Practical_Antenna_Handbook_0071639586

C h a p t e r 4 : T r a n s m i s s i o n L i n e s a n d I m p e d a n c e M a t c h i n g 143
Special Cases
If we use an impedance bridge or other instrument to determine the input impedance
at one end of an infinitely long transmission line, we will obtain the value Z 0 —the characteristic
or surge impedance for that particular type of line. If we attach a load impedance
equal to Z 0 at the far end of a much shorter length of transmission line, we will again
measure Z 0 at the input. But if we attach a load impedance Z L ≠ Z 0 , we have no idea
what input impedance we will see unless we know Z L , Z 0 and the exact length of the
line in electrical wavelengths. As we have seen in the preceding paragraphs, that is because
the impedance “looking into” a transmission line at the input is the result of the
line transforming the load impedance in a manner determined by the length of the line
and the relationship between the line and load impedances. Here are some specific
combinations that are important to know.
Matched Line and Load Impedances
Assuming a reasonably low loss transmission line, a purely resistive load impedance
Z L = Z 0 appears as Z 0 at the line input for any length of line. Any other load impedance,
whether a pure resistance ≠ Z 0 or a resistive component R 0 accompanied by a reactive
component, will transform to some other R ± jX value at the line input; the value (relative
to Z L ) will be solely determined by the length of the line (in wavelengths).
Half-Wavelength Section of Line
A half-wavelength section of transmission line is “magical” because it repeats any load
impedance, whether matched or not. Thus, for a single frequency or band of frequencies,
a transmission line that is any integer multiple of l/2 long can be used to remotely
measure and monitor the feedpoint impedance of an antenna. The two caveats are:
• An accurate knowledge of the line’s velocity factor is needed before cutting the
line to length.
• A given length of line is l/2 only over a very narrow range of frequencies.
Quarter-Wave Matching Section
A quarter-wavelength line exhibits a transforming property, converting low-resistance
loads to higher ones, and capacitive reactances to inductive. The best way to understand
and use this feature is with the Smith chart (explained in detail in Chap. 26) or a
similar tool. One important application of this property is to transform a load impedance
to a higher (or lower) main transmission line impedance. For instance, suppose an
antenna for 10 MHz has a feedpoint impedance of 100 Ω resistive. It’s not a very good
match for 52-Ω coaxial cable, but a l/4 section of 75-Ω RG-59 or RG-11 coaxial cable for
television systems will transform the antenna feedpoint impedance from 100 to 52 Ω.
Impedances for the l/4 transformer are calculated (for resistive loads) as follows:
Z Z = Z 2
(4.54)
L S 0
where Z L = load or antenna feedpoint impedance
Z 0 = characteristic impedance of l/4 section
Z S = characteristic impedance of system transmission line
The l/4 transmission line transformer, shown in Fig. 4.12, is sometimes called a
Q-section matching network.