3-Lesson_Notes_Lecture19_ee205

# 3-Lesson_Notes_Lecture19_ee205 - Lecture 19 In this lecture...

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Lecture 19 In this lecture, We introduce the concept of transfer functions Solve three examples demonstrating how to find transfer functions. This includes electronic circuits also We introduce the concept of poles and zeroes Solve several examples showing pole zero determination Transfer Function Transfer function, H(s), is defined as the ratio of the response (or, output) phasor to the excitation (or, input) phasor in the s-domain, or ( ) () ) output or respsonse in terms of s Hs input or excitation = (21-1) When applied to electrical circuits, sometimes the term network function is also used. Examples: Is Ys Vs = , 1 2 = (21-2) While studying the transients in RLC circuits, you may have noticed that the input voltage v i and output voltage v o are related by differential equations of the form, 1 1 11 1 ....... ....... mm nn oo i i no o m i nm n dv d v aa a v bb dt dt dt dt −− ++ + = 1 o m b v + (21-3) We have seen that if the input is, ; st ii m v V e where phasor V V and s j θ σ == ω = + (21-4) Then the output will be of the form,

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; V o vV e V st oo o m φ == o (21-5) Differentiating v i and v o in (4) and (5) successively, and substituting in (3) we can get , (21-6) 11 [ .... ] [ .... ] n n st m m st no o m i nm as a s a Ve bs b s b Ve −− ++ += + + +
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3-Lesson_Notes_Lecture19_ee205 - Lecture 19 In this lecture...

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