Practical_Antenna_Handbook_0071639586

144 P a r t I I : F u n d a m e n t a l s
Z L
Load
impedance
Example 4.9 A 50-Ω source must be matched to a load impedance
of 36 Ω. Find the characteristic impedance required of a
Q-section matching network.
Solution
Z0
=
Z Z
S
L
= (50 Ω) (36 Ω)
= 1800 Ω
= 42 Ω
2
Z o
Z s
/4 Q section
Figure 4.12 Quarter-wavelength
Q section.
Clearly, the key to success is to have available a piece of
transmission line having the required characteristic impedance.
Unfortunately, the number of different coaxial cable impedances
available for the Q-section is limited, and so its
utility for matching an arbitrary pair of impedances is also
limited.
On open-wire transmission line systems, on the other
hand, it is quite easy to achieve the correct impedance for the
matching section. As before, we use the preceding equation to
find a value for Z 0 , and then calculate the conductor spacing
and diameter needed for a short length of a custom transmission
line! Armed with information about the diameter of common
wire sizes, once we know the feedpoint impedance, we
can use Eq. (4.55) to calculate the appropriate conductor spacing:
S = d × 10
( Z0
/ 276)
(4.55)
where S = spacing between conductors of parallel line
d = conductor diameter expressed in same units as S
Z 0 = desired surge impedance for Q-section
Assuming true open-wire line (with air dielectric) is used, the length of the
quarter-wave section in feet can be calculated using the familiar 246/F, where F is in
megahertz.
A quarter-wavelength shorted stub is a special case of the stub concept that finds particular
application in microwave circuits. Waveguides (Chap. 20) are based on the properties
of the quarter-wavelength shorted stub. Figure 4.13 shows a quarter-wave stub
and its current distribution. The current is maximum across the short, but wave cancellation
forces it to zero at the terminals. Because Z = V/I, when I goes to zero, the impedance
becomes infinite. Thus, a quarter-wavelength stub has an infinite impedance at its
resonant frequency, and acts as an insulator. This concept may be hard to swallow, but
the stub is a “metal insulator”.