Practical_Antenna_Handbook_0071639586

92 P a r t I I : F u n d a m e n t a l s
A
B
C
E
E
E
Figure 3.5 Electric field
between conducting plates
at various angles.
the current “leads” the voltage by that amount. Specifically,
I=CDV/Dt. In calculus, we would say the current flowing to the
upper capacitor plate is the first derivative of the voltage across
the capacitor. (Similarly, in an inductor the current “lags” the voltage
by 90 degrees.)
Of course, once the capacitor plates are charged, a steady
E-field exists between them. Since it is a static field, it does not create
a magnetic field. However, during the very short instant when
current is flowing in the wires connected to the capacitor, its amplitude
is constantly changing as well, which means electrons are
being accelerated or decelerated and a changing magnetic field encircles
each of the wires. On each wire we have both a changing
current and a changing voltage within the same region of space
and thus the potential for radiation, depending on the length of the
wires, the space between them, and other factors. (Have you ever
turned on a lamp or appliance in your home and heard a “click” in
an AM broadcast receiver? That’s an example of radiation caused
by the sudden change in current and voltage on the wire that runs
between the switch and the appliance.)
Other geometries and orientations are possible for the two capacitor
plates, and they will result in different E-field patterns in
the space between the plates, as shown in Fig. 3.5. If the two plates
of the capacitor are spread farther apart at one end than at the
other, the electric field between them must curve to always meet
the plates at right angles (Fig. 3.5B and C). The straight lines in A
become arcs in B, and approximately semicircles in C, where the
plates are in a straight line, 180 degrees apart. But in addition to
altering the orientation of the two plates with respect to each other,
we can also change their shape. For instance, instead of the flat
rectangular metal sheets we started with, we can make the two elements from cylindrical
metal rods or wires.
The Hertzian Dipole
Now suppose the circle marked E in Fig. 3.6 is a transmitter or other source supplying
sinusoidal RF energy at a single frequency whose wavelength is much larger than the
length of the rods or wires in B. Electrons are simultaneously pushed onto one rod or
wire and pulled from the other in direct response to the sinusoidal source voltage applied
to the two rods. Of course, the amplitudes of the static and quasi-static E- and
H-fields in the vicinity of the two rods are changing at the same sinusoidal rate as the
applied voltage, but it turns out these fields exist only near the wires or rods and die out
rapidly with increasing distance from the antenna.
Since the velocities of the electrons are constantly changing as they shuttle back and
forth between the rods and the sinusoidal source, they are in a state of continuous acceleration
and deceleration, thus setting up linked time-varying electric and magnetic
fields in the space enclosing the rods. Above and beyond the conventional static and
quasi-static fields, Maxwell’s equations predict the existence of new fields resulting
solely from the acceleration of electric charge in the region between the two rods. Spe-