Practical_Antenna_Handbook_0071639586

C h a p t e r 2 6 : T h e S m i t h C h a r t 577
extension of the radius circle, drop a line vertically to the topmost of the radially scaled
parameters at the bottom of the chart. For this example, we find an input VSWR of approximately
2.6:1. In decibel form, the VSWR is 8.3 dB (next scale down from VSWR),
and this is confirmed by
VSWR
dB =
20log (VSWR)
= (20) log (2.7)
= (20) (0.431)
= 8.3 dB
(26.16)
The transmission loss coefficient is found in a similar manner, using the radially scaled
parameter scales. In practice, once we have found the VSWR we need only continue the
vertical line from the 2.6:1 VSWR line across the other scales below. In this case, the line
intersects the voltage reflection coefficient scale at 0.44 and the power reflection coefficient
line at 0.20, which is, of course, (0.44) 2 .
The return loss can found by reading the “RET’N LOSS, dB” line where the same
vertical line intersects it; the value is found to be approximately 7 dB, which is confirmed
with the use of Eq. (26.13):
Loss = 10log ( Γ ) dB
RET
= 10 log (0.21) dB
= (10) ( – 0.677) dB
= – 6.77 dB
The angle of reflection coefficient is found from the outer circles of the Smith chart. The
line connecting the center to the load impedance (Z′ = 0.72 + j0.8) is extended to the
angle of reflection coefficient in degrees circle, and intersects it at approximately 84 degrees.
The total magnitude + phase description of the reflection coefficient is therefore 0.44/84
degrees.
To find the transmission loss coefficient (TLC) from the radially scaled parameter
scales, drop a vertical line from the rightmost extension of the impedance radius to the
uppermost radially scaled parameter scale, the loss coefficient scale, where it is found to
intersect 1.5. This value is confirmed with Eq. (26.14):
PWR
TLC = 1 + Γ
1 − Γ
PWR
PWR
1 (0.20)
= + 1 − (0.20)
1.20
=
0.80
= 1.5