# Dielectric Loss

**Dielectric Loss:**** **Capacitors are used for a wide variety of purposes and are made of many different materials in many different styles. For purposes of discussion we will consider three broad types, that is, capacitors made for ac, dc, and pulse applications. The ac case is the most general since ac capacitors will work (or at least survive) in dc and pulse applications, where the reverse

may not be true.

It is important to consider the losses in ac capacitors. All dielectrics (except vacuum) have two types of losses. One is a conduction loss, representing the flow of actual charge through the dielectric. The other is a dielectric loss due to movement or rotation of the atoms or molecules in an alternating electric field. Dielectric losses in water are the reason for food and drink getting hot in a microwave oven. One way of describing dielectric losses is to consider the permittivity as a complex number, defined as

..........................2

One reason for defining a complex capacitance is that we can use the complex value in any equation derived for a real capacitance in a sinusoidal application, and get the correct phase shifts and power losses by applying the usual rules of circuit theory. This means that most of our analyses are already done, and we do not need to start over just because we now have a lossy capacitor.

Equation 1 expresses the complex permittivity in two ways, as real and imaginary or as magnitude and phase. The magnitude and phase notation is rarely used. Instead, people

Dielectric properties of several different materials are given in Table 1 [4, 5]. Some of these materials are used for capacitors, while others may be present in oscillators or other devices where dielectric losses may affect circuit performance. The dielectric constant and the dissipation factor are given at two frequencies, 60 Hz and 1 MHz. The righthand column of Table 1 gives the approximate breakdown voltage of the material in V/mil, where 1 mil = 0.001 inch. This would be for thin layers where voids and impurities in the dielectrics are not a factor. Breakdown usually destroys a capacitor, so capacitors must be designed with a substantial safety factor.

It can be seen that most materials have dielectric constants between one and ten. One exception is barium titanate with a dielectric constant greater than 1000. It also has relatively high losses which keep it from being more widely used than it is.

We see that polyethylene, polypropylene, and polystyrene all have small dissipation factors. They also have other desirable properties and are widely used for capacitors. For high power, high voltage, and high frequency applications, such as an antenna capacitor in an AM broadcast station, the ruby mica seems to be the best. Each of the materials in Table 1 has its own advantages and disadvantages when used in a capacitor. The ideal dielectric would have a high dielectric constant, like barium titanate, a low dissipation factor, like polystyrene, a high breakdown voltage, like mylar, a low cost, like aluminum oxide, and be easily fabricated into capacitors. It would also be perfectly stable, so the capacitance would not vary with temperature or voltage. No such dielectric has been discovered so we must apply engineering judgment in each situation, and select the capacitor type that will meet all the requirements and at least cost.