# Filters: what kind of capacitor?

Until recently, I (foolishly) believed that the capacitance of a given capacitor was the capacitance given by the datasheet +- the tolerance.

I recently learned about the DC derating of MLCC (multi-layer ceramic capacitors), which can be quite huge (I have seen some with 80% reduction in capacity). What's more, this derating curve seems to be missing from datasheets (you have to dig though the manufacturer's website to find it).

So, for filtering signals with a DC component (for example an RC filter), what kind of capacitors do you usually use? Do you still use MLCC and look up the derating every time? Or do you use another type that is more stable?

Sometimes, of course, you don't care at all about the precise cut-off frequency of your filter, and you can accept a factor 5 (or you can just derate by something smaller (50%?), so you know you will have an error one way or the other, but smaller.

But sometimes, you really have a trade-off between getting a well-filtered signal but still have the output of the filter changing "quickly" if the output changes, and then it would be nice if the cut-off frequency remains within 10-20% of what you decided.

• Those cheap MLCCs are typically used as decoupling caps for digital ICs, where the DC bias is well known, and you usually don't mind if the capacitor is 5 times larger as strictly necessary. You certainly don't use those caps in precision RF filters. Jan 13 at 14:24

The options (not all good) are:

1. Don't care: tolerate/accept large variations in capacitance. Not always possible, depending on the application.
2. Remove the DC bias (AC-couple the signal) (and then possibly re-bias post-filter). Not always possible, depending on the application.
3. Try to calculate the derating and compensate for it. As you noticed, not all datasheets include derating curves. That's because the derating depends very heavily on the dielectric and even the package size and is very difficult to precisely control. This is even harder if the bias level isn't fixed.
4. Use a different type of capacitor with stable capacitance in the presence of DC bias. Film capacitors are popular in the filtering role for many applications.

So, for filtering signals with a DC component (for example an RC filter), what kind of capacitors do you usually use? Do you still use MLCC and look up the derating every time? Or do you use another type that is more stable?

I use C0G/NP0 capacitors and accept that I have to pay a lot of money for high value types or high voltage types (or both). I also consider that stacking a few together gives me options of tweaking filter performance. I might consider X7R dielectrics for some sloppier filters but would go for over-sized components because the capacitance change with applied voltage is less of a problem: -

Picture stolen from Bobflux's answer here.

You should also be aware that not only does the capacitance change with DC voltage but, cyclically, for an AC signal, distortion may be introduced due to the capacitance changing with instantaneous signal amplitude.

Usually filters are designed so that the resistance and capacitance values are chosen in such a way that you don't need to go to capacitors that are made with Class 2 or Class 3 materials that exhibit the DC bias effect and can simply use capacitors with Class 1 materials which do not exhibit the DC bias effect.

Class 1 capacitor types such as C0G and NP0 are widely used in circuits with stability concerns.

Capacitance of Class 2 dielectrics (X7R, etc) varies a lot with temperature and electric field, the latter being dependent on voltage across the cap and distance between electrodes.

So if you make a filter with a class 2 ceramic cap, its cutoff frequency will move around in a wide range depending on DC bias and temperature.

However this isn't just about DC bias: in a filter, there is also a non-negligible AC voltage across the cap, and that changes the capacitance too. This introduces harmonics (ie, distortion) in your signal. How annoying this is depends on the application. I remember someone used MLCCs as DC coupling caps in a headphone amp, they got ridiculous THD like 30% in the bass.

But it doesn't stop there... Class 2 ceramics are also piezoelectric, which means they're pretty good microphones/acoustic transducers. This manifests as a current coming out of the cap, which is proportional to how much it bends with board flex. So the effect depends on circuit impedance. On a low impedance node, like a power supply, it is negligible, and the regulator will compensate for the piezo current coming out of the cap. But on a high impedance node, like the "VREF decoupling" pin of the LDO, or in a filter, you can expect every vibration of your board being injected into your signal.

So if you need a high value cap for your filter, use an electrolytic. Leakage current can be a problem, but if you need a high value cap, you're probably using low enough impedance that it doesn't matter. If you need a low value cap, use C0G or film. C0G tends to be near perfection ; with film, some are better than others, but the differences are all below -90dB THD so it's pretty safe.

Note film caps are microphonic too, but not piezo. When they get compressed or vibrate, distance between plates varies so there is a capacitance variation ; if there is a DC voltage bias, charge being conserved, this will translate into a change in voltage and/or current. This only matters if you build low noise, very high impedance circuits, like instrumentation preamps, mic/phono preamps, EEG/ECG, etc.

• Agree to most things. But I think they are ok for AC coupling, if you make their value so high that they are basically a short anyway. That way they are still smaller than electrolytics and class I. Jan 12 at 12:53

... which can be quite huge (I have seen some with 80% reduction in capacity).

This depends on the dielectric material of the capacitor: Y5V, X5R, X7R, C0G/NP0, etc. - Y5Vs change the most while NP0s change the least.

So, for filtering signals with a DC component (for example an RC filter), what kind of capacitors do you usually use? Do you still use MLCC and look up the derating every time? Or do you use another type that is more stable?

Depends on some factors:

• Size of the board
• Overall performance
• Cost (Material and production costs)

Size: One may think that using an MLCC with higher rated voltage or same rated voltage but larger package mostly overcomes the capacitance-drop issue. This might be true but if size is a limitation, larger packages may not be possible to place on the board therefore smaller packages can be preferred. This pushes the designer to select MLCCs with lower rated voltages, but without exceeding the design limits. For example, if the maximum DC voltage across a capacitor is 6V and the maximum AC voltage is 1Vpk then the designer might consider using a 10V capacitor (e.g. 0402 case) rather than a, say, 50V capacitor (e.g. 0805 case).

Overall Performance: This covers operating conditions, application, and the target market. Not always only DC bias is considered, but the frequency, target application and operating conditions as well. If the capacitor is a 100nF decoupling capacitor then its capacitance change is neglected most of the time. But if the application involves audio frequencies for example (e.g. coupling / DC blocking, filtering) then things may change.

Cost: There are capacitors having less capacitance change versus DC bias but they might be more expensive and not easy-to-find. For example, X7Rs' capacitance change can be as low as ±7% but if the cost target allows, the designer might consider using these.

• Is there some ressource anywhere that would allow selecting capacitors for low DC bias dependence ? For sure shops don't offer this, but even the parametric searches at Murata, Taiyo etc. were unsatisfying Jan 12 at 12:56
• @tobalt I don't think there is. We consult the manufacturers or distributors when needed. Jan 12 at 13:59

Class II are ok. Even with 80% derating they are still much denser than class I. For generic filters such as antialiasing, snubbers and decoupling, you can easily tolerate not knowing the exact value and expect a factor 2 variation due to DC bias. And they work bipolar and are small, which electrolytics aren't. So there is definitely a huge application space for them. When simulating, I usually use 30% .. 50% of their nominal value, when DC biased. That seems to be a good average figure after checking many of the $$\C(V_{DC})\$$ curves that you mentioned.

However, there are applications where they suck:

• slew control (ramp) circuits such as for timing
• high impedance RC filters such as for reference voltages (due to piezoelectricity/microphony)
• as signal load capacitance (e.g. for inductive guitar pickups)