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EE 230 Lecture 5 Spring 2010

# EE 230 Lecture 5 Spring 2010 - EE 230 Lecture 5 Linear...

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EE 230 Lecture 5 Linear Systems Poles/Zeros/Stability Stability

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Quiz 4 Obtain the transfer function T(s) for the circuit shown. ( ) ( ) ( ) = s V s V s T IN OUT
And the number is ? 1 3 8 4 6 7 5 2 9

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And the number is ? 1 3 8 4 6 7 5 2 9
Quiz 4 Obtain the transfer function T(s) for the circuit shown. ( ) ( ) ( ) = s V s V s T IN OUT Solution: ( ) 1 T s 2 RCs = +

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Test Equipment in the EE 230 Laboratory 984 Pages ! The documentation for the operation of this equipment is extensive Critical that user always know what equipment is doing Consult the users manuals and specifications whenever unsure Review from Last Time
Key Theorem: Theorem: The steady-state response of a linear network to a sinusoidal excitation of V IN =V M sin( ω t+ γ ) is given by ( ) ( ) ( ) ( ) OUT m V t V T j ω sin ω t+ γ + T j ω = This is a very important theorem and is one of the major reasons phasor analysis was studied in EE 201 The sinusoidal steady state response is completely determined by T(j ω ) The sinusoidal steady state response can be written by inspection from the and plots ( ) T j ω ( ) T j ω P s=j ω T (s) = T (j ω ) Review from Last Time

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Solution of Differential Equations Set of Differential Equations Circuit Analysis KVL, KCL Time Domain Circuit X i (t) = X M sin( ω t+ θ ) X OUT (t) Solution of Linear Equations Set of Linear equations in j ω Circuit Analysis KVL, KCL Phasor Domain Circuit X i (j ω ) X OUT (j ω ) Phasor Transform Inverse Phasor Transform Solution of Linear Equations Set of Linear equations in s Circuit Analysis KVL, KCL s-Domain Circuit X i (S) X OUT (S) s Transform Inverse s Transform T(s) T P (j ω ) Formalization of sinusoidal steady-state analysis Review from Last Time
Formalization of sinusoidal steady-state analysis - Summary ( ) ( ) ( ) ( ) OUT M X t X T j ω sin ω t + θ + T j ω = Solution of Linear Equations Set of Linear equations in s Circuit Analysis KVL, KCL s-Domain Circuit X i (S) X OUT (S) s Transform Inverse s Transform T(s) X OUT (t) X i (t) ( ) ( ) IN M X t X sin ω t + θ = s-domain The Preferred Approach L sL 1 C sC All other components unchanged Review from Last Time

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Gain, Frequency Response, Transfer Function
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