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Estimating PC pad capacitance?

Discussion in 'Electronic Design' started by Tom Bruhns, Mar 23, 2007.

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  1. Tom Bruhns

    Tom Bruhns Guest

    Anyone have any favorite reasonably accurate applets or formulas or
    the like for calculating the capacitance of a small rectangular
    surface against an extensive ground plane? That is, for example, the
    capacitance of the pad for a surface-mount part, where there's a
    ground plane about 1.5mm behind the pad, through FR4 PC board
    material, er about 4.5.

    I have a clue that the fringing effects for small pads is significant,
    in that I can use a simple-minded calculator that only uses the plate
    area for a cap with two equal size plates, and doesn't consider
    fringing effects, and get one value -- and then look at the pad as if
    it were a short section of microstrip transmission line, calculate the
    capacitance per unit length of that geometry line, and multiply by the
    length of the pad to get an estimate of the pad capacitance. For one
    example get about two times higher capacitance than the "dumb" plate
    area/separation applet gives. Given that there is additional fringing
    for the pad versus what's considered in the microstrip, I suppose the
    actual capacitance is even higher.

    I know there are full-blown geometry calculators, some available for
    free, but I'm hoping for something simpler to use, along the lines of
    typical microstrip applets where you enter length, width, dielectric
    thickness, pad thickness, and dielectric relative permittivity, and an
    answer with perhaps 10% accuracy pops out.

  2. John Larkin

    John Larkin Guest

    It would be handy to have a graph of c versus size for, say, square
    pads at a unit distance above a ground plane, namely a fringing graph.

    If you google "fringing" it's usually preceded by the word

  3. Tom Bruhns

    Tom Bruhns Guest

    Yes, good idea, John. If I don't find the simple applet I'm looking
    for, maybe I can make such a graph. I do have applications that can
    do the calculation accurately, and if I fire one up to make one calc,
    it should be fairly easy to just change the pad size and run it for a
    range of sizes. I'd probably do it for not only square but for
    perhaps 1.2:1, 1.5:1 and 1:2 ratio rectangles too.

  4. John Larkin

    John Larkin Guest

    If you do that, I'd love to get a copy.

  5. Joerg

    Joerg Guest

    Sorry if this spoils the fun with Maxwell's equations:

    Scroll down to "Pad Capacitance Extraction for IBIS Models", select and
    request the paper at the bottom. But check whether they charge for it.

    John, if there is a charge maybe they give you access to that for free
    since you are a PADS customer.
  6. Tom Bruhns

    Tom Bruhns Guest

    Well, it's not Maxwell's equations I'm using directly, but ADS, to do
    what the abstract for the paper you reference suggests. I just put an
    ideal 1uH inductor in series with 50 ohms to a pad whose size I can
    vary easily, and look for the resonance, indicated by a sharp dip in
    S11. It's just a bit tedious. It does suggest that even with a pad
    an inch square on 1/16-inch thick FR4, the fringing is still a
    moderately significant effect. I got sidetracked and didn't finish
    the work today. Maybe next week.

  7. Fred Bartoli

    Fred Bartoli Guest

    Tom Bruhns a écrit :

    what I'd try is to adapt the microstrip formula.

    With the ustrip you get the fringing correction value along the
    perimeter of your square pad. I'll be twice the value of the ustrip line
    of your pad width. Then you'd have to correct for the 'corner effect',
    which we can assume to be reasonably constant, given your pad width is
    sufficiently larger than the plane-pad separation. You just have to
    evaluate this corner effect with a solver, for a few height of interest
    and maybe add a curve fitting there for fanciness and voilà.
  8. Joerg

    Joerg Guest

    Possibly. Initially I thought to post a microstrip link but it won't
    take the corner distortion into effect. Anyhow, for microstrip this can

    And here is a collection of FEM routines and field solvers:
  9. joseph2k

    joseph2k Guest

    Not speaking for anyone else it sounds like simple paper and pencil from
    basic physics is the fastest approach. Get your answer, optionally
    including fringing, in less time than firing up and inputting the geometry
    into a program.
  10. Tom Bruhns

    Tom Bruhns Guest

    Hi Joseph,

    Thanks for your posting. At the very least, it's gotten me thinking
    more deeply about the calculation, which is of a sort I seldom need to
    deal with.

