Chapter 39: Dielectrics and Dielectric Loss

Date: 13-08-2020

Introduction

In AC circuits with capacitors, loss occurs as the direction of charging and discharging changes, resulting in heat. This is a treatment of dielectric loss.

39.1 Electric Field, Capacitance, and Permittivity

The capacitance C of a capacitor is given by:

The electric flux density D is:

The electric field strength E is:

The permittivity \epsilon; is the ratio of flux density to electric field strength:

Where ε₀ is the permittivity of free space and ε_r is the relative permittivity of the material.

Compared with conductors, dielectric materials have very high resistivity and hence poor conductivity. Because of this, they are used to separate conductors which are at different potentials, such as power lines, capacitor plates, or a parallel plate capacitor.

39.2 Polarization

In an insulator, the electrons cannot move freely. When an insulator is put between two plates, a slight separation of the differently charged bodies in the nucleus and the electrons occurs, resulting in a “dipole”. This induced dipole acts in a direction against the electric field that causes it, resulting in a reduction in voltage (V). Since C = Q/V, this causes an increase in capacitance.

The relative permittivity (or dielectric constant) ε_r is the factor by which the capacitance is increased above that obtained with a vacuum. There are two main ways in which polarization takes place:

• Induced dipoles: The electric field pulls the nucleus in one direction and the electrons in the opposite direction. Because the mass of each atom is small and they are very light, this polarization takes place rapidly. Thus, if the applied electric field varies, the polarization follows the field and is independent of the frequency.
• Permanent dipoles: Some atoms have a permanent dipole in their structure. When an electric field is applied, these permanent dipoles tend to align with the field. However, because these molecules have mass, their movement is hindered. As a result, this type of polarization decreases with an increase in frequency.

39.3 Dielectric Strength

This is the maximum applied electric field strength a dielectric can withstand without breaking down. A capacitor’s insulation resistance R = ho (d/A), where ho is the resistivity, d is the thickness, and A is the area of the capacitor plates. Leakage current occurs through this resistance.

Reducing the thickness d of a dielectric film increases the capacitance, but it also reduces the voltage the capacitor can withstand before breaking down (since E = V/d). This is the main factor limiting the voltage that may be applied to a capacitor. All capacitors have a maximum safe working voltage printed on them.

39.4 Thermal Effects

The insulation resistance of most dielectrics falls with an increase in heat. This causes the leakage current to increase, generating further heat. If the heat is generated faster than it is dissipated, this will cause “thermal runaway” and the eventual failure of the dielectric.

39.8 Dielectric Loss and Loss Angle

In capacitors with solid dielectrics, losses are caused by two main things:

• Dielectric Hysteresis: A loss analogous to hysteresis loss in a magnetic material. The internal energy dissipated as heat is the result of the reversal of electrostatic stress in a dielectric subjected to an alternating electric field.
• Leakage Current: Currents that may flow through the dielectric or along paths between the terminals.

The total dielectric loss can be represented by an additional resistance connected to the plates. It can be represented either as a small resistance in series with an ideal capacitor or as a large resistance in parallel with an ideal capacitor.

Series Representation

Using a series resistance R_S and series capacitance C_S:

Also, an \delta = 1 / Q, where Q is the quality factor. When \delta is small, \cos \phi pprox an \delta.

The Dissipation Factor (D) is defined as:

Parallel Representation

Using a parallel resistance R_P and parallel capacitance C_P:

For equivalence between series and parallel representations, C_P pprox C_S pprox C.

From the parallel circuit, the power loss is: