# lecture11 - 1 11. Frequency-Domain Analysis Frequency...

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Unformatted text preview: 1 11. Frequency-Domain Analysis Frequency Response Definition: Frequency response = the magnitude and phase of the output from a system when the input is a sinusoidal sweep of frequency from 0 to infinity. Mathematically: U(s) G(s) Y(s) U(j ) G(j ) Y(j ) ( 29 = = + = = phase Bode 20log gain Bode magnitude ) t sin( B ) t ( y ; t sin A ) t ( u A B 10 2 Example Given differential equation If u(t) = 3sint, i.e. 1 rad/sec sine wave with amplitude 3. What is the steady-state y(t)? Since this is a linear system, the output y(t) will also have the same frequency, i.e. 1 rad/sec. Here it can be shown: y(t) = 0.707sin(t- /4) Therefore, Bode gain = 20log 10 (0.707) dB -3 dB Bode phase = /4 radian. ) t ( u ) t ( y ) t ( y = + 3 Bode Functions Bode gain function: Bode phase function: =...
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## This note was uploaded on 11/09/2009 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.

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lecture11 - 1 11. Frequency-Domain Analysis Frequency...

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