Capacitor Self-resonance: The Madness

I’d wondered whether suppressing RFI by picking capacitors by their self-resonant frequency, so that each cap would suppress a known input signal. Turns out that’s entirely possible, even for the amateur VHF and UHF bands:

Wouxun PCB - 100 nF 680 80 pF AVX - PTT

Wouxun PCB - 100 nF 680 80 pF AVX - PTT

The three caps producing that trace look like this on the brassboard PCB for the Wouxun GPS+voice interface,  with spectrum analyzer input & output through RG-174 coax with 22 Ω and 470 Ω SMD resistors tombstoned on the pads at the end of the string:

GPS voice PCB - SMD caps on PTT input

GPS voice PCB - SMD caps on PTT input

The scattered solder blobs cover Z-wires connecting the top ground plane to the continuous ground pour on the bottom surface. The solder strip along the edge joins the copper tape bonding the surfaces together around the perimeter. Basically, this is as well-controlled a layout as one can rationally get, without full RF matched-impedance zaniness.

However, the whack-a-mole RFI suppression concept makes absolutely no sense whatsoever for anything other than a mass-production board with rigidly controlled component parameters, which isn’t what you see here. Basically, ceramic caps have poor tolerances, bad thermal stability, and standard values too far apart to make fine tuning practical: lining up the self-resonance with a desired frequency requires trial-and-error selection for every capacitor.

Those peaks between the self-resonances can be much higher than you’d expect, too, because they represent parallel resonances where the total impedance can approach an open circuit. Remember that caps above resonance look like inductors and caps below resonance look like caps, so two parallel caps form a nice RL tank circuit for signals between their self-resonant frequencies. The caps have very low ESR, making the Q unreasonably high.

If you were hoping for / requiring broad-spectrum RFI suppression, paralleling caps will definitely make things worse, which is probably not what you expected, either.

The whole scheme also suffers from measurement error due to parasitic inductance from the position of the SA and TG “probes”. Compare this trace:

Wouxun PCB - 330 pF - HTPTT near

Wouxun PCB - 330 pF - HTPTT near

Made with the SA and TG connected to the same pad:

SA and TG - same pad

SA and TG - same pad

With this trace:

Wouxun PCB - 330 pF - HTPTT far

Wouxun PCB - 330 pF - HTPTT far

Which involves moving the SA input to a pad on the other end of the trace, the better part of 8 mm away:

SA and TG - different pads

SA and TG - different pads

Yes, those layouts are identical when you’re talking about signals near DC.

The pigtail leads certainly contribute some inductance, as does the the PCB trace itself. I suspect you could model that effect, but I’m not sure you could generate a predictive model without a 3D field solver and a whole bunch of calibration measurements. If you really care about the location of that self-resonant peak, I’m not sure which trace / layout you’d trust.

Of course, if you use a cap with a very broad self-resonant peak, then it’s all good. Except, equally of course, that I have no idea how you’d specify one of these to your purchasing agent:

Wouxun PCB - 992 pF - HTMIC

Wouxun PCB - 992 pF - HTMIC

That’s a 1 nF cap from the same assortment (made by AVX, a nominally reputable manufacturer, if the eBay vendor is to be believed) that produced the other peaks. Obviously there’s something different about those caps (and the 1.5 nF caps in the next compartment of the assortment, too): it’s not a measurement error! Notice that it has the expected high impedance at low frequencies, so you’d probably want a larger cap in parallel, which would give you at least a moderate parallel-resonant peak in between.

So if there’s a single frequency that needs squelching you can probably find a suitable cap by rummaging around in your assortment. More than that, though, just isn’t practical.

Just about the only other discussion I’ve seen about this comes from the folks at Ultracad Designs, who have run the numbers much further than may seem be reasonable, even by my standards.

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  1. Capacitor Self-resonance Calculator « The Smell of Molten Projects in the Morning
  2. GPS+Voice Interface for Wouxun KG-UV3D: Brassboard « The Smell of Molten Projects in the Morning
  3. Wouxun HT GPS+Voice Interface: Circuitry! « The Smell of Molten Projects in the Morning

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