Practical_Antenna_Handbook_0071639586

570 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
The angle of transmission coefficient and angle of reflection coefficient scales are shown
in circle C in Fig. 26.4C. These scales report the relative phase angle between reflected
and incident waves at each point on the line resulting from a given load impedance.
Recall from transmission line theory (see Chap. 4) that a short circuit (R = 0) at the
load end of the line results in the reflected voltage headed back toward the generator
being 180 degrees out of phase with the incident voltage at the reflection point, and
an open line (i.e., infinite impedance) results in the reflected voltage headed back
Âtoward the generator being in phase (i.e., 0 degrees) with the incident voltage at the
load. On the Smith chart, a short circuit at the load corresponds to the left-Âhand end
of the pure resistance line, where 180 degrees is printed on circle C. Similarly, an open
circuit at the load corresponds to the right-Âhand end of the pure resistance line, where
0 degrees is printed. Note that the upper half-Âcircle is calibrated 0 to +180 degrees,
and the bottom half-Âcircle is calibrated 0 to –180 degrees, reflecting how the load impedance
is transformed into either inductive or capacitive reactance, respectively, depending
on how far back from the load the observation point has moved along the
transmission line.
Radially Scaled Parameters
There are six scales laid out on four lines (D through G in Fig. 26.4C and in expanded
form in Fig. 26.5) at the bottom of the Smith chart. These scales are called the radially
scaled parameters—and they are not only very important but often overlooked. With
these scales, we can determine such factors as VSWR (both as a ratio and in decibels),
return loss in decibels, voltage or current reflection coefficient, and the power reflection
coefficient.
As discussed in detail in Chap. 4, the reflection coefficient G is defined as the ratio
of the reflected signal to the incident (or forward) signal. For voltage or current:
VREF
Γ = (26.6)
V
FWD
and
IREF
Γ = (26.7)
I
FWD
Power is proportional to the square of voltage or current, so:
2
Γ
PWR
= Γ (26.8)
or
Γ
PWR
= P P
REF
FWD
(26.9)
Example 26.2 10W of microwave RF power is applied to a lossless transmission line;
2.8W of the 10W total incident power is reflected from the mismatched load. Calculate
the reflection coefficient.