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 569
impedance. For example, using the normalized impedance of Eq. (26.4), the normalized
admittance will be:
1
Y′ =
Z′
1 1.9 − j1.1
= ×
1.9 + j1.1
1.9 − j1.1
1.9 − j1.1
=
3.6 + 1.2
1.9 − j1.1
= = 0.39 − j0.23
4.8
Now compare your answer with the coordinates of the left-Âhand end of the line in Fig.
26.4D. Simply extend the impedance radius through the 1.0,0.0 center point until it
intersects the VSWR circle again. This point of intersection represents the same
normalized load as that found in Eq. (26.4); the only difference is that it is now specified
as a normalized admittance. As you can see, one of the delights of the Smith chart is that
calculations like these are reduced to a quick graphical construction!
Outer Circle Parameters
The standard Smith chart contains three concentric calibrated circles on the outer perimeter
of the chart. Circle A has already been covered in Fig. 26.4C; it is the pure reactance
circle. The next larger circle B defines the distance in wavelengths as you travel
around the circle. Clockwise motion is toward the generator or transmitter, and counterclockwise
is toward the load or antenna. Circle B is important when transforming an
impedance at one point on a transmission line to the resulting impedance at another
point some distance away.
There are two scales on the wavelength circle (B in Fig 26.4C), and both have their
zero origin at the left-Âhand extreme of the pure resistance line. On both scales one complete
revolution represents a distance of one half-Âwavelength along the line. The scales are
calibrated linearly from 0 through 0.50 such that these two points are identical with
each other on the circle. In other words, starting at the zero point and traveling 360 degrees
around the circle brings one back to zero, which represents one half-Âwavelength,
or 0.5l.
Although both wavelength scales span the same range (0 to 0.50l), they are traversed
in opposite directions. The outer scale is calibrated clockwise and it represents
wavelengths toward the generator; the inner scale is calibrated counterclockwise and
represents wavelengths toward the load. These two scales are complementary at all
points. Thus, 0.12 on the outer scale corresponds to (0.50 minus 0.12) or 0.38 on the
inner scale.