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# Chebyshev Lowpass Filter Poles

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 the online filter calculators and plotters here.

Pole locations are calculated as follows, where K=1,2,...,n. n is the filter order.

where

 0.01 dB Ripple Order(N) Re Part(-σ) Im Part(±jω) 1 20.82774 2 2.22776 2.33729 3 0.794691.58937 1.62621 4 0.410870.99192 1.355530.56148 5 0.252510.661090.81715 1.228200.75907 6 0.171470.468450.63992 1.158670.848200.31046 7 0.124260.348180.503130.55844 1.116640.895480.49695 8 0.094290.268520.401870.47404 1.089340.923500.617060.21668 9 0.074050.213210.326650.400700.42641 1.070600.941470.698790.37182 10 0.059710.173290.269910.340110.37701 1.057200.953710.756870.485940.16744
 0.10 dB Ripple Order(N) Re Part(-σ) Im Part(±jω) 1 6.55220 2 1.18618 1.38095 3 0.484700.96941 1.20616 4 0.264160.63773 1.122610.46500 5 0.166530.435990.53891 1.080370.66771 6 0.114690.313350.42804 1.056520.773430.28309 7 0.083840.234920.339470.37678 1.041830.835490.46366 8 0.063980.182200.272680.32165 1.032180.875040.584680.20531 9 0.050440.145230.222510.272940.29046 1.025510.901820.669350.35616 10 0.040790.118370.184370.232320.25753 1.020710.920800.730750.469170.16166
 0.25 dB Ripple Order(N) Re Part(-σ) Im Part(±jω) 1 4.10811 2 0.89834 1.14325 3 0.383610.76722 1.09155 4 0.212520.51306 1.056780.43773 5 0.135030.353500.43695 1.037880.64145 6 0.093390.255150.34854 1.026890.751730.27515 7 0.068450.191780.277140.30760 1.020010.817980.45395 8 0.052320.149000.222990.26304 1.015450.860850.575200.20198 9 0.041300.118900.182170.223470.23781 1.012270.890180.660710.35156 10 0.033420.097000.151080.190370.21102 1.009980.911120.723070.464240.15997
 0.50 dB Ripple Order(N) Re Part(-σ) Im Part(±jω) 1 2.86278 2 0.71281 1.00404 3 0.313230.62646 1.02193 4 0.175350.42334 1.016250.42095 5 0.111960.293120.36232 1.011560.62518 6 0.077650.212140.28979 1.008460.738240.27022 7 0.057000.159720.230800.25617 1.006410.807080.44789 8 0.043620.124220.185910.21929 1.005000.852000.569290.19991 9 0.034450.099200.151990.186440.19841 1.004000.882910.655320.34869 10 0.027900.080970.126110.158910.17615 1.003270.905070.718260.461150.15890
 1.0 dB Ripple Order(N) Re Part(-σ) Im Part(±jω) 1 1.96523 2 0.54887 0.89513 3 0.247090.49417 0.96600 4 0.139540.33687 0.983380.40733 5 0.089460.234210.28949 0.990110.61192 6 0.062180.169880.23206 0.993410.727230.26618 7 0.045710.128070.185070.20541 0.995280.798160.44294 8 0.035010.099700.149200.17600 0.996450.844750.564440.19821 9 0.027670.079670.122050.149720.15933 0.997230.876950.650900.34633 10 0.022410.065050.101320.127670.14152 0.997780.900110.714330.458630.15803

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.