Digital Signal Processing Reference
In-Depth Information
Table 6.6
π
-matching
network component values at
3.7 GHz for
R
opt
=
18
Table 6.7
π
-matching
network component values at
5.2 GHz for
R
opt
=
18
variables is an iterative process requiring some constraints to be established. The
optimum resistance is first determined by the loadline method [
6
, Chap. 2]. This
resistance is used to calculate the components of the output
π
-matching network.
The two frequencies of interest are 3.7 and 5.2 GHz. For each frequency, the values
of
L
1
and
Q
u
will be different, but the values of
C
1
and
C
2
will remain constant.
The value of
L
1
is limited by the technology and cannot be lower than 0.35 nH.
There are also constraints regarding the designability of the
π
-matching net-
work [
27
]. The values of
C
1
and
C
2
must be chosen carefully so that they provide
the desired transformation for the two frequencies of interest—knowing that
C
1
and
C
2
do not change with frequency. Tables
6.6
and
6.7
show the values required for
C
1
,
L
1
, and
C
2
to transform the 50
antenna impedance into the required optimum
resistance of 18
at 3.7 and 5.2 GHz. The values are given for different
Q
0
.As
already mentioned earlier in this chapter, the required values of
C
1
and
C
2
vary less
with frequency for high
Q
0
.
Three cases of interest are highlighted. With
Q
0
=
7
.
77 at 5.2 GHz (
solid line
linking rows of the two tables), the values required are
C
1
=
9
.
85 pF,
L
1
=
0
.
25 nH,
and
C
2
=
5
.
97 pF. At 3.7 GHz, the values required are
C
1
=
9
.
85 pF,
L
1
=
0
.
48 nH,
and
C
2
=
6
.
02 pF, which shows that the required values at 3.7 and 5.2 GHz are
very close for
C
1
and
C
2
. This means that by varying the inductor from 0.48 nH at
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