Practical_Antenna_Handbook_0071639586

104 P a r t I I : F u n d a m e n t a l s
Figure 3.11 presents the same information for the standing current waveforms on a
l/2 dipole.
Important facts to take away from Figs. 3.10 and 3.11 are:
• The standing voltage waveform is always minimum at the center of a l/2
dipole.
• The amplitude of the standing voltage waveform is always maximum, but of
opposing polarities, at the two ends of the dipole.
• The standing current waveform is always maximum at the center of the l/2
dipole.
• The standing current waveform is always zero at both ends of the dipole
(because of the boundary condition there—it’s an open circuit!).
Note If a radiator is longer than l/2, the standing wave of current reverses direction every
half-wavelength along the conductor. Starting with the boundary condition that the current
at either end of a center-fed dipole must be zero, we arbitrarily choose a polarity for the
current throughout the first half-wavelength from either end as we move toward the
feedpoint. When we reach the next current node, l/2 back from that end, the current reverses
polarity for the next half-wavelength along the radiator (or as much of a half-wavelength as
exists before reaching the feedpoint). In the center-fed dipole of Fig. 3.9, for instance, the
length of each side is 3 l, or six half-wavelength sections. Observe that the standing wave of
current is positive on every other one and negative on the alternate three.
To see why the current reverses, we can use the following argument: If a positive current
in a l/2 section corresponds to the left end of the section having a positive voltage and the
right end having a negative voltage, a negative current in such a section must correspond to
the right end having a positive voltage. Since the right end of one l/2 section is the same
point on the conductor as the left end of the next l/2 section (except, of course, when we get
to the end), having the same (positive or negative) voltage on the right end of one section and
the left end of the next section must necessarily mean that the currents are of opposite
polarity, or direction, in the two adjacent sections.
Remembering that the current reverses in each adjacent l/2 section of a conductor will
be key to understanding the patterns of loops, folded dipoles, collinear arrays, and other
antenna types discussed in later chapters.
Velocity of Propagation and Antenna Length
In free space, electromagnetic waves travel at a constant velocity of 300,000 km (or approximately
186,000 mi) per second, according to the equation
1
c = µ ε
O O
(3.29)
where m 0 , the permeability = 4p • 10 −7 H/m
1
e 0 , the permittivity =
36π • 10−9 F/m