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Unformatted text preview: 1 Review: Bode Plots H(s) , the Laplace transform of h(t) , is called the transfer function of a system. It leads directly to the frequency response ) ( j H by replacing s by j . In general, the transfer function takes on the following form: 1 1 1 1 .. .. ) ( b s b s a s a s a s H n n n m m m m + + + + + + = This can be rewritten as: ) )...( ( ) ( ) )...( ( ) ( ) ( 2 1 2 1 n m m p s p s p s z s z s z s a s H = Here, p i are called the poles of the system and z i are the zeros . Important remarks: 1. Poles and zeros always appear in complex conjugates pairs. The reason is that the a i and b i coefficients in the equation above can only be real numbers for practical systems (as they are the result of elements such as capacitor, inductors, resistors). [ ] [ ] ) ( ) ( ) ( jb a s jb a s s H + = 2 2 2 2 b a s a s + + = 2. For stability, all poles have to be in the left half plane, i.e. have a strictly negative real part. We will discuss this further in the chapter on feedback....
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- Winter '04