wide-band applications. If both R and Cant are doubled, then the -3 dB bandwidth must
necessarily decrease by a factor of four, yielding fo a 26.5 MHz.
If the frequency range of interest lies far below the -3 dB point, then the
expression for the response of the dE/dt antenna in the frequency domain becomes
GdE (o) = oApiateR (3-20)
dt
The above expression is only valid for frequencies which satisfy the condition
CO <(c o =RCa (3-21)
If the same condition is applied to Equation 3-14 (assuming Cit = 0), then the
output voltage of the dE/dt antenna in the frequency domain becomes:
Vout (O) = jCWOoAplateREnorm (CO) (3-22)
To find the output voltage in the time domain, the inverse Fourier transform is
used.
F {X(m)} = x(t) =X(co)ejXtdco (3-23)
27c
However, the integral need not be computed in this case since the differentiation
property of the Fourier transform can be used. Therefore, the expression for the output
voltage in the time domain is
Vot (t) = oAplateR dEOm(t) (3-24)
dt
Although this is a time-domain expression, the frequency constraint still applies
since the time-domain expression is derived from a frequency-domain expression
with that constraint. In other words, the above expression is only valid if the dE/dt
waveform has no significant frequency content above coo.