Practical_Antenna_Handbook_0071639586

114 P a r t I I : F u n d a m e n t a l s
Transmission Line Characteristic Impedance (Z 0 )
If we take a very short length of two-conductor transmission line of any kind and measure
its electrical characteristics at some operating frequency with simple test equipment,
we will discover four parameters:
• Each of the two conductors exhibits a very small series resistance between its two
ends, measured at the operating frequency. In a balanced line, the resistance of
the two conductors is identical, but that is not necessarily the case for coaxial or
other unbalanced lines. Regardless of the type of line, we shall define R′ as the
sum of the resistive losses in the two conductors.
• Similarly, each of the two conductors has a small series inductance between its
two ends. All wires—even straight ones—have some inductance. Again, this
inductance is the same for both conductors of perfectly balanced lines but may
differ in unbalanced lines. We shall define L′ as the sum of these inductances.
• At one end or the other we measure a small shunt capacitance, C′, between the
two conductors. This is a measure of the capacitive coupling between two
closely spaced wires; of course, it depends greatly on the dielectric material
between them.
• At the same end of the short length of transmission line we measure a very high
shunt resistance (usually alternatively stated as a very low shunt conductance, G′,
where G′ is the reciprocal of the shunt resistance) across the two conductors.
This conductance is a characteristic of the dielectric material(s) filling the space
between the two conductors. Sometimes the dominant part of it (lowest
resistance, highest G′) is unintended—as might result from unwanted moisture
in the line!
In defining these four parameters, we have primed each of them to indicate that the
value we are measuring is for a unit length of transmission line. Of course, the unprimed
values of all four are directly proportional to the total length of the transmission line.
How short is “very short”? The length of transmission line used to obtain these data
must be much shorter than the wavelength of the highest frequency we intend to send
through the line.
If we now use these four parameters to draw a lumped element model of this short
length of transmission line, we obtain the equivalent circuit of Fig. 4.2. This single-ended
circuit is equally valid for balanced (parallel wire) transmission lines and unbalanced
(coaxial) lines.
Z s
R ' L '
R ' L '
Gen
C '
G '
C '
G '
Z L
Source
Unit length of line
{
Load
Figure 4.2 Transmission line equivalent
circuit.