Page 295 - Complete Wireless Design

Filter Design

294 Chapter Six

wavelength, or 90 degrees; and is grounded by a via directly to the ground
plane.
1. To calculate how wide a 100-ohm microstrip must be for the substrate in
use:
377
Z
1 E E r

0 W

r
h
where Z characteristic impedance of the microstrip, ohms (in this case it
0
must be 100 ohms)
W width of the microstrip conductor (use same units as h)
h thickness of the substrate between the ground plane and the
microstrip conductor (use same units as W)
E dielectric constant of the board material
r
2. To calculate exactly how long the microstrip must be to be a quarter of a
wavelength, with the chosen board material and frequency:
a. Find the effective dielectric constant of the microstrip.
1
E 1 E 1
r
r
E 12h

EFF W
2 2 1
where E effective dielectric constant that the microstrip transmission
EFF
line actually sees as a result of the dielectric/air interface
E rated dielectric constant of the PCB’s substrate material (found
r
on the PCB’s data sheet)
h thickness of the substrate material between the top conductor
and the bottom ground plane of the microstrip; requires the
same units as W
W width of the top conductor of the microstrip; requires the same
units as h

b. After obtaining the effective dielectric constant of the microstrip sub-
strate, find the propagation velocity of the microstrip transmission line:

1
V
P E
EFF
where V fraction of the speed of light for the microstrip transmission line
P
compared to light in a vacuum and E effective dielectric constant as seen
EFF
by the microstrip transmission line.
c. Calculate the wavelength of the frequency of interest in a perfect vacuum:

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