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 119
Some practical considerations arise from the fact that the physical length of a real
transmission line is shorter than its electrical length. For example, in certain types of
phased-array antenna designs, radiating elements are spaced a half-wavelength apart
and must be fed 180 degrees (half-wave) out of phase with each other. The simplest and
least expensive connection between the two elements is a transmission line of a length
that provides an electrical half-wavelength. Unfortunately, because of the velocity factor,
the physical length for a one-half electrical wavelength cable is shorter than the freespace
half-wave distance between elements. In other words, the cable will be too short
to reach between the radiating elements!
Clearly, velocity factors must be known before transmission lines can be selected
and cut to length for specific situations. Table 4.1 lists the velocity factors for several
popular types of transmission lines. Because these are at best nominal values, the actual
velocity factor for any given line should be measured, using techniques and instruments
described in Chap. 27.
Type of Line Z 0 (ohms) Velocity Factor
1
⁄2-in TV parallel line (air dielectric) 300 0.95
1-in TV parallel line (air dielectric) 450 0.95
TV twin-lead 300 0.82
UHF TV twin-lead 300 0.80
Polyethylene coaxial cable * 0.66
Polyethylene foam coaxial cable * 0.79
Air-space polyethylene foam coaxial cable * 0.86
Teflon coaxial cable * 0.70
CATV hardline 75 0.8–0.9
* Various impedances depending upon cable type.
Table 4.1 Transmission Line Characteristics
Loss in Transmission Lines
As we saw earlier, loss in a two-conductor transmission line is modeled in the series R′
and shunt G′ terms of Eq. (4.1), repeated here as Eq. (4.12) for convenience. Up until this
point we have discussed only lines with zero loss or negligible loss.
Z
0
=
R'
G'
+
+
jwL'
jwC'
(4.12)
As you can see, when R′ and G′ are zero, the expression under the square root sign simplifies
to L′/C′. When either R′ or G′ or both are large enough to affect things, the math
gets too messy for us to go through in detail, so much of the following will have to be
taken on faith.