Bode_Tutorial - Bode Plot Tutorial Contents 1 Introduction...

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Unformatted text preview: Bode Plot Tutorial Contents 1 Introduction 1 2 Bode Plots Basics 1 2.1 Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 Combining Poles and Zeroes 4 1 Introduction Although you should have learned about Bode plots in previous courses, this tutorial will give you a brief review of the material in case your memory is fuzzy. 2 Bode Plots Basics Making the Bode plots for a transfer function involves drawing both the magnitude and phase plots. The magnitude is plotted in decibels (dB) while the phase is plotted in degrees ( ). For both plots, the horizontal axis is either frequency ( f ) or angular frequency ( ), measured in Hz and rad / s respectively. In addition, the horizontal axis should be logarithmic (i.e. increasing by factors of 10). Most of the transfer functions we will encounter in this lab manual can be rearranged into the general form: H ( j ) = A j/ z 1 (1 + j/ z 2 ) (1 + j/ z 3 ) ... j/ p 1 (1 + j/ p 2 ) (1 + j/ p 3 ) ... , (1) where A is an arbitrary constant and j is 1. Besides the exception of j/ c , the basic component of this transfer function is 1 + j/ c , where c is some numerical constant. Let us analyze this basic component first before we analyze the transfer function as a whole. 2.1 Magnitude Recall the definition of magnitude (measured in dB): | H ( j ) | dB = 20 log | H ( j ) | = 20 log radicalBig ( [ H ( j )]) 2 + ( [ H ( j )]) 2 (2) Let us apply this definition to our basic component (1+ j/ c ), which is also called a zero when it appears in the numerator of the transfer function: | 1 + j/ c | dB = 20 log | 1 + j/ c | = 20 log radicalBig 1 + ( / c ) 2 (3) For small values of , we have 20 log | 1 + j/ c | 0 dB. For large values of , 20 log | 1 + j/ c | ....
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This note was uploaded on 04/06/2009 for the course ECSE 2050 taught by Professor Monahella during the Spring '08 term at Rensselaer Polytechnic Institute.

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Bode_Tutorial - Bode Plot Tutorial Contents 1 Introduction...

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