This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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 ) ( ω j H by replacing s by j ω . 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....
View Full Document
- Winter '04
- Frequency, Decibel