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PLL loop filter design

Discussion in 'Electronic Design' started by [email protected], Mar 31, 2007.

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  1. Guest

    Hello,

    I'm trying to design a loop filter for PLL. I have a stable reference
    signal (RF REF=70 MHz) and output from VCO (RF IN=70 MHz, but very
    small tunnig range, few Hz). I want to synchronize my VCO with RF REF
    (this freq. won't be changed, all freqs. are fixed). Levels of these
    signals are about +7dBm, and this is sufficient for MiniCircuits RPD-2
    phase detector. I tried to desing filter according to simple guide in
    R. Best "Phase-Locked Loops" but I had a stange values (for example
    capacitance in femtofardars). Any hints how to start?
     
  2. Andrew Holme

    Andrew Holme Guest

    I normally express open loop gain in terms of the Laplace 's' operator, and
    generate Bode plots using SCILAB. I adjust the various parameters, keeping
    an eye on gain and phase margins, to optimise performance.

    Download SCILAB from www.scilab.org

    Try running this script:

    c1 = 680e-12;
    c2 = 100e-12;
    r = 1800;
    kvco = 2e6;
    kpd = 0.5e-3;
    s = poly(0,'s');
    f = 1/s/c1 * (1+s*r*(c1+c2)) / (1+s*r*c2);
    g = kpd * f * kvco/s;
    g = syslin('c', g);
    xbasc(0);
    bode(g, 1e3, 1e7, .01);

    You can also plot closed loop gain, step response and much more.
     
  3. MooseFET

    MooseFET Guest

    Add noise to that list.

    Watch the noise voltage at the control input of the VCO.

    Dont do this:

    ---/\/\-----+-------/\/\-------+--------VCO
    ! !
    --- C(small) \
    --- /
    ! \
    GND !
    ---
    ---
    !
    GND

    Do do this:

    --------------------/\/\-------+----+---VCO
    ! !
    \ ---
    / --- C(small)
    \ !
    ! GND
    ---
    ---
    !
    GND

    Even though they can have the same phase margin, the lower one has a
    low impedance on the VCO's control input, at frequencies above the
    gain cross over.
     
  4. I can recommend the PLL designer available for
    download at the Analog Devices website. A key
    figure is the steepness of the slope of the VCO.
    How many MHz/volts does ist make and is it
    moreless linear ? Then, a key part is the operational
    amplifier for the filter. The Analog Device designer
    shows how the input bias current influences the
    performance of the loop.

    Rene
     
  5. Tom Bruhns

    Tom Bruhns Guest

    In addition to the advice from Andrew and MooseFET, I'd suggest you
    download the free PLL design software from the Analog Devices web
    site. It takes a lot of the work out of PLL design. I'll caution
    that no software I know of is a substitute for engaging your brain,
    but it can at least be very helpful for gaining insights into how
    things work. For example, the software won't TELL you what loop
    bandwidth to use. You have to think carefully about that, and make an
    intelligent choice based on your requirements and the characteristics
    of the VCO, reference, and the rest of the circuit.

    (Having just designed a loop not too different from what you describe,
    I can say I'm surprised by the femtofarad value. I'd expect with a
    very narrow tuning range that you would implement a loop with narrow
    bandwidth, and that should have relatively large capacitances in it.
    My problem is more commonly finding physically small microfarad-size
    caps that have very low dielectric absorption and low noise.)

    Cheers,
    Tom
     
  6. John  Larkin

    John Larkin Guest

    We recently did this, locking a 40 MHz VCXO to an external 10 MHz
    reference. We divided the 40 down to 10, xor'd it with the external
    input (both in an FPGA) and used a simple r-c lowpass from the xor
    output to the VCXO control input. So the whole phase locked loop costs
    a few cents. Just figure out the natural loop unity-gain frequency and
    set the r-c rolloff to be, say, 10x that... typically on the order of
    a few KHz rolloff for a VCXO. You get a bulletproof first-order loop
    and excellent phase noise behavior.

    This works because your maximum possible error frequency is small, so
    acquisition range is not a problem.

    John
     
  7. Guest

    Hm, I found only ADIsimPLL, and I can't choose
    different phase detectors and I don't see how to input
    other values.
    Pure VCO without any amplifier may be tuned from 69.999.975 Hz
    (Vtune=0V) to
    70.000.025 Hz (Vtune=12V), with good linearity. With constant Vtune
    output frequency from VCO is quite stable,
    it changes about 5-10Hz during 10min. period.
    I think that I'll use a simple passive lag filter like this:

    R1
    ----/\/\/\/\/\-----+---------
    |
    |
    /
    \ R2
    /
    \
    /
    |
    |
    |
    ___ C
    ___
    |
    |
    |
    GND


    with inverting opamp amplifier with gain=10 connected to the output of
    this filter
    (becouse output from phase detector is negative). So, pure Kvco is
    4.16 Hz/V and
    with opamp amplifier it will be 41.6 Hz/V = 130 rad/Vs. From RPD-2
    datasheet we know, that
    Kd = 8mV/deg = 0.460V/rad. I choose damping factor at xi=0.707. For
    this type of filter,
    we have relations (I took it from E. Best book):

    1: tau_1 = R1C
    2: tau_2 = R2C

    3: w_n^2 = Kvco*Kd/(tau_1 + tau_2)
    4: xi=0.5 * w_n (tau_2 + 1/(Kvco*Kd))

    where w_n is a natural frequancy and it will be w_n=31.4 rad/s
    (=10Hz). From 4th relation we
    have tau_2=0.0276 s, and from 3rd we have tau_1=0.061 s. These values
    are reasonable,
    E. Best wrote in his book, that tau_1 should be about 5 to 10 times
    larger than tau_2.
    I assume, that 100k for R1 will be a good choice. From 1st relation we
    have C=61nF, and from 2nd R2=450k.
    And finally, filter looks like this:


    R1
    --|----/\/\/\/\/\-----+---------
    | |
    | |
    \ /
    / \ R2
    \ 500 /
    / \
    \ /
    | |
    | |
    | |
    | ___ C
    | ___
    | |
    | |
    GND |
    GND


    Parallel resistor (500 Ohm) at the input is for impedance match
    (output impedance of RPD-2
    phase detector is 500 Ohm). Are this calculations correct?
     
