Capacitance – How Capacitance Depends on AC Voltage

accapacitancevoltage

I am aware of the dependence of some ceramic capacitors (e.g. X7R) capacitance on DC voltage. I assumed that if a high enough AC voltage is applied, capacitance changes in its rhythm causing distortion of the sine wave. So far so good.

I came across this datasheet for a C0G capacitor that also contains some general info. On p.11 there is the familiar graph of capacitance vs. DC voltage. Following that is another graph of capacitance vs. AC voltage, here it is:

capacitance change vs AC RMS voltage

This seems to be an altogether different phenomenon – the most pronounced drop in capacitance is at very low AC voltages. Also, the change is apparently independent of frequency. I can't find anything on this.

Does anyone know how this works? (Dielectric types, frequency dependence, DC and AC phenomena combined, etc.)

Best Answer

This effect in Class 2 ferroelectric MLCC capacitors is due to hysteresis in polarization, as illustrated in this paper.

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At low AC voltage the hysteresis causes an effective loss in capacitance.

This graph from this white paper shows the effect clearly:

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At low AC voltages (the green curve) the K is low, it increases for higher voltages (yellow) and then decreases again for higher AC voltages (purple and red). Incidentally, the yellow curve represents typical measurement conditions for determining the capacitor datasheet characteristics (1.0V +/- 0.2V RMS).

As to the physics behind the ferroelectric behavior of barium titanate used in X7R capacitors, this paper describes it as follows:

These dipoles arise due to the fact that in the tetragonal unit cell of BaTiO3 , the Ti4+ cation is surrounded by Six O-2 anions in a slightly deformed octahedral configuration, and can occupy one of two asymmetrical sites, as illustrated in Figure H-3. In either position, the Ti4+ cation is not coincident with the negative charge center of the oxygen anions by a small fraction of an Angstrom, creating an electric dipole. The energy barrier between the two possible Ti atom positions is sufficiently low to permit motion of the atom between sites by the coercion of an electric field, and the material can thus be directionally polarized with ease. The interaction between adjacent unit cells, in fact, is sufficient to create domains of parallel polarity the instant the material assumes its ferroelectric state on cooling through the Curie Point.

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