Practical_Antenna_Handbook_0071639586

C h a p t e r 3 : A n t e n n a B a s i c s 91
tions, the possibility of electromagnetic waves—presumably traveling through his mystical
æther—as well as the speed at which these waves must travel through space.
Maxwell then went a step further: Based on the most accurate measurements of the
speed of light at the time, he concluded that visible light was itself comprised of electromagnetic
waves!
Nearly a quarter century passed before the German scientist Heinrich Hertz demonstrated
in 1887 that he could create, transmit, and receive what we now call radio
waves. Hertz thus took the first baby steps in determining the physical geometry of
conductors (antennas, in other words) that would allow the generation and detection of
the EM radiation predicted by Maxwell. Of course, Hertz did not have any of the conveniences
or inventions of the modern world; in particular, he did not have a tunable
receiver or transmitter. Instead, he generated a spark (which contains a nearly infinite
number of frequencies) across a gap between two curved conductors of a certain length
with some laboratory equipment and attempted to detect the fields from that spark
with a similar set of conductors a few feet away. The signal from his detector was then
used to make a laboratory meter wiggle. And so it was that Heinrich Hertz was quite
likely the first to experience the magic of radio!
V BAT
I(t)
V(t)
V = V(t) = V (1- e R s
C )
CAP BAT
I
CHG
R s
= I(t) = V
BAT
R s
e
- t
- t
R s
C
Area A
V(t)
V BAT
Conducting plates
I(t)
V BAT /R s
R = the sum of all resistances in the circuit, including
s
the resistance of the interconnecting wire and
the internal resistance of the battery itself.
C = A
d
d
t
t
Linked Electric and Magnetic Fields
Now let’s return to the example of charging a capacitor from a battery. The flow of these
charges constitutes a conduction current in the connecting wires that lasts for a very
short time—only until the voltage
across the plates of the capacitor
is equal to that of the battery
itself. That interval depends, of
course, on the amplitude of the
current, which initially is limited
only by the combined resistance
of the wires plus the internal
resistance of the battery itself.
(That’s why the wire in automobile
jumper cables is so fat!) The
final value of the current is zero,
just as the final voltage across the
capacitor is the full battery voltage,
V BAT . As shown in Fig. 3.4,
both voltage and current follow
exponential curves during the
transition period.
If R s is very small, the voltage
and current at the capacitor
are in quadrature relationship to
each other; we say they are 90
degrees out of phase, and that
Figure 3.4 Exponential voltage and
current when charging a capacitor.