Explanation Given data: The transfer function is, H ( s ) = 2 ( s + 1 ) ( s + 2 ) ( s + 10 ) (1) Calculation: Substitute j ω for s in equation (1) to find H ( ω ) . H ( ω ) = 2 ( j ω + 1 ) ( j ω + 2 ) ( j ω + 10 ) = 2 ( 1 + j ω ) 2 ( 10 ) ( 1 + j ω 2 ) ( 1 + j ω 10 ) = 0.1 ( 1 + j ω ) ( 1 + j ω 2 ) ( 1 + j ω 10 ) From the above equation, the corner frequencies ( ω c ) are 1 , 2 and 10 . Re-write the transfer function H ( ω ) using its magnitude and phase functions as follows, H ( ω ) = | 0.1 | | 1 + j ω | ( | 1 + j ω 2 | ) ( | 1 + j ω 10 | ) ∠ ( tan − 1 ( 0 0.1 ) + tan − 1 ( ω 1 ) − tan − 1 ( ( ω 2 ) 1 ) − tan − 1 ( ( ω 10 ) 1 ) ) = | 0.1 | | 1 + j ω | ( | 1 + j ω 2 | ) ( | 1 + j ω 10 | ) ∠ ( tan − 1 ( 0 ) + tan − 1 ( ω ) − tan − 1 ( ω 2 ) − tan − 1 ( ω 10 ) ) = | 0.1 | | 1 + j ω | ( | 1 + j ω 2 | ) ( | 1 + j ω 10 | ) ∠ ( 0 ° + tan − 1 ( ω ) − tan − 1 ( ω 2 ) − tan − 1 ( ω 10 ) ) { ∵ tan 0 ° = 0 } H ( ω ) = | 0.1 | | 1 + j ω | ( | 1 + j ω 2 | ) ( | 1 + j ω 10 | ) ∠ ( tan − 1 ( ω ) − tan − 1 ( ω 2 ) − tan − 1 ( ω 10 ) ) (2) From equation (2), the magnitude function of H ( ω ) is expressed as follows: | H ( ω ) | = | 0.1 | | 1 + j ω | ( | 1 + j ω 2 | ) ( | 1 + j ω 10 | ) Write the above equation in decibel (dB)

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 14, Problem 15P

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Construct the Bode magnitude and phase plots for the given transfer function.

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