Page 15 - Analog and Digital Filter Design

1 2 Analog and Digital Filter Design

Denormalization 400
Lowpass Filter Design 40 1
Highpass Frequency Scaling 403
Bandpass Frequency Scaling 405
Bandstop Frequency Scaling 406
IIR Filter Stability 407
Reference 408

Appendix Design Equations 409
Bessel Transfer Function 409
Butterworth Filter Attenuation 412
Butterworth Transfer Function 41 2
Butterworth Phase 41 3
Nonstandard Butterworth Passband 414
Normalized Component Values for Butterworth Filter with
RL >> RS or RL << RS 41 5
Normalized Component Values for Butterworth Filter:
Source and Load Impedances within a Factor of Ten 41 5
Chebyshev Filter Response 41 6
Equations to Find Chebyshev Element Values 41 7
Chebyshev with Zero or Infinite Impedance Load 41 7
Chebyshev Filter with Source and Load Impedances
within a Factor of Ten 41 8
Load Impedance for Even-Order Chebyshev Filters 419
Inverse Chebyshev Filter Equations 419
Elliptic or Cauer Filter Equations 42 1
Noise Bandwidth 422
Butterworth Noise Bandwidth 423
Chebyshev Noise Bandwidth 424
Pole and Zero Location Equations 426
Butterworth Pole Locations 426
Chebyshev Pole Locations 427
Inverse Chebyshev Pole and Zero Locations 429
Inverse Chebyshev Zeroes 43 1
Cauer Pole and Zero Locations 432
Scaling Pole and Zero Locations 434
Digital Filter Equations 435
Finding FIR Filter Zero Coefficient Using L'Hopital's Rule 435
Appendix References 436

Bibliography 437

Answers 439
Index 447