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PLL loop filter - phase margin problems

Discussion in 'Electronic Design' started by steve, Nov 29, 2005.

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  1. steve

    steve Guest

    Hi,

    I'm trying to design a 2nd order loop filter for a PLL but I'm running
    into difficulties following the analysis in National Semiconductors
    Application Note AN-1001.

    In the App note, they find that the time constant T1 of the loop filter
    is:

    T1=(sec(phi) - tan(phi))/w

    However, when I do the derivation, I get:

    T1=(sqrt(tan^2(phi) + 4) +/- tan(phi))/2w

    This latter is very similar to what is given in PLL Performance,
    Simulation and Design by Dean Banerjee, although he's got a gamma
    symbol in there for some reason. I'm not too worried about the gamma as
    it doesn't make a significant different to the bode phase plot for
    small values of gamma.

    However, there is a big difference in the phase plots between my
    derivation of T1 and the AN1001 derivation of T1 - does anyone have any
    idea why this is?

    I've included a fuller description of the problem (my derivation of T1,
    the bode plots etc...) at the following location:

    http://www.teamlinux.org.uk/steve/pll_3rd_order_filter.pdf

    If anyone has got any idea why these results differ, please let me
    know!

    Thanks,

    Steve
     
  2. Andrew Holme

    Andrew Holme Guest

    I think you made a mistake at equation 10.

    If phi = arctan(a) - arctan(b), tan(phi) is not a-b
     
  3. Jim Thompson

    Jim Thompson Guest

    "Gamma" is the damping factor... 0.7 to 1 is a desirable range.

    Why are you trying a second order filter? They're treacherous.
    Definitely NOT for the novice.

    The safest way is to design first order, then add a roll-off well
    above the zero-crossing frequency to kill reference ripple.

    ...Jim Thompson
     
  4. John Miles

    John Miles Guest

    Note that there are a couple of editions of the Banerjee book out there,
    and they have very different equations in many places. I'll leave
    further conclusions for others to draw.

    Dean is (or at least was) pretty good about answering support questions
    posted to the wireless.national.com board for their WeBench product.

    Unless you're just a glutton for mathematical punishment, or doing
    something truly offbeat, just use the free NatSemi or Analog Devices
    simulators. They work.

    -- jm
     
  5. maxfoo

    maxfoo Guest

    Did you try using National free online WEBENCH tools to see if your design
    matched to theirs?
     
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