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loop filter question

Discussion in 'Electronic Design' started by frank, Jul 30, 2003.

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  1. frank

    frank Guest


    Loop filter transfer functions are of the type:


    Vcont(s) is the control voltage in laplace format.
    Icp(s) is the charge pump current in laplace format.

    Thus, if H(s) is an impedance, how is bandwidth understood ?

    Usually, when H(s) is Vout(s)/Vin(s), bandwidth is understood as the
    frequency where H(s) is at -3dB. However to get a decibel value, H(s)
    must be an absolute number. 10log(X ohms) or 20log(X ohms) makes no

    Help me.

  2. Mike

    Mike Guest

    You don't necessarily need to know the input to calculate the bandwidth.
    For an opamp, you can measure vout(freq1)/vout(freq0) to find the
    bandwidth, assuming the input is held constant. This tells you nothing
    about the gain of the opamp circuit, but that's a different calculation.

    In mathematical terms, here's the bandwidth calculation you're doing:

    20*log(H(jw1)) - 20*log(H(jw0)) = -3

    20*log(Vout(jw1)/Vin(jw1)) - 20*log(Vout(jw0)/Vin(jw0)) = -3

    20*log((Vout(jw1)*Vin(jw0))/(Vout(jw0)*Vin(jw1)) = -3

    It is often the case that Vin(jw0) = Vin(jw1). If that is true, then

    20*log(Vout(jw1)/Vout(jw0)) = -3

    The Vin terms have canceled, leaving only the Vout terms.

    If the loop filter in question is in a PLL, then you may well have other
    problems with your calculation. The loop filter in a charge pump PLL is
    often a series RC from the filter node to ground, which has the transfer

    Vo/Ii = (sRC + 1)/(sC)

    When s = 0, the transfer function is infinite, so the bandwidth isn't well
    defined. The unity gain frequency, on the other hand, is well defined, and
    is often of more use when looking at an open loop system.

    If you put the filter in a PLL loop with an integrating VCO and close the
    loop, you'll obtain a more traditional second order transfer function, with
    a traditionally defined bandwidth and damping factor.

    -- Mike --
  3. frank

    frank Guest


    I was looking at the following website:

    It focuses on 3rd order loop filters. Assuming VCO gain, Charge pump
    currents, PFD gain are available (and they are), how am I to
    comprehend the loop bandwidth ? (yes, back to the original question)
    What I am actually looking here for is a quick explanation on what is
    a loop filter bandwidth.

    For example if a loop filters's bandwidth is 20kHZ (picked at random),
    does this mean that the reference frequency cannot exceed this ?
    should not exceed this ? the PLL will not lock if the reference
    frequency does not respect the loop bandwidth criteria ?
    A loop filter is not low-pass filter rigth. although their electrical
    architecures are similar, they have different purposes i assume.

    And yes, I am planning to read up on loop filters tonite, i am just
    looking for a nudge in the rigth direction.I know nobody enjoys
    explaining at lenght material that is deemed basic/common knowledge.

    BTW, I am working on a PLL with a 3rd order LPF. I understand pretty
    much all the modules (CP,PFD,Frequency divider,prescaler ...), except
    for the LPF!!

  4. Ban

    Ban Guest

    I also do not understand the page you have referenced. It has quite heavy
    errors in it. I do not think these guys who made it up have any idea what
    they were doing. Seems to me at technicians level copying from some books or
    other docs.

    First and utmost, the filter shown is of 2nd order only despite the 3 caps
    used and there are only poles on the real axis, thus limiting available Q to
    less than 0.5 The most significant filter parameter, the output impedance
    of the phase-detector is not even shown.

    The literature Jim selected is probably at another level, I personally
    haven't read these books, but I have seen him being familiar with PLLs.

    ciao Ban
  5. Jim Thompson

    Jim Thompson Guest

    PLLs aren't something for amateurs to do anything with except copy

    To analyse requires a good understanding of Laplace notation.

