Can you filter out power supply noise by using a capacitor with a resonant frequency that matches the noise frequency?

From my limited understanding, the self-resonant frequency of a capacitor is also where typically impedance is at its minimum, and where Z = ESR.

I have a power rail that has some ringing at around 61MHz. What would happen if I place a 10nF capacitor that has a self-resonant frequency of 61MHz, such as the one below, between the rail and ground?

Is it bad to attempt to try to use a capacitor at its self-resonant frequency?

Why don't people just select filtering capacitors based on the least ESR/Z at the frequency of concern (sometimes that means selecting capacitor and value that has a self-resonant frequency at the frequency of concern). What am I missing here?

• you are already screwed if your power supply rings in a band you want to be quite. just get another power supply. Commented Oct 27, 2017 at 23:13
• Think of this as theoretical example. You are working at a company where the power supply is permanent and irreplaceable and they pay you the big bucks to filter this out. Commented Oct 28, 2017 at 1:34
• What if the PCB inductance varies, because the dielectric thickness varies, and the spacing of trace to Plane (trace-to-return) varies, altering that inductive contribution? Commented Oct 28, 2017 at 3:11
• @analogsystemsrf, I suspect I am missing something along the lines of what you mentioned. I want to know other contributing factors in selecting s capacitor besides SRF. Also, I am wondering if it's bad to operate a capacitor at it's SRF....Why do people say to select a capacitor with SRF much higher than the subject frequency? Why not select it closer (yet still higher). Commented Oct 28, 2017 at 3:23

In the particular example you have in front of you, if ...

a) the power supply has narrowband 61MHz noise and
b) your capacitor has an SRF of 61MHz

then yes, that capacitor in shunt would provide a good reduction in the noise voltage, and probably the best you'd get for a single cheap component

However, the SRF of capacitors, and with that the notch frequency, is not well controlled. As it depends on a residual parameter, the inductance, it may change. As that parameter is Bad, manufacturers are trying to improve it all the time, and may just improve it between batches. Different manufacturers may achieve a different inductance in parts that look the same. This means that SRF is neither consistent across different sources, or even reliable for one source.

Using a notch filter to improve a power supply only works if there's a single frequency of noise, and that's consistent between all examples. If it's broadband, or moves with time, or between supplies, then a fixed frequency notch is no good.

A single shunt component will have only a certain depth of attenuation. If you need more, you will need to build a larger filter anyway.

The thing to do is to design and build a lowpass filter from several components. Choose them with SRFs well above the highest frequency of interest, so that if (when) those SRFs change, they do not affect the performance of the filter significantly. Design the filter to have a stop band covering all of the potential problem frequencies, with a stopband deep enough keep it clean at the load.

It would work in theory...

In practice though, the SRF depends on inductance and capacitance as you no doubt know.

X7R and similar dielectrics have YUGE variations in capacitance. Even C0G will have several % tolerance.

Inductance depends on mounting, vias, traces, PCB thickness, and will also change if the cap is soldered 100% straight or a little bit skewed... You can guesstimate inductance by looking at the layout, but there will be a large margin of error (like 20% at least).

So in practice the SRF of the mounted cap will vary between PCBs in your batch, it will never land exactly where you want.

If your power rail rings, it means the decoupling was badly designed, you need to check it with a network analyzer (or simulate it with proper models). Most likely there are 2 caps, or 2 groups of caps of same value, which don't have enough ESR and thus create an undamped LC tank with their mounting inductance. One of the caps may be hidden inside a chip/MOSFET/diode/whatever, or it may be your interplane capacitance. The ringing can also be caused by a strong IO driver driving traces or wires that ring, and then the chip draws this ringing current from the supply. It could be an opamp getting unstable and injecting noise into the supply. The ringing could also be an artifact of how you probe the power rail. Plenty of possible causes... which you need to narrow down.

If you need help with that, feel free to post another question with layout, schematics, scope traces, etc...

• Thanks for the answer. When you say "don't enough enough ESR", do you mean that the ESR isn't low enough? or high enough? I'm assuming you mean low enough. I looked into the schematic of the powersupply and it seems that they have a 10uF and 22uF MLCC with low ESR after the switching regulator, which is running at 1.5MHz. Commented Oct 28, 2017 at 15:56
• ESR is a bit of a can of worms: too high and the capacitor is useless, too low and you get a resonating LC tank with the next cap and trace inductance (remember resistance damps resonances, see damping factor). That said, 10/22µF MLCCs won't give you a 61MHz resonance, it would be much lower in frequency, so you'll have to post scope traces and board pictures I guess... Commented Oct 28, 2017 at 16:49

Model this in Spice. In particular, compare a 0.1uF and 1uF capacitor, both in the same package (let's say 0603).

You will find that the 1uF capacitor has a SRF which is approximately ~3.16 (sqrt(10)) times lower, because the inductance is (approximately) the same for different capacitors in thee same package.

However, you will also find the 1uF capacitor still has the same or lower ESR at the SRF of the smaller capacitor (as well as a much lower ESR at lower frequencies). There is nothing special about resonance here - you have a small and a large capacitor, both in series with the same effective inductance which limits their high frequency performance to about the same extent.

So, no, you don't gain anything by "tuning" a capacitor to the noise. Just pick the smallest package you can, and the largest value available in that package, subject to cost/manufacturing/voltage rating considerations. (And remember to look at DC bias de-rating too - that can be huge when you get close to the max voltage!)

The corners of what is available, like 4.7uF in 0201 size is probably not what you want most of the time, and neither is a 220uF in 1206; both of these are specialty parts.

However, there is basically no situation in which a 1uF in 0603 would perform worse at bypassing than a 0.1uF in 0603, as long as both meet your voltage specs. You'd only pick the 0.1uF for the (minor) cost savings, or to save a line item on the BOM.