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["Spreadsheet to compute Butterworth and Chebychev low-pass filters up to 16th order"]
["lpf_design.xls",null,"Written by Kenneth A. Kuhn",null,null,null,"Version 1.3"]
["Based on Analysis and Design of Integrated Electronic Circuits by Paul M. Chirlian,"]
["second edtion, Harper & Row, pp 912 - 921"]
[]
["Instructions:"]
["1.  Enter the two response pairs (in red) that define the desired filter response.  (other cells locked)"]
["2.  The Butterworth and Chebyshev filter poles are then calculated."]
["3a. Rp and Rs are response factors between 0 and <1."]
["3b. For Butterworth filters Rp should generally be greater than 0.7"]
["3c. For Chebyshev filters Rp should generally be greater than 0.9"]
["3d. For either filter, Rs should generally be less than 0.3"]
["4.  Fs must be greater than Fp"]
["5b. The pole sections are listed from the highest damping down to the lowest damping."]
["5a. The filter should be implemented in the same order as the pole sections."]
["6a.  Each pole is given in three formats: s-plane location; wn, zeta; Fn (Hz), Q"]
["6b. Color is used to separate each of the three forms of the poles"]
["7.  The poles are numbered from 0 to n-1.  The 0 and n-1th poles are closest to jw axis."]
["8.  The spreadsheet is designed so that the Butterworth solution prints on page 1 and"]
["     the Chebyshev solution prints on page 2."]
[]
["Enter the two response pairs that define the desired filter response"]
[3500,"Hz., Fp, The highest frequency of interest in the passband"]
[0.9441,"       Rp, The minimum tolerable response factor in the passband"]
[6000,"Hz., Fs, The lowest frequency of interest in the stopband"]
[0.1,"       Rs, The maximum tolerable response factor in the stopband"]
[]
["Butterworth filter:"]
["Raw calculations",{"$nulls":5},"Temporary pole pairs"]
["1/(Rs*Rs)-1 =",null,98.99999999999999,null,null,null,3,3]
["1/(Rp*Rp)-1 =",null,0.12192546283997174,null,null,null,2,4]
["The required order:",null,6.2147576304455985,null,null,null,1,5]
["Rounded up order:",null,7,"n","Odd",null,0,6]
["Lowest cutoff freq:",null,4067.682198640479,"Hz",null,null,-1,7]
["Highest cutoff freq:",null,4321.215043545826,"Hz",null,null,-2,8]
["Average cutoff freq:",null,4194.448621093153,"Hz",null,null,-3,9]
[null,null,26354.49794777217,"rad/sec",null,null,-4,10]
[]
[1.5707963267948966,"=pi/2","---- s plane poles ----",null,"-- wn, z coefficients -",null,"-- F, Q coefficients --"]
["--- Pole Numbers ---",null,"sigma","+-jw","wn","zeta","Fn (in Hz)","Q"]
[3," ",-26354.49794777217,0,26354.49794777217," ",4194.448621093153," "]
[2,4,-23744.58218014092,11434.788112145405,26354.49794777217,0.900968867902419,4194.448621093153,0.5549581320873712]
[1,5,-16431.76070354287,20604.77620020737,26354.497947772175,0.6234898018587334,4194.448621093153,0.8019377358048384]
[0,6,-5864.427497288033,25693.73566082168,26354.49794777217,0.22252093395631434,4194.448621093153,2.2469796037174676]
[" "," "," "," "," "," "," "," "]
[" "," "," "," "," "," "," "," "]
[" "," "," "," "," "," "," "," "]
[" "," "," "," "," "," "," "," "]
[" "]
[]
[]
[]
["Chebyshev filter:"]
["Raw calculations",{"$nulls":5},"Temporary pole pairs"]
["1/(Rs*Rs)-1 =",null,98.99999999999999,null,null,null,1,2]
["1/(Rp*Rp)-1 =",null,0.12192546283997174,null,null,null,0,3]
["epsilon =",null,0.34917826799497664,null,null,null,-1,4]
["The required order:",null,3.5662737511864675,null,null,null,-2,5]
["Rounded up order:",null,4,"n","Even",null,-3,6]
["Cutoff freq:",null,3500,"Hz",null,null,-4,7]
[null,null,21991.14857512855,"rad/sec",null,null,-5,8]
[{"$nulls":6},-6,9]
[0.4436237554831927,"=(1/n)*asinh(1/epsilon)"]
[1.5707963267948966,"=pi/2","---- s plane poles ----",null,"-- wn, z coefficients -",null,"-- F, Q coefficients --"]
["--- Pole Numbers ---",null,"sigma","+-jw","wn","zeta","Fn (in Hz)","Q"]
[1,2,-9311.738291755397,9257.427096376303,13130.438928644613,0.7091718976310413,2089.7742604600408,0.7050476783840827]
[0,3,-3857.048289713962,22349.406048751844,22679.78774682803,0.1700654491466043,3609.6003281826806,2.940044568188432]
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[" "]

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