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16_Bode_Plots

# 16_Bode_Plots - Chapter 16 Bode Plots Chapter Outline 16.1...

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615 Chapter 16 Bode Plots Chapter Outline 16.1 INTRODUCTION TO BODE PLOTS. .................................................. 617 16.1.1 Introduction. ............................................................................................................................... 617 16.1.2 Bode Plots. ................................................................................................................................. 618 16.2 BODE PLOTS OF CONSTANTS AND REAL POLES AND ZEROS . ..... 620 16.2.1 Real Poles and Zeros. ........................................................................................................... 620 16.2.2 Constant Factors and Poles and Zeros at the Origin . ............................................ 628 16.3 BODE PLOTS OF TWO COMPLEX POLES AND ZEROS. .................. 630 16.3.1 Introduction. 630 16.3.2 Two Complex Poles . ............................................................................................................. 630 16.3.3 Two Complex Zeros . 635 16.4 GRAPHICAL CONSTRUCTION OF BODE PLOTS. ............................. 640 16.4.1 Construction Procedure. ....................................................................................................... 640 16.4.2 Examples . ................................................................................................................................... 641 16.4.3 MATLAB Experiments. 647 16.5 CHAPTER SUMMARY. ....................................................................... 648 16.5.1 Constructing Bode Plots. ..................................................................................................... 648 16.5.2 Summary. .................................................................................................................................... 650 16.6 HOMEWORK FOR CHAPTER 16. ...................................................... 650 In Chapter 14 we introduced the frequency response theorem and the frequency response function. If the input signal to a system is a sinusoid, the frequency response function relates the steady state response (the output signal) to the system representation. This foundational result relates the structure of the input and output signals to the structure of the system . This linkage is of immense importance in both system analysis and design. The key quantity in this relationship between signals and systems is the frequency response function, visualized in its graphical form. The shape of the magnitude and phase graphs are key in interpreting this frequency domain information. Motivated by the frequency response theorem, in this chapter we study the structure of the frequency response function by using the system’s (Laplace) transfer function. We relate the general shape of the frequency response function to the poles and zeros of the transfer function. This relationship is established using a traditional method for graphically constructing the Bode plots of the frequency response function. With an understanding of this method, it is easy to visualize the shape of the frequency response function from the poles and zeros of the transfer function.

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616 Chapter 16 Bode Plots This information is useful in three ways. First, the computation software that is currently available presumes some understanding of the general shape of the frequency response function and the frequency intervals so that an accurate Bode plot can be obtained. A lack of a clear understanding of the shape of the Bode plots can lead to inaccurate computer graphs for some systems. Second, the frequency response function plays a central role in the frequency domain synthesis of systems. The general flow of the design methodology is to first construct the frequency response function. Then the transfer function is constructed from a given frequency response function. To effectively construct the transfer function it is essential that the designer understands the relationship between the poles and zeros of the system and the frequency response function. In this section we will develop this relationship between the pole or zero locations of the transfer function and the shape of the corresponding frequency response function. Hence, the designer can go from frequency response function to poles and zeros of transfer functions and vice versa.
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16_Bode_Plots - Chapter 16 Bode Plots Chapter Outline 16.1...

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