Page 98 - Analog and Digital Filter Design

Poles and Zeroes 95

The equations in the Appendix give the normalized pole positions for a
Butterworth response with a 3 dB cutoff point at w = 1.

Using the formula given, pole positions have been obtained and are listed in
Table 3.2.

Order, n Real Part, -U Imaginary Part, %C.D
1 1 .om0

2 0.7071 0.7071
3 0.5000 0.8660
1 .oooo
4 0.9239 0.3827
0.3827 0.9239
5 0.8090 0.5878
0.3090 0.951 1
1 .oooo

6 0.9659 0.2588
0.7071 0.707 1
0.2588 0.9659

7 0.9010 0.4339
0.6235 0.7818
0.2225 0.9749
1 .oooo

8 0.9808 0.1951
0.8315 0.5556
0.5556 0.8315
0.1951 0.9808
9 0.9397 0.3420
0.7660 0.6428
0.50OO 0.8660
0.1737 0.9848
1 .OoOo
10 0.9877 0.1564
0.8910 0.4540
0.7071 0.7071
Table 3.2 0.4540 0.8910
0.1564 0.9877
Butterworth Pole Positions