Practical_Antenna_Handbook_0071639586

C h a p t e r 2 7 : T e s t i n g a n d T r o u b l e s h o o t i n g 611
so, by substitution,
⎡⎛
⎞
= ω
⎝
⎜
⎠
⎟ ± ⎤
e j M V I
⎣⎢
Z0
⎦⎥
(27.15)
At any given point in a transmission line, V is the sum of the forward (V FWD ) and
reflected (V REF ) voltages, and the line current is equal to
I= V Z
FWD
0
– V Z
REV
0
(27.16)
where Z 0 is the transmission line impedance.
We may specify e in the forms
jwM
(2 VFWD)
e=
Z
0
(27.17)
and
jwM
(2 VREV
)
e=
Z
0
(27.18)
The output voltage e of the coupler, then, is proportional to the mutual inductance
and frequency (by virtue of jwM). But the manufacturer terminates R in a capacitive
reactance, so the frequency dependence is lessened (see Fig. 27.18C). Each element is
Relative, response dB
0
5
10
0
5
10
0
5
10
10C element: 10 W, 100-250 MHz
100C element: 100 W, 100-250 MHz
500C element: 500 W, 100-250 MHz
20 40 60 80 100 200 400 600 800 1000
Figure 27.18C Power-Âfrequency calibration.
Frequency in MHz