# Capacitors... Capacitance Changes - Why?

## Technical Bulletin No. 3

In our circuit applications, the capacitor can be and is subjected to various electrical, mechanical, and environmental stresses. One of the most notice­able effects of these stresses is the phenomena of capacitance variation.

Now, the fact that the capacitance does vary will come as no surprise to most design engineers. Further, the fact that different kinds of capacitors will vary in different ways is also fairly common know­ledge to those concerned. Our purpose in this arti­cle is to examine what causes this variation, deter­mine why the capacitance changes, and compare the extent of the variation for the common capac­itor dielectrics.

First, let's analyze our basic formula for capaci­tance:

We note that C varies directly with A and K, and inversely with d. Any change in C must come as a result of some change or combination of changes in A, K, or d.

A (effective area of electrodes) is set by design and once a capacitor is made, it is almost impossible for C to change due to a change in A. This, then, is not a normal factor in capacitance variation.
d (distance between the plates) is also set by de­sign. Some small changes in d can occur on com­pleted units due to external or internal pressure changes resulting in mechanical movement of the electrodes. This is not usually critical nor does it result in any large variations.

K (dielectric constant) is also initially set by design in the choice of dielectric material used to make the capacitor. Now, however, the complications begin - many factors will cause the K to change, and this change in K will vary for different materials. We see, then, that the major factor involved in why the capacitance changes is the fact that K does vary.

In order to clearly understand the various factors that cause K to change, and to what extent these changes take place for the common dielectrics, the following clarification is of interest.

The K (dielectric constant) in our basic formula is the effective dielectric constant of the total "space" between the electrodes. This "space" will consist of the dielectric material (or materials if a multiple dielectric design), air, impregnate (if an impregna­ted unit), and even moisture (if present). All of these dielectrics are effectively in series and there­fore the resultant Kr would be:

The major factors that will cause a change in K are moisture, voltage, frequency, and temperature.

MOISTURE

Whenever moisture vapor penetrates into the di­electric of a capacitor, the capacitance will in­crease somewhat depending on the amount and effectiveness of the penetration, the percent of the total distance between the electrodes that is repre­sented by air, and the percent of the air that is satu­rated or, in effect, replaced by the moisture.

For illustration purposes, let us assume the follow­ing:

For this illustration - we see approximately a 27% increase in capacitance due to the moisture.

Of course, you would not normally see this kind of gross moisture penetration, but - increases up to 5% are not uncommon on non-hermetically sealed commercial units when tested to the MIL-STD ac­celerated moisture tests.

VOLTAGE

With the exception of the General Purpose (high K) ceramics, voltage stress has only a very minor ef­fect on the K of the standard dielectric materials. In the case of the high K ceramics an AC voltage will cause the K to increase while a DC voltage will cause a decrease in K. The amount of charge will depend upon the original value of K for that particular ceramic mixture.

As an example, for a K = 1200 mix, it is not uncom­mon to see changes amounting to approximately +20% with 20 VAC (RMS) applied and -30% with 200 VDC applied.

FREQUENCY

For our primary area of application interest, we are concerned mainly with the low-frequency band of O to 30K Hz. In this area, the K of mica, glass, Teflon, polystyrene, and N PO type ceramic dielectrics, does not exhibit any measurable change. Polycar­bonate film will show a slight decrease in K of about .4% at 30K Hz. Mylar will drop about 1.5 to 2.0%, high K (1200) ceramics approximately 2.0 to 2.5%, and paper-impregnated units between 3.0 to 6.0%, depending on the impregnate. Reference mea­surement frequency here is 1000 Hz.

TEMPERATURE

Temperature will have an effect on the K of all standard dielectric materials. This effect will be fairly small on some dielectrics and quite extensive on others.

The following charts compare the average curves of various dielectrics relative to the capacitance variations with temperature. Special processing and other factors can be used to alter these curves somewhat.