DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

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A Signal Processing Perspective 375 The Delyiannis Second-Order All-Pass Circuit In Figure 11.11 is shown one form of a Delyiannis second-order all-pass circuit. The transfer function for the circuit shown in Figure 11.11 is as follows: where and It is recognized that (11.51) has two poles and is the magnitude of the poles, and where are the poles. In order for (11.51) to be a second-order all-pass transfer function, it is necessary that Equating (11.54) to the negative of (11.53), it follows that 3 See Section 2.12. Section 11.2 Second-Order Stages
376 DESIGN AND ANALYSIS OF ANALOG FILTERS: For convenience, let and let It follows, therefore, from (11.56) that Substituting (11.52) into (11.53) it follows that From (11.57) and (11.58): From (11.52) it follows that Note that all that is required for initial circuit component values is the value of Q. That is, and and are given by (11.59), (11.58) and (11.60), respectively. To summarize the design of this stage, what is needed initially are the values of the non-normalized and Then, is normalized to unity: Q remains unchanged. The component values of the normalized circuit are expressed above and are repeated here for convenience: After obtaining the initial component values indicated in (11.61) for a desired Q value and a normalized then frequency scaling may be applied for the desired value of the non-normalized circuit, and impedance scaling may be applied for more convenient component values. Note that neither frequency scaling nor impedance scaling will affect the value of Q. Note also, from (11.55), that the magnitude gain of the circuit is independent of frequency. The above first- and second-order stages shown in Figure 11.3 through Figure 11.11, combined with attenuators and gain stages (Figure 11.2) for gain adjustment if required, are sufficient for implementation of any transfer function, including allpass, presented in this book. The following section illustrates details as to the implementation of desired transfer functions. 4 See Section 2.12. Chapter 11 Active Filters
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DESIGN AND ANALYSIS OF ANALOG FILTE
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Design and Analysis of A Signal Pro
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PREFACE nalog filters, that is cont
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The term “approximation” is use
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PREFACE Chapter 1. 2. INTRODUCTION
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6.7 6.8 6.9 6.10 6.11 6.12 TABLE OF
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CHAPTER 1 INTRODUCTION Iimportance
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CHAPTER 2 ANALOG FILTER DESIGN AND
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114 DESIGN AND ANALYSIS OF ANALOG F
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130 (f) (g) (h) DESIGN AND ANALYSIS
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CHAPTER 5 CHEBYSHEV TYPE II FILTERS
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CHAPTER 7 BESSEL FILTERS Although a
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CHAPTER 8 OTHER FILTERS In this cha
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