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    butterworth and chebyshev 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 ?

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    Re: butterworth and chebyshev filter

    Quote Originally Posted by promach View Post
    1) How to derive expression (3.11) for chebyshev filter ?
    Definition of Chebyshev polynomials.

    Quote Originally Posted by promach View Post
    2) Why there is a factor of 2 in gi expression (3.24) and n expression (3.25) for butterworth filter ?
    (3.24) is due to complex conjugate pair of poles.

    (3.25) is from (3.7).



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  3. #3
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    Re: butterworth and chebyshev filter

    (3.24) is due to complex conjugate pair of poles.
    I understand that butterworth function uses complex conjugate poles, but that does not justify the use of a factor of 2 in gi expression.



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    Re: butterworth and chebyshev filter

    Quote Originally Posted by promach View Post
    I understand that butterworth function uses complex conjugate poles,
    but that does not justify the use of a factor of 2 in gi expression.
    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....eros-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 by pancho_hideboo; 2nd July 2019 at 12:03.



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