    ...Jim Thompson
  6. Jim Thompson

    Jim Thompson Guest

    Three caps in the filter plus the pole in the VCO? Ought to be fun to
    watch ;-)

    ...Jim Thompson
  7. James Meyer

    James Meyer Guest

    I beg to differ. You don't learn to drive by first studying
    thermodynamics until you can design an internal combustion engine from first
    principles. Likewise, if you pay attention while you're fiddling, you *can*
    learn a lot about circuit dynamics.

  8. Jim Thompson

    Jim Thompson Guest

    Jim, Driving a car and *designing* a car are entirely different

    Methinks you argue for the sake of argument... you must have nothing
    better to do this week ;-)

    ...Jim Thompson
  9. Tim Shoppa

    Tim Shoppa Guest

    A novice was trying to fix a broken Lisp machine by turning the
    power off and on.

    Knight, seeing what the student was doing, spoke sternly: "You cannot
    fix a machine by just power-cycling it with no understanding of what
    is going wrong."

    Knight turned the machine off and on.

    The machine worked.
  10. James Meyer

    James Meyer Guest

    And twiddling is a good first step toward gaining understanding and

    To learn something, first you need to identify what it is that you want
    to know. Twiddling gives you the opportunity to see what you need to know.

  11. James Meyer

    James Meyer Guest

    :cool: Illustrating the difference between uninformed and intelligent
    tinkering, I suppose.

    The first rule of intelligent tinkering... save all the parts.

  12. James Meyer

    James Meyer Guest

    Last week I had a colonoscopy sans sedation. They found nothing that
    would explain my anemia. This week I had the complementary upper GI examination
    again sans sedation. Even with biopsy sampling, they found nothing remarkable.
    Hope they washed the machine in between times.

    Nothing better to do?

    Even highly trained doctors aren't above a little "tinkering" from time
    to time.

  13. One offs like this don't a case make. Many a time I've pulled the plug
    of a spark lead and put it back on, and the car still did not run.

    Kevin Aylward
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
  14. wrote...
    No doubt it was running a Microsoft Windows operating system.

    - Win
  15. James Meyer

    James Meyer Guest

    You may only *want* to do it once, but the Dr.s may have other ideas.
    They recommended once every five years for me. 8-(

    Jim "Now this thread is *really* OT." Meyer
  16. Jim Thompson

    Jim Thompson Guest

    I came out perfect in all those "scopes". One doctor was even joking
    with me, "Want to see a perfect appendix?"

    ...Jim Thompson
  17. James Meyer

    James Meyer Guest

    Yeah, right... There's a quick and easy test for GI bleeding that
    involves a tiny stool sample and a reagent that detects blood. I've always
    scored zero on that test.

    It's like somebody suggesting that poor bypass capacitor selection is
    always responsible for a wildly unstable feedback loop. Ignore the evidence and
    apply knee-jerk cookbook solutions.

    It's too bad that Dr.s aren't required to have at least some exposure to
    an engineering discipline or two.

  18. Jim Thompson

    Jim Thompson Guest

    Getting back to the OP, see:

    Newsgroups: alt.binaries.schematics.electronic
    Subject: Re: loop filter question on S.E.D - PLL-Equations.pdf
    Message-ID: <>

    The attachment show Laplace representation of a second-order PLL in
    response to the original question here on S.E.D

    Adding addition reactive elements to the "filter" will raise the order
    and complicate the achievement of stability.

    The real world complicates matters by giving different gains as the
    circuit is powered-up, often producing instabilities that don't cease
    at equilibrium.

    However spur filters may be added outside of the loop bandwidth.

    ...Jim Thompson
  19. maxfoo

    maxfoo Guest

    The loop filter can be easily understood if you look at the phase
    noise plot. basically it limits the noise from the center frequency of
    the VCO.
    and yes its a lpf...
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