course, "very large" and "very low" are relative terms which are determined by the
requirements of the experiment.
The expression for the antenna output voltage can be simplified somewhat if the
electric-field waveform is constrained to be of the following form.
Eorm(t) = s(t)u(t) (3-47)
The quantity s(t) is an arbitrary function of time and u(t) is the unit-step response
which was defined in Equation 3-39. If this is substituted into Equation 3-46, the
antenna output voltage becomes
vot (t e) (t)(t)- Apatee-R t s(l)eRdl (3-48)
C RC2 1J=o
The antenna output voltage can be specified exactly if the electric field waveform
is specified exactly. The response of the antenna to a step-function is of particular
interest since it can be used to crudely approximate the electric field waveform from a
return stroke. If s(t) is defined as the constant Eo, then the electric field waveform is
given by
Eorm (t) = Eou(t) (3-49)
The quantity Eo is amplitude of the step function. The corresponding antenna
output voltage is
LoAplate Ft OAplate
Vout(t) = oApatEoe R + Eo [u(t) -1] (3-50)
C C
The second term in the above expression is zero for all times t > 0, therefore the
expression reduces to
/ Plate
Vout(t) = AplatEoe RC (3-51)
C