Page 319 - Analog and Digital Filter Design

3 1 6 Analog and Digital Filter Design

If Zo = 81 Q, Dlw = 7.33. Since D = 1.6mm, 12: = 0.2183mm. The ratio wlD is
less than 0.6, so the equation used is valid. Substituting this ratio into the full
equation for impedance gives:

Zo =-~=gkn(5)+0.185(;) 2 ]
59.96
[ ( 5s~)+0.1S5(0. 136426)l 1
Z, = 27.6575 Ln -

This is the required impedance, so the approximation is good and a track width
of 0.2 183 mm can be used. The same equation can be tried for the 35 Q imped-
ance line, although it may require a wlD ratio greater than 0.6 and have to be
recalculated.

w/D = 0.719, so the wide line equation must be used:

Substituting this back into the original equation:

94.18
20 =
(w/D +0.44)a
Z, = 35 Q, as required.

Alternative equations exist for microstrip lines, which are easier to produce
as standard double-sided printed circuit boards. Equations have been pro-
duced by Hammerstad for use on boards where the relative dielectric constant,
ER< 16.

If wlh < 2 the narrow line equation is:

w 8
-=
h e" -2e-"

+
where A= zom ---(0.46+ F)
(ER-1)
119.9 2kR + 1)