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PLL loop compensation

Discussion in 'Electronic Design' started by Genome, Dec 5, 2003.

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  1. Genome

    Genome Guest

    Now I've got an EXOR gate with a gain of X/180 volts per degree

    And I've got a VCO with a gain of -j360(Fmax-Fmin)/Xf degrees per volt

    I multiply them together and get a gain of

    Gbum = -j2(Fmax - Fmin)/f

    That's a first order system with a constant 90 degrees phase lag.

    Setting the gain of my bum to unity and rearranging gives me the crossover
    frequency as

    fco = 2(Fmax - Fmin)

    Now I'm a simple sort so I'm not going to beat my head over the various
    barrels of some such otherwise. I don't know!

    You know this is fun. The first loop I ever stabilized was a 4046 one. I
    pissed about soldering bits in and out of the piece of shit and it really
    fucked me off. Then I read what Horrowitz and Hill said about it..... did
    the sums and the bastard worked. I smiled so much the top of my head fell

    I will now introduce something called the smegabout. Smegabout is the amount
    of jitterybug you want from the VCO and it's something to do with the
    ripplyness divided by something else at the input to the VCO.

    See... I do not have a basic clue.

    Never mind.... I will pick a smegabout figure of 1/100 and that defines the
    two resistors that sit in between my EXOR output and my VCO input. I can,
    near enough, just set up a voltage divider with the resistor in series with
    the output 100 times the one that goes to no volts.

    Putting that in the sum gives me

    fco = (Fmax - Fmin)/50

    I'll call the input thing Fin and I'll set up my VCO so it produces the same
    frequency when its input is at X/2. Then I'll pick a crossover frequency of

    OK... My center frequency is Fin and, if my VCO is linear then...

    Fmax = Fin + abit
    Fmin = Fin - abit

    and fco = Fin/10


    Fin/10 = (Fin + abit - Fin + abit)/50

    Fin/10 = 2abit/50

    abit = 2.5Fin

    So.... I set up my VCO so

    Fmax = 3.25Fin


    Fmin = -1.5Fin

    Oooooooooooh Shit! Who said life was easy?

    Taking four steps back.......

    Fmax - Fmin = 3.25Fin + 1.5Fin

    Fmax - Fmin = 4.75Fin

    And I'll throw away that idea about it sitting at X/2 when it's happy.

    Then I'll set Fmin at Fin/2 which gives me Fmax at 5.25Fin. And it locks
    with questionmark volts at the VCO input.

    I can't help thinking that there might be a better solution. Knob.

    Anyways, having done all that, it's a thing that crosses over at Fin/10
    first order. I go and stick a capacitor in series with the resistor to
    ground such that its value is something like 1/2piRg(Fin/20) or sum such.

    Yazza Yazza Yazza.

  2. Genome wrote...
    ROFLOL, more fun than a barrel of monkeys. I imagine.

    - Win

  3. Genome

    Genome Guest

    That would be ROTFLMAO.

  4. Tim Auton

    Tim Auton Guest





  5. John Larkin

    John Larkin Guest

    The VCO is an integrator, at least as far as we (you, me, and the XOR
    gate) are concerned.

    Suppose we had a vco with a sensitivity of 1 MHz/volt. It drives an
    xor phase detector powered by vcc, and suppose the reference freq is
    the same as the vco freq. Now whack the vco input by one volt, and you
    get a 1 MHz triangle wave out of the xor (plus some hf trash which
    we'll ignore.) So the integration constant is 1e6 * 2 * Vcc, or
    kvco*2*vcc to be academic. So this


    has a transfer function of 2*vcc*kvco/s,

    where s is the integration operator and where xorin is pronounced

    That has a 90 degree lag at all freqs, but also a declining gain as
    1/f. So if you close this loop with a simple r-c lowpass filter, it
    rings like a bandit, or more likely oscillates.

    But because it's an integrator, it's fairly insensitive to ripple on
    the vco control voltage, so high-frequency ripple at the filter output
    tends not to be a big deal.
    Smegabout isn't just a linear thing because of this 1/f rolloff, so
    jitter will be better than the ratio of the resistors in the filter...
    much, much better if kvco is small, like for an LC or especially a
    crystal oscillator. In a crystal oscillator PLL, you can often get by
    with no lowpass filter at all, which is sure nice for loop dynamics:
    all that's left is negative feedback onto an integrator.

    Or something like that, within a factor of 2*pi or so, conditional on
    Chardonnay content.

  6. Genome

    Genome Guest

    Yeah, I almost believed/knew that but I feel a bit iffy about spuking out
    the sum without being able to justify it. You will guess that my maffs is
    crap and I can't take things at face value........

    I'll give it another go.

    My VCO has a gain of (Fmax - Fmin)/X hertz per volt. I want to convert that
    to degrees per volt. Now, if I sit about and count the number of degrees
    that have gone by I get the impression that time comes into things. If I'm
    counting then perhaps my VCO is doing the same and it's called intygrating.

    Fair enough?

    So now my VCO gain becomes Pickatime(Fmax - Fmin)/X pickanangledefinition
    per volt. Pickatime is 1/frequency so my VCO gain becomes (Fmax-Fmin)/Xf
    pickanangledefiniton per volt. One lot of oscillation is 360 degrees which
    defines my pickanangle so my VCO gain becomes 360(Fmax - Fmin)/Xf degrees
    per volt.

    Now.... at the moment I can't justify throwing in the 90 degrees phase lag
    of a -j without just saying that things that go at 1/f just have that one
    associated with them.
    Errrr..... that would be a 'square' wave, not exactly but you get the
    picture?(I'm a fucking pedant me) Back on the party. My XOR gate gain was
    X/180 volts per degree so I multiply them together and get what I said
    before -j2(Fmax - Fmin)/f. Which agrees with what you are saying, kind of.

    This is the thing about these things, you work out all the bits in between,
    dibble about with it and bung something else in....
    If you want to be a bit more solid about kvco. I mean..... you can't just
    puke out stuff without justifying it.
    Where s is the obsfucation operator...... as used by..... Narf, s is jw and
    w is 2pif.

    Why not use d instead?
    Well, that would be me minus j....... which I still can't prove other than
    the fact it's a 1/f thing.

    What you mean to say is a voltage divider does VOUT = VIN.RG/(RIN + RG)
    Where RIN is in series with the EXOR output and RG is the one down to
    ground. If you replace RG with a capacitor then you deal with XC, impedance
    of the capacitor. XC is 1/j2pifC or 1/jwC or 1/sC....

    Lazy bones, lying in the sun, how you going to get the days work done?

    Now, I can sort of believe in a capacitor having a -j between its volts and
    its amps.

    In the limit (maniacal larf) above the frequency where the capacitor has the
    same impedance as the resistor the thing reduces to VOUT = VIN.XC/RIN or
    something like -jVIN/RIN2pifC

    And that -j gives me another 90 degrees of phase shift. Add that to the 90
    ones from the VCO and things hit 180. It's a feedback loop so I adds the 180
    to get 360 and it's unstable.

    Mind you...... I might be a bit wicked and set the corner frequency of me RC
    filter at half the dooo daah and have a stable one.
    Perhaps I was worrying unecessarily, like I said 'I'm Clueless'.... Mind you
    I don't thick the 'it's an integrator' argument cuts it. The best I can
    dribble is that 'it makes its decision at the same point of the ripple'....
    or some such.
    What on earth is smegabout?

  7. Genome wrote...
    Surely it's a simple matter of tetragametic chimera fusion.
    Multiple types of DNA, in a true Genome conglomeration.

    - Win

  8. Jim Thompson

    Jim Thompson Guest

    Sheeesh, Win, You live such a sheltered life. Surf on "smega' and see
    what you get ;-)

    ...Jim Thompson
  9. Jim Thompson wrote...
    OK. Southwestern Michigan Economic Growth Alliance?

    Smega Technologies (thermostats, thermocouples, etc.)?

    Europe's Accounting and Financial Reporting Guidelines
    for Small and Medium-sized Enterprises (SMEGA)?


    - Win

  10. Jim Thompson

    Jim Thompson Guest


    ...Jim Thompson
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