The general time-domain expression for Vot (t) can be found by performing the
inverse Fourier transform on Equation 3-83. Equation 3-83 can be rearranged to yield
1 () = RloadAloop joB or(o)) (3-91)
Rloop+Rload Loop +
\ Lloop i o
This expression can be viewed as the multiplication of two functions of co. This
can be expressed as
Vout(o) = X(o)Y(o) (3-92)
The quantities X(m) and Y(o) are defined as
X() = 1 (3-93)
Rloop+Rload1 + j
Y(co) = RloadAloop jBr ) (3-94)
Lloop
Therefore, the time-domain expression for the antenna output voltage, Vo,t(t), can
be found by the convolution property of the Fourier transform.
Vot (t) = x(t) y(t) (3-95)
The operator denotes linear convolution and is evaluated using the convolution
integral. The quantities x(t) and y(t) denote the inverse Fourier transforms of X(o)
and Y(o), respectively. The inverse Fourier transform of X(o) can be found by using a
Fourier transform table.
(Rloop +Rload t
x(t) =e Lloop / u(t) (3-96)
The quantity u(t) is the unit-step function, as defined by Equation 3-39. The
inverse Fourier transform of Y(co) is found by invoking the differentiation property of
the Fourier transform.
t RloadAloop dBnorm (t) (-
y(t) p (397)
Lloop dt