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Self-resonant Frequencies of Some Ceramic Capacitors

In that version of the GPS+voice interface, I sprinkled 100 nF and 100 pF SMD caps across the input lines in the hope that they’d reduce EMI on the audio board. The board worked fine for years, but now that it’s time to build another board & box, I figured it’d be good to know a bit more about their actual response.

So I cobbled up a test fixture with a 3 dB pad from the tracking generator output and a 20 dB pad to the spectrum analyzer input (both of those are bogus, because the cap impedance varies wildly, but work with me on this):

Ceramic 100 nF cap on copper

Ceramic 100 nF cap on copper

Pulled an assortment of 100 nF ceramic caps from the stockpile:

100 nF ceramic capacitor assortment

100 nF ceramic capacitor assortment

And rubbed them against the HP8591 spectrum analyzer & tracking generator:

Cap Comparison - Detail

Cap Comparison - Detail

Their self-resonant frequencies are much lower than I expected:

Cap Comparison

Cap Comparison

The attenuators produce about 17 dB of loss with no cap in the circuit, so the disk caps are pretty much asleep at the switch from VHF on up. The small bypass cap in the top photo is OK and the SMD cap is pretty good, but they’re all well past their self-resonant frequency and acting like inductors.

The relevant equations:

  • FR = 1/(2π √(LC))
  • XC = 1/(2π f C)
  • Q = FR / BW
  • ESR = XC / Q

The drill goes a little something like this:

  • Find resonant frequency FR and 3 db bandwidth BW
  • Knowing FR and C, find parasitic L
  • Knowing FR and BW, find Q
  • Knowing XC and Q, find ESR

In round numbers, the 100 nF SMD cap has L=2 nH and ESR=60 mΩ.

Now, it turns out a 100 pF SMD cap resonates up at 300 MHz, between the VHF and UHF amateur bands:

SMD - 100 pF Bandwidth

SMD - 100 pF Bandwidth

So I think the way to do this is to pick the capacitance to put the self-resonant frequency in the VHF band, parallel another cap to put a second dip in the UHF band, and run with it. A back of the envelope calculation suggests 470 pF and 47 pF, but that obviously depends on a bunch of other imponderables and I’ll just interrogate the heap until the right ones step forward.

Just to show the test fixture isn’t a complete piece of crap, here’s a 12 pF cap resonating up around 850 MHz:

SMD - 12 pF Bandwidth

SMD - 12 pF Bandwidth

For the combination of components, sweep speeds, bandwidths, and suchlike in effect, the spectrum analyzer’s noise floor is down around -75 dBm. I think the 12 pF cap is actually better than it looks, but I didn’t fiddle around with a narrower resolution bandwidth.

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  1. #1 by hexley ball on 2011-11-09 - 12:27

    For a sanity check, you might take a look at this: http://www.home.agilent.com/upload/cmc_upload/All/exp79.pdf?&cc=US&lc=eng

    The author reports a 94 MHz self-resonance for 100nF ceramic disk with 2mm leads.

    BTW, I can’t help wondering about your resistor in what appears to be a blue vitreous enamel case — wouldn’t an SMD resistor likely have lower parasitic inductance?

    • #2 by Ed on 2011-11-09 - 19:59

      94 MHz self-resonance for 100nF ceramic disk ceramic disk with 2mm leads

      If I read that table correctly, it’s actually 1 nF. Increase that by a factor of 100 and the resonant frequency drops by a factor of 10, right down around the 10 MHz I’d measured.

      Back in Jan 2005 I’d done a Circuit Cellar column that ran the numbers for a straight wire lead: about 1 nH per mm. So 2.9 nH for 4 mm sounds about right.

      wouldn’t an SMD resistor likely have lower parasitic inductance?

      Yup, but then it wouldn’t have those long leads for easy soldering!

      Fiddling with the simulation models shows that the inductance in the attenuator pads doesn’t matter all that much. Hard to imagine, but there it isn’t. [grin]

  2. #3 by peter on 2011-11-09 - 16:13

    Very interesting…. I thought that SMD caps were generally ok till about 1 GHz…. but may need to rethink that.

    Two weeks ago I modified my HP8558b from 75 ohm to 50 ohm by removing the resistive pad (which also attenuated 7.5dB…). During that operation, the 100nF coupling capacitor at the SA’s input connector broke. I replaced it with SMD ceramic ones of 100nF, paralleled with 100pF, paralleled with 10pF.

    I hope that’s good enough….

    I joked with a fellow ham about it: if capacitors become inductive above resonant frequency, does this mean inductors become capacitive above their resonant frequency too, and, if so, could I use a coupling *inductor* in the SA connector…. :-p

    • #4 by Ed on 2011-11-09 - 20:29

      I thought that SMD caps were generally ok till about 1 GHz

      It looks like cheap ceramic SMDs have 2 nH of inductance, no matter what: 1 GHz self-resonance with a 13 pF cap. I think fancy porcelain SMD caps have (somewhat) lower inductance, but none of them live in my parts heap!

      could I use a coupling *inductor*

      Well, there’s probably something about DC blocking that you’d miss pretty quickly… maybe a fast-blow fuse would suffice? [wince]

      • #5 by peter on 2011-11-10 - 06:18

        There’s already a quick-blow fuse in it: the Schottky mixer diodes in the first mixer…..

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