Phase response formula for Butterworth filters?

Discussion in 'Electronic Design' started by Carlos, Dec 8, 2003.

  1. Carlos

    Carlos Guest

    Hi all,

    I'm looking for the phase response formula of a Butterworth filter as
    a function of its order and (f/fc), equivalent to the well known
    amplitude one:

    1
    --------------------
    SQRT(1+(f/fc)^(2*n))

    If there isn't a single formula depending on n, I'd be grateful if you
    could give me the formulas for 1st (I think that one is just
    -Arctan(f/fc), right?), 2nd and 3rd order.

    Many thanks in advance,

    Carlos
     
    Carlos, Dec 8, 2003
    #1
    1. Advertising

  2. Carlos

    Baphomet Guest

    "Carlos" <> wrote in message
    news:...
    > Hi all,
    >
    > I'm looking for the phase response formula of a Butterworth filter as
    > a function of its order and (f/fc), equivalent to the well known
    > amplitude one:
    >
    > 1
    > --------------------
    > SQRT(1+(f/fc)^(2*n))
    >
    > If there isn't a single formula depending on n, I'd be grateful if you
    > could give me the formulas for 1st (I think that one is just
    > -Arctan(f/fc), right?), 2nd and 3rd order.
    >
    > Many thanks in advance,
    >
    > Carlos


    Google [phase response butterworth filter]

    http://www.crbond.com/papers/btf.pdf

    http://www.kemo.com/data/datasheets/responsecurves/fr_sfr.pdf
     
    Baphomet, Dec 8, 2003
    #2
    1. Advertising

  3. Carlos

    Carlos Guest

    "Baphomet" <> wrote in message news:<>...
    >
    > Google [phase response butterworth filter]
    >
    > http://www.crbond.com/papers/btf.pdf
    >


    Thanks, I had actually found this one, but wasn't sure if I could just
    replace W by (f/fc) and also wondered whether there would be a general
    formula depending on N (which would be very convenient for the
    crossover spreadsheet I'm working on). Anyway, I have plotted those
    and they seem to match the curves shown in Dickason's Loudspeaker
    Cookbook, so I'll go with them.

    Thanks again

    Carlos
     
    Carlos, Dec 9, 2003
    #3
  4. Carlos

    Ban Guest

    Carlos wrote:
    || Hi all,
    ||
    || I'm looking for the phase response formula of a Butterworth filter as
    || a function of its order and (f/fc), equivalent to the well known
    || amplitude one:
    ||
    || 1
    || --------------------
    || SQRT(1+(f/fc)^(2*n))
    ||
    || If there isn't a single formula depending on n, I'd be grateful if
    || you could give me the formulas for 1st (I think that one is just
    || -Arctan(f/fc), right?), 2nd and 3rd order.
    ||
    || Many thanks in advance,
    ||
    || Carlos

    Carlos,
    The phase response of a filter of arbitrary order and type is:

    phi= -SUM arctan ai*(f/fc) / (1-bi(f/fc)^2)
    i
    with ai, bi being the coefficients of 2nd-order blocks.


    --
    ciao Ban
    Bordighera, Italy
    electronic hardware designer
     
    Ban, Dec 9, 2003
    #4
    1. Advertising

Want to reply to this thread or ask your own question?

It takes just 2 minutes to sign up (and it's free!). Just click the sign up button to choose a username and then you can ask your own questions on the forum.
Similar Threads
  1. erthlink

    3 phase power formula

    erthlink, Feb 25, 2004, in forum: Electronic Basics
    Replies:
    5
    Views:
    43,989
    Lord Erdel
    Feb 25, 2004
  2. Lord Erdel

    Re: 3 phase power formula

    Lord Erdel, Feb 25, 2004, in forum: Electronic Basics
    Replies:
    1
    Views:
    1,620
    John Popelish
    Feb 25, 2004
  3. N Cook

    Response 400 answer machine - no response

    N Cook, Nov 1, 2005, in forum: Electronic Repair
    Replies:
    2
    Views:
    322
    N Cook
    Nov 2, 2005
  4. Peter Hiscocks

    Audio Frequency and Phase Response

    Peter Hiscocks, Sep 14, 2006, in forum: Electronic Design
    Replies:
    0
    Views:
    313
    Peter Hiscocks
    Sep 14, 2006
  5. Takoma Park Volunteer Fire Department Postmaster

    Formula 3 phase amps from watts

    Takoma Park Volunteer Fire Department Postmaster, Jan 23, 2004, in forum: Electrical Engineering
    Replies:
    9
    Views:
    1,185
    Operator Jay
    Jan 29, 2004
Loading...

Share This Page