Re: NEC-LIST: Fano criteria

Good day George, et. al.,

    The broadbanding efforts and the autotuners are trying to solve
two different problems, although at one time they were considered to
be two approaches to the same problem. The autotuner provides the
best match to a single desired frequency, which may change from time
to time, so that the tuner-antenna combination may be said to be
usable over some frequency range. The broadbanding efforts are trying
to get the same quality of match over a specified frequency range,
with a fixed network. If the signal bandwidth is narrow relative to
the possible carrier frequencies in the desired range, the autotuner
will always give the best performance, because it is optimizing over a
narrow (zero) bandwidth at any one time. If the signal bandwidth is
wide (as in spread spectrum) relative to the range of carrier
frequencies, the autotuner will not be adequate.

    Fano's theory (and Bode before him) says that for any complex load
impedance there is a tradeoff between bandwidth and gain. That is, if
you want flat gain over a specified bandwidth, the wider you make that
bandwidth the lower the level of flat gain you have to accept. There
are two tracks to arrive at a fixed metwork that gives the maximum
flat gain over specified bandwidth, the analytical and the numerical.

    The analytical track starts from Fano, was developed by
D. C. Youla and culminates in the works of Wai-Kai Chen, the
J. S. Bach of analytical impedance matching. To use this approach,
you must have a lumped-element load model for your antenna.

    The numerical track is subdivided into two different approaches.
one, pioneered by H. Carlin, finds the optimum resistance function
looking from the load back into the network. Once the resistance
function is found the network can be synthesized by classical methods.
The other approach exemplfied by T. Cuthbert, optimizeds element
values directly in a network structure you choose as a candidate. In
both cases, the load can be represented by measured or computed
impedance data, no model needed.

    I have done some work in this area, developing from Carlin's
approach. As an example, I was able to get nearly 4 MHz half-power
bandwidth centered at 15 MHz from a small (volume-loaded) dipole[1].
However, the transducer gain was -3 dB, or a little above, at all
frequencies in the band. If you wanted to handle a 25 % bw signal
with a small antenna, this would be a way to go. But if you only want
to deal with 10 kHz bw signals over the same range, the autotuner
would be the best choice.

Doug Miron

[1] D. B. Miron, "Some Simplifications for Numerical Impedance
Matching with a Small Antenna Example", Proceedings of RF Expo West
1995, published by Argus Business, Atlanta, GA, pp74-80.

P.S. Sorry I can't give references for the authors mentioned, most of
my stuff is still in storage.
Received on Tue Feb 15 2000 - 02:50:02 EST