Page 31 - Complete Wireless Design

Wireless Essentials

30 Chapter One

where E effective dielectric constant that the microstrip sees
EFF
E actual dielectric constant of the PCB’s substrate material
r
h thickness of the substrate material between the top conductor
and the bottom ground plane of the microstrip
W width of the top conductor of the microstrip

Then:
1
V
P E
EFF
where V fraction of the speed of light compared to light in a vacuum.
P
Then calculate the wavelength of the signal of interest in a perfect vacuum:
11,800

VAC f

where wavelength of the frequency of interest (f) , mils, in a true
VAC
vacuum
11,800 speed of light value to obtain a in mils while using an f
VAC
in GHz
f frequency of the signal of interest, GHz

Then multiply the velocity of propagation (V ) times the wavelength ( ) of
P VAC
the signal as calculated above in order to arrive at the wavelength of the sig-
nal of interest ( ), in mils, when the signal is placed into the microstrip:
V
P VAC
Distributed parallel (shunt) capacitor. First, knowing the capacitance of the
desired component for your circuit, calculate the reactance of the shunt capac-
itor required, at the frequency of interest, by the common formula

1
X
c 2 fC
Second, utilize 30-ohm microstrip (Z 30 ohms) for the substrate’s
L
dielectric. Find the microstrip width required for this 30-ohm value by using
one of the many microstrip calculation programs available free on the Web
(such as HP’s AppCad, or AWR’s TXLine, or Daniel Swanson’s MWTLC), or
use the formula above. As shown in Fig. 1.38, the microstrip of the equiva-
lent shunt capacitor is open, and not grounded, at its end. The capacitor sec-
tion is also attached to the 50-ohm microstrip transmission line by a small
tapered section to improve the transition. A further improvement is possible
by splitting the capacitor in two and placing it on both sides of the trans-
mission line.

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