Page 320 - Analog and Digital Filter Design
P. 320
Transmission Lines and Printed Circuit Boards as Filters 31 7
If id12 > 2, the wide line equation is:
59.96~'
where E = ~
z,& '
On a standard circuit board (FR4 material, approximately 1.6mm thick) a
5OQ transmission line is about 2.5mm wide; this is a ivlh ratio of 1.5625. The
35Q line will be wider and, using the wide line equation. it has a wlk ratio of
3.359 (equating to a width of 5.3744mm). The 81 Q line will be narrower than
a 50Q line so the narrow line equation can be used: A = 2.4455, so wlh = 0.70404
(which equates to a width of 1.1265mm).
Printed Circuits as Filters
I have already shown how transmission lines can be used to construct filters.
Transmission lines were shown as being realized as microstrip or stripline
printed circuits. An alternative filter construction using printed circuit boards
(PCBs) will now be described. Narrow and wide sections of track will be used
to replace inductors and capacitors, respectively. The length of each section will
be much less than a quarter wavelength in the filter's passband. Only a broad
outline of designing lowpass filters using this technique will be described and
presented as an example. Capacitors are produced from wide sections of track.
The width of these sections must be less than a quarter wavelength at the highest
operating frequency, to avoid resonance in the direction transverse to the prop-
agation.
Let's assume the board is a standard fiberglass resin type (FR4) with a thickness
of 1.6 mm and a relative permitivity of E~ = 4.7. The required filter has a cutoff
frequency of 1 GHz. At this frequency the wavelength of a signal in the PCB is
300/m= 138.38mm; this is a worst case approximation because the actual
relative effective permitivity will be less than that of the board material alone,
because of the air path, and therefore the wavelength will be longer. The capaci-
tors can be replaced by a track w < 34.59mm; let IV = 25mm.
The ratio of track width to board thickness is i.vlh, which is greater than one.
The impedance of this track is given by:
