|
Chebyshev poles lie along an ellipse, rather than a circle like the Butterworth and Bessel.
Prototype value real and imaginary pole locations (ω=1 at the ripple attenuation cutoff point)
for Chebyshev filters are presented in the table below.
See
Espresso Engineering Workbook (free) for a calculator.
Pole locations are calculated as follows, where K=1,2,...,n.
n is the filter order.
where
| 1 |
20.82774 |
|
| 2 |
2.22776 |
2.33729 |
| 3 |
0.79469 1.58937 |
1.62621 |
| 4 |
0.41087 0.99192 |
1.35553 0.56148 |
| 5 |
0.25251 0.66109 0.81715 |
1.22820 0.75907 |
| 6 |
0.17147 0.46845 0.63992 |
1.15867 0.84820 0.31046 |
| 7 |
0.12426 0.34818 0.50313 0.55844 |
1.11664 0.89548 0.49695 |
| 8 |
0.09429 0.26852 0.40187 0.47404 |
1.08934 0.92350 0.61706 0.21668 |
| 9 |
0.07405 0.21321 0.32665 0.40070 0.42641 |
1.07060 0.94147 0.69879 0.37182 |
| 10 |
0.05971 0.17329 0.26991 0.34011 0.37701 |
1.05720 0.95371 0.75687 0.48594 0.16744 |
|
| 1 |
6.55220 |
|
| 2 |
1.18618 |
1.38095 |
| 3 |
0.48470 0.96941 |
1.20616 |
| 4 |
0.26416 0.63773 |
1.12261 0.46500 |
| 5 |
0.16653 0.43599 0.53891 |
1.08037 0.66771 |
| 6 |
0.11469 0.31335 0.42804 |
1.05652 0.77343 0.28309 |
| 7 |
0.08384 0.23492 0.33947 0.37678 |
1.04183 0.83549 0.46366 |
| 8 |
0.06398 0.18220 0.27268 0.32165 |
1.03218 0.87504 0.58468 0.20531 |
| 9 |
0.05044 0.14523 0.22251 0.27294 0.29046 |
1.02551 0.90182 0.66935 0.35616 |
| 10 |
0.04079 0.11837 0.18437 0.23232 0.25753 |
1.02071 0.92080 0.73075 0.46917 0.16166 |
|
| 1 |
4.10811 |
|
| 2 |
0.89834 |
1.14325 |
| 3 |
0.38361 0.76722 |
1.09155 |
| 4 |
0.21252 0.51306 |
1.05678 0.43773 |
| 5 |
0.13503 0.35350 0.43695 |
1.03788 0.64145 |
| 6 |
0.09339 0.25515 0.34854 |
1.02689 0.75173 0.27515 |
| 7 |
0.06845 0.19178 0.27714 0.30760 |
1.02001 0.81798 0.45395 |
| 8 |
0.05232 0.14900 0.22299 0.26304 |
1.01545 0.86085 0.57520 0.20198 |
| 9 |
0.04130 0.11890 0.18217 0.22347 0.23781 |
1.01227 0.89018 0.66071 0.35156 |
| 10 |
0.03342 0.09700 0.15108 0.19037 0.21102 |
1.00998 0.91112 0.72307 0.46424 0.15997 |
|
| 1 |
2.86278 |
|
| 2 |
0.71281 |
1.00404 |
| 3 |
0.31323 0.62646 |
1.02193 |
| 4 |
0.17535 0.42334 |
1.01625 0.42095 |
| 5 |
0.11196 0.29312 0.36232 |
1.01156 0.62518 |
| 6 |
0.07765 0.21214 0.28979 |
1.00846 0.73824 0.27022 |
| 7 |
0.05700 0.15972 0.23080 0.25617 |
1.00641 0.80708 0.44789 |
| 8 |
0.04362 0.12422 0.18591 0.21929 |
1.00500 0.85200 0.56929 0.19991 |
| 9 |
0.03445 0.09920 0.15199 0.18644 0.19841 |
1.00400 0.88291 0.65532 0.34869 |
| 10 |
0.02790 0.08097 0.12611 0.15891 0.17615 |
1.00327 0.90507 0.71826 0.46115 0.15890 |
|
| 1 |
1.96523 |
|
| 2 |
0.54887 |
0.89513 |
| 3 |
0.24709 0.49417 |
0.96600 |
| 4 |
0.13954 0.33687 |
0.98338 0.40733 |
| 5 |
0.08946 0.23421 0.28949 |
0.99011 0.61192 |
| 6 |
0.06218 0.16988 0.23206 |
0.99341 0.72723 0.26618 |
| 7 |
0.04571 0.12807 0.18507 0.20541 |
0.99528 0.79816 0.44294 |
| 8 |
0.03501 0.09970 0.14920 0.17600 |
0.99645 0.84475 0.56444 0.19821 |
| 9 |
0.02767 0.07967 0.12205 0.14972 0.15933 |
0.99723 0.87695 0.65090 0.34633 |
| 10 |
0.02241 0.06505 0.10132 0.12767 0.14152 |
0.99778 0.90011 0.71433 0.45863 0.15803 |
|
|
Data taken from "Filter Design," by Steve Winder, Newnes Press, 1998.
This is a great filter design book, and I recommend you purchase a copy of it.
|
