The term RC is known as the decay time constant and is typically denoted by T.
The time constant is the inverse of coo.
1
S= RC =- (3-52)
(CO
oo
When the electric field is a step-function, the output of the antenna at time t = T
is a factor of 1/e less than it was at time t = 0. Therefore, the output of the antenna
is only valid for a short period of time relative to T. This is exactly what is expected
since the response of the electric field flat-plate antenna is that of a high-pass filter in
the frequency domain.
For times t << the output of the antenna, given a step-function input of amplitude
Eo, becomes
0oAplate
Vout (t) = Apa Eo (3-53)
C
If the example circuit parameters R= 500 kQ and C = 0.1 rF are again considered,
the decay time constant is
T = (500 kQ) (0.1 F) = 50 ms (3-54)
Given a step-function input, the output of this example electric field antenna is
only valid for times much less than 50 ms. Depending on the application, this time
constant may or may not be acceptable.
Increasing the time constant by increasing the capacitance necessarily decreases
the output of the antenna by a factor of 1/C. The resistance can be increased with
no effect on the gain, but there are practical limits to how high this resistance can be
increased. Typically both R and C are increased with C being adjusted to yield an
acceptable gain.
It should be noted that if Equation 3-46 is solved for En orm(t) as a function out(t)
it may be possible to "correct" the measured electric field. In other words, it may be