electric field antenna and a high-frequency roll-off when speaking in terms of a dE/dt
antenna.
The general time-domain expression for the output voltage of an electric field
antenna is found by performing the inverse Fourier transform on the frequency-domain
expression. Rearranging Equation 3-14 (substituting C = Cant +Cit ) yields
Vout(m) = ate --jo Enorm(0) (3-31)
This expression can be viewed as the multiplication of two functions of co. This
can be expressed as
V(o)() = X(o)Y(co) (3-32)
The quantities X(m) and Y(o) can be defined as
X(o) = (3-33)
C + CO
Y(o)= ApateE (C) (3-34)
Therefore, the time-domain expression for the antenna output voltage, Vo,t(t), can
be found by the convolution property of the Fourier transform.
Vout (t) = x(t) y(t) (3-35)
The operator denotes linear convolution and x(t) and y(t) are the inverse Fourier
transforms of X(co) and Y(co), respectively. Convolution is performed by means of the
convolution integral
Vout(t) = x(l)y(t )dl (3-36)
Alternatively, since linear convolution is a commutative operation, Vout(t) can be
expressed as
Vot(t) = y(l)x(t- l)dl (3-37)
J/ o--0