This module examines a stripline, one example of a transmission line.
As an example, and also because it even has some
practical importance, let's look at one kind of transmissionline. It is called a
stripline and it looks like
. It consists of a flat conductor, located
between two ground planes. It is supported by an insulatingdielectric with dielectric constant
. This is kind of like
the situation you would find on a multi-level PC board, whereperhaps the bus lines would be running on an inner layer with
ground planes above and below them.
A stripline
Between the center conductor and the ground plane, there will be
some capacitance,
. If we can
assume that the electric field is more or less confined to theregions between the strip conductor and the ground plane (which
occurs when the ratio of
is not too small) then for either capacitor (assuming
unit length into the picture) we will get a value
since the value of a capacitor is just the dielectric constant
times the area of the plates, divided by the spacing of theplates.
Looking quickly at
you
might think the two capacitors are in series, but you would bewrong! Note that each capacitor has one lead connected to the
center conductor and the other lead connected to ground, and sothe two capacitors are in fact, in parallel, and hence their
capacitances add. Thus, for the capacitance per unit length forthis line, we can write:
It can be shown (although we won't do it here) that for
any transmission line where the electric
and magnetic fields are perpendicular to one another (called
TEM or
transverse electromagnetic ) the
speed of propagation of the wave down the line is just
Where
is called the
relative dielectric constant for the material. Well, we also know that
From which we can write
We can now insert this value for
into the expression for
, the impedance of the line.
And so, we have derived an equation for the impedance
of the line in terms of the dimensions
and
, the dielectric constant of the
insulating material,
,
and
, the speed of light. How
good is this expression, and in particular how good is ourassumption that the electric field is all confined to the region
under the conductor? Not so great actually
.
Exact and approximate impedance for a stripline
Exact and approximate
for a stripline
shows the results from using
and a more exact calculation, which takes into
account the fringing fields. As you can see we have to get theratio
up to about 4 or so before the two match. But at least
we get the right behavior and we're not totally out of the ball park.
