At the interface between
two different dielectric regions, region 1 and
region 2, the normal component of the flux density and the tangential
components of the field intensity are continuous:
, .
On the other hand, the tangential components of
the flux density and the normal
component of the electric intensity are discontinuous
(they change with a jump):
, .
As a result, the orientation
of the streamlines (the E-field) and the
equipotential surfaces changes abruptly. This orientation
is usually represented by the angles and between the E vector
and the unit normal to the interface in regions
1 and 2, respectively (see Figure
1). We can show that
.
Thus, by looking at
the field map at the dielectric interface, we can
tell what the ratio of the dielectric permittivities
is.
Figure
2 shows the cross-section of a transmission
line often used in microwave engineering: the
microstrip line. It consists of a dielectric
(alumina) slab ( ) backed by a grounded
metallic plate. A metallic strip is printed on
top of the slab. The region above the slab is
air ( ). The direction
of the equipotential lines changes abruptly at
the dielectric-to-air interface.
The continuity of the
tangential field component
and the discontinuity of the normal component
are best seen in Figure
3 where their values are plotted versus
a vertical line originating at the ground plate.
The jump in corresponds
to a change by a factor of 9.8.
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