poles-zeros-2nd-order

# poles-zeros-2nd-order - ECE 382 Poles, Zeros, Open-Loop...

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ECE 382 Poles, Zeros, Open-Loop Poles, and Closed-Loop Poles Poles and Zeros A complex function F ( s ) , which is a function of s , has a real part and an imaginary part as F ( s ) = real part + imaginary part = F x + jF y where F x and F y are real numbers. The magnitude and the phase angle of F ( s ) are, respectively, | F ( s ) | = q F 2 x + F 2 y ; F ( s ) = θ = tan - 1 ± F y F x ² A rational transfer function is a complex function that can be described either as a ratio of 2 polynomials in s G ( s ) = N ( s ) D ( s ) = b m s m + b m - 1 s m - 1 + ... + b 1 s + b 0 a n s n + a n - 1 s n - 1 + ... + a 1 s + a 0 or in a factored zero-pole form as G ( s ) = N ( s ) D ( s ) = K m i = 1 ( s - z i ) n j = 1 ( s - p j ) = K ( s - z 1 )( s - z 2 ) ··· ( s - z m ) ( s - p 1 )( s - p 2 ) ··· ( s - p n ) where K is the transfer function gain. The roots of the numerator z 1 , z 2 ,..., z m are called the ﬁnite zeros of the system. The zeros are locations in the s -plane where the transfer function is zero. If s = z i , then G ( s ) | s = z i = 0. The roots of the denominator p 1 , p 2 ,..., p n are called the poles of the system. The poles are locations in the s -plane where the magnitude of the transfer function becomes inﬁnite. If s = p i , then G ( s ) | s = p i = . Open-Loop Poles and Closed-Loop Poles

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## This note was uploaded on 02/04/2012 for the course ECE 382 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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poles-zeros-2nd-order - ECE 382 Poles, Zeros, Open-Loop...

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