over the surface of the plate, then surface charge density along the plate must also be
uniform. For a circular plate, the electric field along the surface of the plate can be
considered non-uniform when the plate diameter is larger than about a sixteenth of a
wavelength. If the highest frequency component of Enorm is 30 MHz then the smallest
wavelength will necessarily be 10 m. One sixteenth of a wavelength is 0.625 m, which
is larger than the diameter of the plates used in the MSE (discussed in Section 3.3.1.2).
If the electric field is uniform across a plate of area Aplate, then the total charge on
the plate can be expressed as
Qplate = coAplateEnorm (3-6)
The Norton equivalent short circuit current, i(t), is necessarily the time-derivative
of the charge.
d d dE, (t)
i(t) = d Qplate() = d (EoAplateEnorm(t)) = oAplate dEnt (3-7)
Hence, the flat-plate antenna in the presence of a uniform time-varying electric
field can be viewed as a current source whose magnitude is proportional to the time
derivative of the normal component of the electric field. This Norton equivalent current
source is the basis of the equivalent circuit. The Thevenin equivalent voltage, which
yields the same results, could also be used by performing a simple transformation. The
equivalent circuit analysis is most often performed in the frequency domain. However,
a solution can be found directly in the time domain by solving a first-order differential
equation. The relationship between the time domain and the frequency domain is given
by the Fourier transform. The Fourier transform, X(o), of a time-domain signal, x(t),
is
F {x(t)} = X(o) = x(t)e-jtdt (3-8)
Differentiation with respect to time in the time domain corresponds to multiplication
by the complex number jo in the frequency domain. Therefore, the expression for the