Hello. At a given frequency the antenna can most certainly be viewed
as an equivalent series R-L-C (or parallel G-L-C) circuit with
appropriate values of resistance or reactance. The caveat is that the
antenna is assumed to provide values of R, L, and C that are
invariant with frequency over the frequency range that encompasses
the 3-dB (half power) points. If the driving point impedance
characteristics of the antenna do not meet this criterion we will not
arrive at the correct values. Also, if a matching network is required
to tune out the antenna reactance at the center frequency of interest
then the network is considered to be a part of the antenna. The
steps are:
1. Establish the center frequency (fo) of interest in which the
antenna or antenna/matching network input impedance is purely (or
nearly) resistive.
2. Find the equivalent L and C values from the reactances (X1 & X2)
obtained by tuning above and below fo respectively:
L = X1/[2 * Pi * f1 * (1 - fo^2/f^2)] f1 > fo
C = 1/(2 * Pi * f2 * X2) * (1 - f2^2/fo^2) f2 < fo
Determining both L and C from two measurments may seem redundant
since if we have one we can get the other from fo = 1/[2 * Pi * fo *
sqrt(L * C)]. The additional measurement/calculation, however,
provides a check above and below fo.
3. Calculate the loaded Q at the center (resonant) frequency:
Qo = 2 * Pi* fo * L/R = 1/(2 * pi * fo * R * C)
4. Calculate the lower (fl) and upper (fu) half-power frequencies:
fl = 2 * Pi * fo/(2 * Qo) * [sqrt(1 + 4 * Qo^2) - 1]
fu = 2 * Pi * fo/(2 * Qo) * [sqrt(1 + 4 * Qo^2) + 1]
5. The 3-dB bandwidth is fu - fl. Note that fo = sqrt(fl * fu)
Remember that R represents the sum of the generator, antenna/matching
network ohmic loss resistance, and antenna radiation resistance. R
could also include cable loss (again assumed to be invariant with
frequency). Sincerely,
--
__ __ ______ __ John Wood
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Received on Tue Apr 02 2002 - 19:25:41 EST
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