Page 9 - Analog and Digital Filter Design
P. 9
6 Analog and Digital Filter Design
Chebyshev Response 58
Normalized Component Values 63
Normalized Element Values for Filters with RS = 0 or RS = - 65
Equal Load Normalized Component Value Tables
67
Inverse Chebyshev Response 69
Component Values Normalized for 1 Rads Stopband 71
Normalized 3dB Cutoff Frequencies and Passive Component
Values 75
Cauer Response 78
Passive Cauer Filters 78
Normalized Cauer Component Values 80
The Cutoff Frequency 81
References 81
Exercises 82
CHAPTER Poles and Zeroes 83
3
Frequency and Time Domain Relationship 84
The S-Plane 84
Frequency Response and the S-Plane 85
Impulse Response and the S-Plane 88
The Laplace Transform-Converting between Time and
Frequency Domains 90
First-Order Filters 90
Pole and Zero Locations 94
Butterworth Poles 94
Bessel Poles 96
Chebyshev Pole Locations 98
Inverse Chebyshev Pole and Zero Locations 1 09
Inverse Chebyshev Zero Locations 1 09
Cauer Pole and Zero Locations 117
Cauer Pole Zero Plot 121
References 122
Exercises 122
CHAPTER Analog Lowpass Filters 125
4
Passive Filters 125
Formulae for Passive Lowpass Filter Denormalization 127
Denormalizing Passive Filters with Resonant Elements 128
Mains Filter Design 129
Active Lowpass Filters 132
First-Order Filter Section 132
