# Capacitance vs. Frequency Graph of ceramic capacitors

I'm looking at ceramic capacitors on TDK and I see this graph

Does this mean above several hundred kiloHertz - or wherever the graph stops - that the capacitor no longer functions probably ?

• Yes, that's what it means. A capacitor will always have some series inductance and for this capacitor it starts affecting the impedance around 100 kHz. Dave from EEVBlog made a video about this, see: youtube.com/watch?v=BcJ6UdDx1vg This is about using caps for bypass (supply decoupling) but that does not matter. The for this question interesting bit starts at around 11 minutes from the start. Dave also explains what to do if your capacitor is not good enough. Commented Sep 7, 2017 at 10:07
• Ah I see - thanks for the video link, super helpful. So for example if I had a 500 kHz switching supply it would be best to find a new capacitor where my switching frequency is on the left of that rise in the graph? EDIT: also why do they show the behavior like ESR vs frequency and impedance vs frequency all the way until the Mega and Gigahertz range? What's the point of doing this if the capacitor is not functioning properly ? Commented Sep 7, 2017 at 10:39
• Correct, in the the left part of the plot the capacitor behaves as a capacitor and not like an inductor (right side). For a 500 kHz application a cap that is not a cap at 500 kHz is pretty useless. Designers do not want a "limited view" of the properties of a component, sure it does not behave as a cap at high frequency but engineers still want to see the plot. We want to know what "goes on there" even if it is not of practical use. And, when the plot is measured, it is trivial to make it up to higher frequencies. Commented Sep 7, 2017 at 11:37
• Also: extending the plot to for example 1 GHz shows there's nothing "funny" going on like an extra dip or peak in the impedance. If a manufacturer does not show it, how can you be sure ? You can't so reputable manufacturers provide the whole picture. Commented Sep 7, 2017 at 11:39

Every component has inductance (Equivalent Series Inductance or ESL), the value is determined by the area of the loop the current has to go through. It includes the mounting inductance on the PCB, vias, traces, etc. An example:

This is purely mechanical. Capacitor value doesn't matter, it would work the same for a resistor, even a 0R, or a piece of wire.

A cap has ESL and ESR, so its impedance is:

$Z = \frac{1}{j\omega C} + R + j\omega L$

(neglecting dielectric absorption, leakage, etc)

Capacitors of same physical size (like, all 0805) tend to have the exact same inductance. So, if we plot their impedance vs frequency:

The low-frequency part shows the expected $\frac{1}{j\omega C}$. At high frequency, $j\omega L$ dominates. Since they're all the same dimension, they all have the same HF impedance.

The dip is the resonance frequency. At its center, Z=R. Low ESR gives a deeper dip.

At high frequency, it's an inductor: you can't measure its capacitance, because C has no influence on the impedance, which is dominated by L. This is why the capacitance curve on your datasheet stops. Its purpose is to show that capacitance stays stable and well-behaved at LF where it matters.

Now, smaller packages have lower ESL:

So, the reason why you often see 10nF // 100nF is not that the 10nF cap is "faster", rather it is that you can get it in 0201 package, thus it has lower inductance. If both caps are 0805, then the 10nF is useless, and a single 1µF would work better.

EDIT: when paralleling caps you are building a LC tank and it can ring. Parallelling low-ESR MLCCs of different values can get nasty. This is why for the simple stuff (like a logic gate or a micro) don't bother with 10n//100n, it will actually be worse. One single value is less risky, 100n or 1µ. Also power traces are inductive, that's another LC tank, ferrites ring with caps too... spice helps!

Now, your caps are stacked ceramics:

You can immediately guess from their construction and the fact they sit above the PCB that they will have a lot more ESL than a SMD capacitor. Probably more like an electrolytic. However these caps are ceramic, so they will handle very high temperatures, also they will have very low ESR, which can be an advantage (it can also cause lots of ringing).

So, for a 500kHz switcher, they are not the right choice, unless you have extreme temperatures or another reason to use these. An electrolytic would probably be cheaper and have a little bit of ESR to prevent ringing.

To filter out the 500kHz noise, you need a cap that has low impedance at this frequency and above. So, you need small MLCCs, if you hand-solder, 1-10µF 0805 is easy to work with. You can put several in parallel to lower the inductance, and take care in the layout, because it's the total inductance that matters, including vias to ground plane and traces.

If you need assistance for your cap choice, you need to tell how much current the DC-DC will handle, its topology (buck, boost...), voltage, frequency, etc.

• Wow, thanks so much! I've posted another question with a more detailed description of the buck converter electronics.stackexchange.com/questions/327986/… EDIT: i've mainly trying to switch to these to save space - so many capacitors! Commented Sep 7, 2017 at 11:14
• Re your 3rd illustration (with the wiggly yellow line). As you say that all capacitors have inductance, and larger packages have higher ESL, I wonder if you'd be more precise about the impedance of a parallel combination of an 0805 gone inductive, and an 0402 still capacitive (hint, the parallel combination of an L and a C is high impedance)(further hint, this situation is often saved from disaster by lossy capacitors or a sniff of impedance between them, but neither of these mitigations apply when multiple different value ceramics are close together) Commented Sep 7, 2017 at 11:37
• Yes, I just grabbed a picture from google images, but antiresonance peaks can be nasty! The old habit of putting 10n//100n on each chip is best avoided... and careful spicing is required. electronics.stackexchange.com/questions/320363/… Commented Sep 7, 2017 at 12:20

Capacitors inevitably have some series inductance. Capacitors have negative reactance (imaginary part of the impedance) while inductors have positive reactance. Capacitive reactance is inversely proportional to frequency while inductive reactance is proportional to frequency.

What this means is that there is a frequency where the capacitive and inductive reactances cancel out. This is known as the resonant frequency.

Below the resonant frequency the component is "more like a capacitor than an inductor". Above the resonant frequency it is "more like an inductor than a capacitor".

What that graph represents is the measured reactance translated back to a capacitance. As we approach resonance the inductive reactance cancels the capacitive reactance and the effective capacitance increases (theoretically going to infinity at resonance). Then the sign of the reactance switches and it's no longer meaninful to think of the component as a capacitor at all.