  8. Guest

    I see now, that I made a stupid mistakes when I calculated this, I
    used some
    loop filter calculator without thinking :)
    For narrow bandwidth loops? I heard that for such a loops digital
    filters
    (ADC->some computations->DAC) are much better than a ordinary RC
    filters,
    because for example capacitor capacity may change with age and ambient
    temperature.
     
  9. Guest


    A little supplement: I made a miscalculation, proper values are:
    Kvco=260 rad/Vs, Kd=0,46 V/rad, w_n=62.8 rad/s, tau_1=0.03s,
    tau_2=0.014s
    R1=100k, R2=46k, C=300nF.
     
  10. Tom Bruhns

    Tom Bruhns Guest

    I would expect the loop to be stable enough--to have enough margin--
    that small changes in capacitance wouldn't make much difference. Even
    as long as the temperature changes are not abrupt, things should be
    fine. But there are other characteristics I do worry about. Size is
    one. I'm not sure I could make a digital filter as small as the
    analog, but it's a good thought. Fortunately, C0G multilayer ceramics
    (which are quite stable over temperature and time and voltage, and
    have low dielectric absorption) are available these days up to rather
    large values, as are tiny op amps with low input bias current.

    I can see that a nearly-all-digital solution would make sense for some
    applications, though probably not for mine, which isn't all that
    narrow a loop bandwidth. Thanks for the suggestion.

    Cheers,
    Tom
     
  11. Tom Bruhns

    Tom Bruhns Guest

    I have not checked the calculations, and I'm just assuming the values
    are right. Just wanted to point out that noise may be a
    consideration. Such large resistor values may add noticably to the
    noise. Of course, as you go to smaller resistor values, the capacitor
    value increases, and that may be a problem. If you have plenty of
    space, consider, say, a 1uF polypropylene part. Then the resistor
    values would scale to give you about 1/4 as much resistor noise.

    Also, with a passive filter, will your phase comparator be able to
    drive it to the full voltage range you need for the VCO? One reason
    to use an op amp based filter is to get some voltage gain--to increase
    the maximum output voltage range.

    Cheers,
    Tom
     
  12. Chris Jones

    Chris Jones Guest

    The OP could also try an ADF4001 which I have used for a similar purpose. I
    used the ADISimPLL program to design the loop filter. They seem to have a
    new version that I have not tried.
    http://forms.analog.com/form_pages/rfcomms/adisimpll.asp
    A microcontroller or similar would be needed to put the frequency division
    ratios into the ADF4001.

    Chris
     
  13. Guest

    There is a small problem in this IC: phase detector works on very low
    frequency
    (REF IN and RF IN signals are divided and after this operation are
    mixed in digital
    phase detector). For phase noise issue, I want to mix these signals on
    high
    frequency (in double balanced mixer or in fast digital phase detector,
    for example AD9901).
     
  14. Tim Shoppa

    Tim Shoppa Guest

    Seems likely he confused the VCO frequency with loop bandwidth.

    I thought things got bad when folks started punching numbers into
    pocket calculators without any regards for what they meant - computers
    make the problem worse. The not-otherwise-encountered units found in
    loop filter calculations (volts per radian and radians per volt both
    represented by a capital K) often confuse folks the first time around!

    Tim.
     
  15. John Larkin

    John Larkin Guest

    Right. The big division magnifies phase noise.

    Once an AD9901 walks the VCO into lock, it becomes an xor. So if you
    don't have a large acquisition range problem, save a lot of money and
    hassle and just use a 20-cent xor.

    John
     
  16. Jim Thompson

    Jim Thompson Guest

    The big boys go "fractional-N".

    ...Jim Thompson
     
  17. Chris Jones

    Chris Jones Guest

    I was not aware that the OP required a frequency ratio that would
    necessitate a low comparison frequency, and if the OP did require a low
    comparison frequency then a simpler phase detector would not solve the
    problem. (I have never seen the complete original post since someone
    trimmed it away.) Unless the OP requires a nasty frequency ratio between
    the reference input and the VCO output, the ADF4001 would allow high
    comparison frequencies. The reference and feedback dividers can divide by
    numbers as low as 1, so it could do just as high a comparison frequency as
    any other integer-N synth could do, (up to the limit imposed by the spec,
    obviously).

    Chris
     
  18. OK, the AD9901 is not low cost and quite hot, but it is fast, reasonably low-noise
    and moves that Kpd wobble away from the lock point.
    I really liked it.

    regards, Gerhard
     
  19. Chris Jones

    Chris Jones Guest

    You can program the dividers in the ADF4001 to divide by ratios down to 1,
    so it is no worse than any other integer-N PLL in that respect.

    Chris
     
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