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Capacitor self-resonant freq question

Discussion in 'Electronic Design' started by Noel, Mar 10, 2005.

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  1. Noel

    Noel Guest

    For 900MHz band operation, I have seen some ac-coupling capacitors in
    the order of 100pF and others in the order of 10nF. If I use generic
    NPO/X7R caps, which is better?

    A typical 100pF NPO cap has self resonant freq around 1GHz while 10nF
    is well below 100MHz. Since above the self resonant frequency, the
    impedance goes up with frequency, looking like an inductor, I thought
    it was better to use a 100pF cap. But then again, with the 10nF cap,
    since the impedance is so much lower before it turns inductive, even
    at 900MHz, its inductive reactance is still small so maybe it doesn't
    really matter???

    Can anyone out there tell me if I am right or wrong?

  2. Terry Given

    Terry Given Guest

    NPO. X7R is IIRC +/-15% over its temperature range, NPO is close to
    zero. X7R also has a voltage coefficient of capacitance - as you
    increase the voltage across the cap, its capacitance drops. This isnt
    much, around 10% or so, but again NPO is almost perfect. X7R is also a
    bit piezoelectric due to the materials used, whereas NPO aint.

    So if you want a particular capacitance over a range of applied voltage,
    temperature and thumping, NPO is the way to go.

    If you only ever use NPO caps, that limits you to about 1nF or so. X7R
    gets you up to about 1uF, but RF caps are almost always much smaller
    than that.
    if they are in the same package (eg 0603) then the inductance is roughly
    constant, ie SRF varies with the square root of capacitance. To answer
    your question, model each cap as R + L + C. use the same fairly low R
    (1-10mOhm, can read off a datasheet maybe, or look at tdk website for
    math models) and the same L. plot the magnitude of impedance vs
    frequency for both caps, and look.

    lets use 100pF and 10nF in the same package, with 0.01Ohms esr

    100pF, 1GHz - L = 250pH (wow, thats low)
    Z = 1.59 Ohms
    ESR = 0.01 Ohms
    Qu = 159

    10nF 100MHz - L = 250pH
    Z = 0.025 Ohms
    ESR = 0.01 Ohms
    Q = 2.5

    so the 10nF is going to have a not-very-sharp dip from 0.025 ohms down
    to 0.01 Ohms (resistive) at 100MHz. At 1GHz the impedance will be about
    1.6 Ohms inductive, at 10GHz its 16 Ohms inductive and at 10MHz its
    about 1.6 Ohms capacitive.

    The 100pF cap is about 160 Ohms capacitive at 10MHz, 16 Ohms capacitive
    at 100MHz and 16 Ohms inductive at 10GHz. At 1GHz it has a sharp
    resonant peak down to 0.01 Ohms resistive.

    So around the resonance of the 100pF capacitor the impedance is a *LOT*
    lower than the 1.6 Ohms inductive of the 10nF cap. Obviously the actual
    ESR is critical, as it directly controls the unloaded Q of the device.
    always model your parts as RLC circuits and you wont be wrong.

  3. Tim Shoppa

    Tim Shoppa Guest

    A typical 100pF NPO cap has self resonant freq around
    Order of magnitude reality check (emphasis on "magnitude"):

    "perfect" 100pF capacitor at 900MHz: 1.8 ohms impedance

    "perfect" 10nF capacitor at 900 MHz: 0.018 ohms impedance.

    "Real" 10nF capacitor at 900 MHz: 80 ohms impedance (mostly inductive).

    So the inductive reactance is not (in relative terms compared to
    capacitive reactance) small at all, it's thousands of times bigger.

    If the circuit impedance is 50 ohms to a few hundred ohms, the
    impedance of the 10nF capacitor will have a measurable effect (gain
    down a fraction of a dB to a few dB). Whether a fraction of a dB or a
    few dB matter or not depends on what the circuit is there for.

    It still decouples... which is probably the only reason it's there!

  4. John Larkin

    John Larkin Guest

    Why does the 10 nf cap have a higher impedance than the 100 pf? If the
    capacitors are the same types (say, both 0805's of similar
    construction) the esl will be pretty much independent of capacitance,
    and the bigger cap may well have lower esl (more layers.)

    I routinely do multi-GHz dc blocks along microstrip transmission
    lines, and TDR them to see how well they work. The only visible
    difference between a 1 nF 0603 cap and a 2.2 uF 0603 is the improved
    low-frequency coupling due to the obvious capacitance difference.

    About the only time a lower-value cap will have a lower impedance is
    when it hits series resonance.

    Our observation is that, in general, bigger caps behave like bigger


  5. I found exactly this too. When I got a spectrum analyser with tracking
    generator, the first thing I did was look at the impedance of various
    chip caps.

    Manufacturers datasheets often show power supply bypassing with
    paralleled chip capacitors of say 100pF || 10nF || 1uF. What do you
    think about this? Is there a reason not to just use say 3 x 1uF?
  6. I read in that John Devereux>) about 'Capacitor self-resonant freq question', on Thu, 10 Mar
    The Z/f characteristics depend critically on where, and how large, the
    parasitic inductances are. Consider, for example, the difference between
    the Z/f characteristics of three equal caps and three with very
    different values, if they are measured via 30 mm long tracks.
  7. John Larkin

    John Larkin Guest

    IC manufacturers all think the world revolves around their part, so
    they want three different caps on every power pin. The idea of
    staggering the srf points of bypass caps is, in my opinion, silly. A
    power plane or island adjacent to a ground plane, scattered with a few
    0.33 uF or whatever surfmount caps, is good enough for most cases.

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