Jul 2, 2019 #1 P promach Advanced Member level 4 Joined Feb 22, 2016 Messages 1,199 Helped 2 Reputation 4 Reaction score 5 Trophy points 1,318 Activity points 11,636 1) How to derive expression (3.11) for chebyshev filter ? 2) Why there is a factor of 2 in gi expression (3.24) and n expression (3.25) for butterworth filter ?
1) How to derive expression (3.11) for chebyshev filter ? 2) Why there is a factor of 2 in gi expression (3.24) and n expression (3.25) for butterworth filter ?
Jul 2, 2019 #2 pancho_hideboo Advanced Member level 5 Joined Oct 21, 2006 Messages 2,847 Helped 767 Reputation 1,536 Reaction score 733 Trophy points 1,393 Location Real Homeless Activity points 17,490 promach said: 1) How to derive expression (3.11) for chebyshev filter ? Click to expand... Definition of Chebyshev polynomials. promach said: 2) Why there is a factor of 2 in gi expression (3.24) and n expression (3.25) for butterworth filter ? Click to expand... (3.24) is due to complex conjugate pair of poles. (3.25) is from (3.7).
promach said: 1) How to derive expression (3.11) for chebyshev filter ? Click to expand... Definition of Chebyshev polynomials. promach said: 2) Why there is a factor of 2 in gi expression (3.24) and n expression (3.25) for butterworth filter ? Click to expand... (3.24) is due to complex conjugate pair of poles. (3.25) is from (3.7).
Jul 2, 2019 #3 P promach Advanced Member level 4 Joined Feb 22, 2016 Messages 1,199 Helped 2 Reputation 4 Reaction score 5 Trophy points 1,318 Activity points 11,636 (3.24) is due to complex conjugate pair of poles. Click to expand... I understand that butterworth function uses complex conjugate poles, but that does not justify the use of a factor of 2 in gi expression.
(3.24) is due to complex conjugate pair of poles. Click to expand... I understand that butterworth function uses complex conjugate poles, but that does not justify the use of a factor of 2 in gi expression.
Jul 2, 2019 #4 pancho_hideboo Advanced Member level 5 Joined Oct 21, 2006 Messages 2,847 Helped 767 Reputation 1,536 Reaction score 733 Trophy points 1,393 Location Real Homeless Activity points 17,490 promach said: I understand that butterworth function uses complex conjugate poles, but that does not justify the use of a factor of 2 in gi expression. Click to expand... Consider coefficients of polynomials. Calculate S11 from S21. Then calculate Zin. Then evaluate g-parameters by continuation fraction expansion of Zin. See https://www.edaboard.com/showthread.php?384998-Selection-of-Zeros-of-S11(s) All zeros of S11 are located at origin for Butterworth filter. So you can get Both S11 and Zin as close form. Last edited: Jul 2, 2019
promach said: I understand that butterworth function uses complex conjugate poles, but that does not justify the use of a factor of 2 in gi expression. Click to expand... Consider coefficients of polynomials. Calculate S11 from S21. Then calculate Zin. Then evaluate g-parameters by continuation fraction expansion of Zin. See https://www.edaboard.com/showthread.php?384998-Selection-of-Zeros-of-S11(s) All zeros of S11 are located at origin for Butterworth filter. So you can get Both S11 and Zin as close form.