The pass-band gain is equal to (AloopRload)/(Rloop +Rload). The -3 dB point
(the frequency at which the output is approximately 0.707 times the output in the
pass-band) of the magnitude response is
SRloop + Rload (3-86)
Lloop
If the frequency range of interest lies far below the -3 dB point, then the
expression for the response of the loop antenna in the frequency domain becomes
GdB () = AloopRload (3-87)
dt Rloop +Rload
The above expression is only valid for frequencies which satisfy the condition
S ( Rloop +Rload) (3-88)
Lloop
If the same condition is applied to Equation 3-83, then the output voltage of the
loop antenna in the frequency domain becomes
Vt (o) = oopRoad Bom () (3-89)
Rloop +Rload
To find the output voltage in the time domain, the inverse Fourier transform
(defined in Equation 3-23) is used. The integral need not be computed in this case
since the differentiation property of the Fourier transform can be used. Therefore, the
expression for the output voltage in the time domain is
VOW (t) AloopRload dBnorm(t) (3-90)
Vot (t) = (3-90)
Rloop +Rload dt
Although this is a time-domain expression, the frequency constraint still applies
since the time-domain expression is derived from a frequency-domain expression
with that constraint. In other words, the above expression is only valid if the dB/dt
waveform has no significant frequency content above coo.