Direct Energy, 2018a

28 2.2 Capacitors
â z
â y
â x
No applied voltage
With applied voltage
Figure 2.1: Illustration of material polarization.
In such cases, the material is called anisotropic. Permittivity of anisotropic
materials is more accurately described by a matrix.
⎛
ɛ xx ɛ xy ɛ xz
⎞
ɛ zx ɛ zy ɛ zz
⎝ ɛ yx ɛ yy ɛ yz
⎠
The left part of Fig. 2.1 shows some atoms of a crystal. The small black
circles represent the location of the nuclei of atoms in the crystals, and
the gray circles represent the electron cloud surrounding the nuclei of each
atom. If an electric eld is applied in the â z direction, the material polarizes,
so the electrons are slightly displaced with respect to the nuclei as
shown in the gure on the right. Since the spacing of atoms is dierent in
the â x and â y direction than the â z direction, the external eld required to
get the same charge displacement will be dierent in the â x and â y directions
than the â z direction for this material. For this reason, the material
illustrated in the gure is anisotropic, and the permittivity is best described
by a matrixas opposed to a scalar quantity.
2.2.4 Capacitor Properties
Capacitors are energy conversion devices used in applications from stabilizing
power supplies, to ltering communication signals, to separating out a
DC oset from an AC signal. Though capacitors and batteries both store
electrical energy, energy in batteries is stored in the chemical bonds of
atoms of the electrodes while energy is stored in capacitors in the material
polarization from bound charges shifting in a dielectric layer.
The rst two measures to consider when selecting a capacitor to use in
a circuit are the capacitance and the maximum voltage. A capacitor can