    I suppose I could assume the charge is distributed uniformly over a
    rectangular surface, and get an approximation of the capacitance, and
    compare that for a few cases against a numerical fields solver to see
    what error there is. Did you have in mind anything more complicated
    than the assumption of uniform charge distribution? I'm pretty sure
    that there are cases where that won't be very accurate.

    Once I decided to do it, it wasn't difficult to fire up ADS and get it
    to run the calcs for me. It's certainly faster than _I_ could do it
    with paper and pen.

    But seriously, I'd be happy to know if there's something I'm missing
    about doing it with a simple calculation.

  11. Tom Bruhns

    Tom Bruhns Guest

    Thanks for the ideas, Fred. I thought some about that, but actually,
    now that I have ADS set up to do it for me, it's no trouble to put in
    any particular pad size, thickness, and dielectric constant. And in
    surface-mount work, I am often dealing with pads whose dimensions are
    similar to or smaller than the separation to the ground plane.

  12. John  Larkin

    John Larkin Guest

    Suppose we have a 62 mil square pad on a 62 mil thick FR-4 pcb with
    ground plane on the far side. How would you go about computing total
    pad capacitance (including to the air) with pencil and paper?

  13. Rich Grise

    Rich Grise Guest

    Suppose we have a 62 mil square pad on a 62 mil thick FR-4 pcb with
    ground plane on the far side. How would you go about computing total
    pad capacitance (including to the air) with pencil and paper?[/QUOTE]

    I'd measure the capacitance, get out the lab notebook, and write down the
    answer. ;-)

  14. Fred Bartoli

    Fred Bartoli Guest

    Rich Grise a écrit :
    Doing this is certainly even not an easy task. I mean measure the
    capacitance :)
  15. Marra

    Marra Guest

    The word negligible comes to mind at 1.5mm
    If your having problems I would look elsewhere.
  16. John  Larkin

    John Larkin Guest

    The cheap little AADE cap-meter is great for 2-wire stuff like this.
    It resolves 10 fF.

    If somebody posts a prediction, I'll confirm it with a measurement.

  17. John  Larkin

    John Larkin Guest

    It's about 0.06 pF without fringing, so may get up towards 0.1 pF
    with. Sometimes that matters. With thinner dielectrics, like on a
    multilayer, c will go up but fringing will be somewhat less.

  18. joseph2k

    joseph2k Guest

    In some cases, like yours, the typical basic equation c=e'e(r)A/d fails to
    give better than correct order of magnitude. It includes the usually
    unstated assumption that A >>> d^2. For various symmetrical cases for A >=
    3*d^2 the fringing can be shown to be equivalent to the base equation. For
    cases like yours where A~=d^2 obtaining C from the work equation can be
    made to do but the time required quickly becomes more than using a finite
    element solver. I am not usually pushing the dimensions quite that hard.

    Just the same, i am glad that i had the limitations of my usual methods
    pointed out to me, and even happier that i got others to step back and
    re-check the limits of their typical practices as well.
  19. Fred Bartoli

    Fred Bartoli Guest

    John Larkin a écrit :
    I wasn't speaking of measurement instrument capabilities, I can easily
    get down to the fF, but rather meant: how do you measure it without
    introducing perturbations, i.e. field modification with your probe,
    wire, whatever...?

    At this pad size I guess you can't neglect this anymore.

    The true test would be a check between a field solver and a careful
    measurement, but we also need to accurately measure Er.
  20. MassiveProng

    MassiveProng Guest

    We used an embedded pad on our HV circuits (those that needed it) to
    achieve a feed forward effect on our feedback loop. It was in
    parallel with our HV feedback resistor voltage divider network.

    It gave us about 15 pF for a quarter inch wide pad at about just
    under an inch length. One "plate" was embedded, and the other was top
    side. Of course where in the embedding makes a huge difference for,
    as we all know, plate proximity distance directly affects capacitance
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