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lecture20 - EE313 Linear Systems and Signals Fall 2010...

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EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin System Realization
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20 - 2 Passive Circuit Elements Laplace transforms with zero-valued initial conditions Capacitor Inductor Resistor ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 s L s I s V s H s I s L s V dt di L t v = = = = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 s C s I s V s H s I s C s V s V s C s I dt dv C t i 1 1 = = = = = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 R s I s V s H s I R s V t i R t v = = = = + v ( t ) + v ( t ) + v ( t )
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20 - 3 First-Order RC Lowpass Filter x ( t ) y ( t ) + + C R X(s) Y(s) + + R s C 1 Time domain Laplace domain C R s C R s X s Y s X s C R s C s Y s I s C s Y s C R s X s I 1 1 ) ( ) ( ) ( 1 1 ) ( ) ( 1 ) ( 1 ) ( ) ( + = + = = + = i ( t ) I(s)
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20 - 4 First-Order RC Highpass Filter x ( t ) y ( t ) + + R C X(s) Y(s) + + s C 1 Time domain Laplace domain C R s s s X s Y s X s C R R s Y s I R s Y s C R s X s I 1 ) ( ) ( ) ( 1 ) ( ) ( ) ( 1 ) ( ) ( + = + = = + = i ( t ) R I ( s ) Frequency response is also an example of a notch filter
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20 - 5 Passive Circuit Elements Laplace transforms
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