Practical_Antenna_Handbook_0071639586

536 p a r t V I I : t u n i n g , T r o u b l e s h o o t i n g , a n d D e s i g n A i d s
pedance. For the special case when both the source and the load impedances are purely
resistive, the design equations are:
R2
Q = −
R 1
(24.2)
1
XL = Q × R
(24.3)
1
X
C
R2 =
(24.4)
Q
where, of course,
X
C =
1
2πfC
(24.5)
and
X = L
2 π fL
(24.6)
The L-Âsection network of Fig. 24.1B differs from the previous circuit in that the coil
and capacitor locations are swapped. As before, values for L and C can be found that
will allow this circuit to match all possible load impedances having R 1 < R 2 , and some
load impedances for the range R 1 > R 2 , depending on the magnitude of X 2 . For the special
case when both the source and the load impedances are purely resistive, the design
equations are:
R2
Q = −
R 1
(24.7)
1
R2
X
L
=
Q
(24.8)
X = R 1
Q
C
(24.9)
Figure 24.1C is similar to Fig. 24.1A with the exception that the capacitor is at the
input rather than the output of the network. Values for L and C can be found that will
allow this topology to match all possible load impedances having R 1 > R 2 , and some load
impedances for the range R 1 < R 2 . The equations governing this network are:
R1
Q = −
R 1
(24.10)
2
X
L
= R 2
Q
(24.11)
R1
X
C
=
Q
(24.12)