# The physics behind DC voltage derating of capacitance

I don't understand this phenomena pointed out in LDO's Capacitor vs. Capacitance where it says:

Given the dynamic nature of capacitors (storing and dissipating electric charge in a nonlinear fashion), some polarization may occur without the application of an external electric field; this is known as “spontaneous polarization.” Spontaneous polarization results from the material’s inert electric field, which gives the capacitor its initial capacitance. Applying an external DC voltage to the capacitor creates an electric field that reverses the initial polarization and then “locks” or polarizes the rest of the active dipoles into place. The polarization is tied to the direction of the electric field within the dielectric. As shown in Figure 1, the locked dipoles do not react to AC voltage transients; as a result, the effective capacitance becomes lower than it was before applying the DC voltage.

1. When applying a DC voltage across a capacitor, all dipoles should align with the positive (negative) end of the dipole pointing the negative (positive) plate. Like charges repel and opposite charges attract, and the dipoles should point one way or the other. But in the image shown, the locked dipoles align with the electric field, and the active dipoles ignore the electric field. So a locked dipole can rotate and an active dipole cannot rotate ... What exactly is a locked dipole and an active dipole?

2. Why won't a locked dipole react to AC transient? If an AC polarity goes one way, the dipole will point to that direction. The dipole should reverse its direction if the AC polarity changes.

I still don't see the physics behind how a DC voltage (or AC) derates the capacitance.

• Generally this is seen with ceramic dielectrics, and not really a concern at all with electrolytics as far as I know. It is also called the "DC-bias effect of capacitors". You might find more info using these search terms. May 29, 2021 at 6:50
• So a dipole align to the electric field is locked dipole, and dipole that remain at its random initial alignment and does not align to any electric field is called the active dipole? Does it mean the active dipole is neutral in charge that it does not attract or repel against an electric field? This is confusing ....
– KMC
May 29, 2021 at 6:57
• It's not satisfying to me either. The implication is that the spontaneous polarization is responsible for the initial capacitance at zero bias, which at least to me, implies polarity (unless you hca have 50% in polarized each direction and still have capacitance?). However, we know that ceramic caps aren't polarized and don't have two different capacitances depending on which orientation you measure the capacitance in. I understand what they mean about locked dipoles but not the initial capacitance mechanism which isn't explained in the app note. May 29, 2021 at 6:59
• I also couldn't find resource that explains the reasoning behind other than shoving in a Capacitance vs. DC Bias curve and accept it as it is. The initial or spontaneous polarization should only effect the time but not the capacitance: if there are more dipoles in the reverse direction to begin with, it'll just take more time for the dipoles in the dielectric to align with the electric field. It shouldn't effect the overall capacitance.
– KMC
May 29, 2021 at 7:08
• You might have to dig into textbooks or material sciences for this one. May 29, 2021 at 7:08

Why won't a locked dipole react to AC transient? If an AC polarity goes one way, the dipole will point to that direction. The dipole should reverse its direction if the AC polarity changes.

You're picturing AC centered around zero, not an AC transient on top of a DC-bias.

In use you shouldn't get AC transients so large and powerful they can actually overcome the DC bias, and then some, by completely discharge the capacitor of its DC bias and begin charging it in the opposite polarity.

I'm not sure this is entirely satisfying though since it also implies that a capacitance experienced zero DC bias with AC flowing through it has a capacitance that varies based on its instantaneous voltage (maybe that's the case, but I've never heard it come up).

I suppose to find out you would have to run AC with a large voltage swing through a ceramic capacitor and measure the current to see if it varies sinusoidally or not. Now I'm curious.

• I think the question should be why some dipoles align to the electric field (locked) while some don't (active). The active dipoles that won't align reduce the capacitance (hence derating) but what makes these active dipoles "active"? The terminologies used are also counter-intuitive if not contradictory: "locked" dipoles are dipoles that rotate (not locked), and "active" dipoles are dipoles that do not rotate (inactive). The whole concept does not make sense.
– KMC
May 29, 2021 at 7:02
• I agree that should be the question. I don't have a problem with the terminology. The locked dipole is the dipole which INITIALLY rotates and is locked into place upon application of the DC-bias, after which it can no longer rotate/oscillate in response to any AC perturbations. The app note seems to imply that the energy is not spread evenly amongst the dipoles and there is an energy level at which a dipole becomes unable to respond to perturbations below a certain energy level. May 29, 2021 at 7:06
• Image a AC transient happen to be a +/-1V fluctuation riding on a 5DC bias. At all times the dielectric is subject to a voltage between 4-6V. Polarity never changes, and all dipoles should align to the polarity. The "active" dipoles that has the positive end pointing to the positive plate just make no sense, or there are more complex physics involved.
– KMC
May 29, 2021 at 7:14
• @KMC I disagree that they all need to align with the polarity (I assume you mean perfectly align). Similar to ferromagnetic domains, it takes work to re-align the domains because they want to snap back to where they were. That's the mechanism by which energy is stored after all so it can't be all or nothing alignment. Individual dipoles could align more or less based on the strength of the electric field and "wobble", not necessarily reversing direction, as they store and release energy in response to the AC but maintain an average amount of alignment to the electric field based on the DC. May 29, 2021 at 7:22