Practical_Antenna_Handbook_0071639586

136 P a r t I I : F u n d a m e n t a l s
Determination of VSWR losses must take into account two VSWR situations. Figure
4.9 shows a transmission line of impedance Z 0 interconnecting a load impedance Z L to
a source with output impedance Z S . There is a potential for impedance mismatch at both
ends of the line.
When one end of the line is matched (either Z S or Z L ), the mismatch loss (ML) caused
by SWR at the mismatched end is
⎡ ⎛ ⎞ ⎤
ML = – 10 log ⎢1– ⎜
SWR – 1
2
⎟ ⎥
⎣ ⎝SWR + 1⎠
⎦
(4.37)
which from Eq. (4.35) is
2
ML = – 10 log (1– G )
(4.38)
Example 4.7 A coaxial transmission line with a characteristic impedance of 50 Ω is connected
to the 50-Ω output (Z 0 ) of a signal generator, and also to a 20W load impedance
Z L . Calculate the mismatch loss.
Solution
(a) First find the VSWR:
VSWR VSWR = Z / Z= Z / Z
0
L
= (50 Ω) = /(50 (20 Ω) / (20 Ω)
= 2.5:1= 2.5:1
0
L
(b) Mismatch loss:
⎡ ⎛ ⎞ ⎤
ML = – 10 log ⎢1– ⎜
SWR – 1
2
⎟ ⎥
⎣ ⎝SWR + 1⎠
⎦
⎡ ⎛ ⎞ ⎤
= – 10 log ⎢1– ⎜
2.5 – 1
2
⎟ ⎥
⎣ ⎝ 2.5 + 1⎠
⎦
⎡ ⎛ ⎞ ⎤
= – 10 log ⎢1– ⎜
1.5
2
⎟ ⎥
⎣ ⎝3.5⎠
⎦
⎡
2
= – 10 log ⎣1– (0.43) ⎤
⎦
= – 10 log [ 1– 0.185]
= – 10 log [ 0.815]
= (–10) (–0.089)
= 0.89