Fred J. Taylor, Professor Lesson Title: Continuous-Time Signal and Systems Lesson Number: 27 (Section 9-5 to 9-10) Challenge: The at-rest RC circuit shown in Figure 1, can be analyzed using basic electric circuit theory. Figure 1: RC Circuit The relationship between the input forcing function v ( t ) and voltage developed across the capacitor ( v o ( t )) is defined by the solution to the ordinary differential equation (ODE): ) ( = ) ( + ) ( 0 0 t v dt t dv RC t v The filter’s impulse response (developed later in the context of a transfer function) is:
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Unformatted text preview: ) ( 1 = ) ( /-t u e RC t h RC t If RC=1 second, what is the maximum value of the output if the input is a 500ms unit amplitude pulse? Response: The response to the filter to a 500ms unit pulse is abstracted in Figure 2 (RC=1). The solution over t [0, 0.5] is y(t)=(1-e-t ). At t=0.5s, y(t=0.5)=0.4. 500ms 1000ms x(t) y(t) 1 EEL 3135: Dr. Fred J. Taylor, Professor Figure 2: Filter response. 2...
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Challenge_27 - ) ( 1 = ) ( /-t u e RC t h RC t If RC=1...

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