I(co) Z, TZL
Figure 3-11. Frequency-domain equivalent circuit, using a Norton equivalent current
source, of a flat-plate antenna sensor feeding a load (represented by ZL).
magnitude of the Norton equivalent current source in the frequency domain becomes
I(CO) = CoAplate (jAEnorm(CO)) (3-9)
The quantity Enorm (o) designates that the normal component of the electric field is
now a function of angular frequency and not time.
The Norton equivalent circuit in the frequency domain is shown in Figure 3-11.
The current source is placed in parallel with the source impedance, Zs, and the load
impedance, ZL. The source impedance is the impedance of the antenna itself and the
load impedance is the impedance of any external elements connected to the plate. In
general, the source and load impedances can be resistive, capacitive, inductive, or a
combination of the three.
If the output of the antenna is taken as the voltage across the load impedance, then
the expression for the output voltage in the frequency domain is
( ZSZL
Vout(mCO) = I(CO)Ztotal = I() (Zs ZL) = joAplateEnorm(CO) ZS ZL (3-10)
The output voltage of the antenna in the frequency domain is the quantity
jCmoAplateEnorm(CO), scaled by the frequency-dependent quantity ZsZL/ (Zs +ZL). The
frequency-independent gain of the antenna is given by the quantity FoAplate. If the
quantity ZsZL/ (Zs +ZL) is equal to unity, then the output is simply jaCEnorm (O), scaled
by the frequency-independent quantity oAplate. If the quantity ZsZL/ (Zs + ZL) is equal
to 1/(jco), then the output is simply Enorm(cn) scaled by the frequency-independent