Page 317 - Analog and Digital Filter Design

3 1 4 Analog and Digital Filter Design

D gives the distance between the two earth planes, while the wire diameter is d.
The circuit board’s dielectric constant is E~.
This expression can be derived from an equation produced by Hammerstad,
where the impedance for a microstrip line (where there is no board or earth plane
above the conductor) is given by:
Z, =-In($) 60
6

Here h is the height (thickness) of the board and bo is the width of the micro-
strip track.

Since in stripline the whole surface of the wire is enclosed in dielectric, the effec-
tive surface width is Rd, the circumference of the wire. The impedance of a wire
in a stripline circuit is equivalent to a track on a microstrip circuit if the wire
2, = -In( 60 s)
circumference replaces the track width:

G

Since is in a board that is homogeneous and 2 h is equal to D, the two
equations are identical.
On a microstrip circuit, a wire has a higher impedance because some of the field
lines will pass through air (E~ = 1). The effective dielectric coefficient in this case
is given by approximately: = + 1).
Having found the series element design equation, you now need to find an equa-
tion for the open-circuit quarter-wave stripline. You need to find the physical
parameters of two lines that have impedance values of approximately 35 R and
81 R.

If the line width is greater than 0.6 times the distance between the two earth
planes, the wide strip equation can be used:

94.18
2, =
+
(w/D 0.44)G
If the line width is less than 0.6 times the distance between earth planes, use the
narrow strip equation that assumes that the strip is effectively a wire: