From Transmitter to Antenna
A collection of articles on electrical and radio theory
"From Transmitter to Antenna" was the original title for what started out as a set of documents intended
to explain how the process of antenna impedance matching can be treated as
a set of operations in the impedance plane or ' Z-plane'. Such a view
leads to the idea that the best way to track and monitor the impedance
matching process, particularly when the antenna is to be used over a wide
range of frequencies (i.e., the 1.6 - 30MHz HF spectrum), is to use a set
of bridges that can give null indications of the load impedance in
relation to unity power-factor and target values of resistance and
conductance. This three bridge R, G, φ system, first proposed by Underhill
and Lewis in 1973 [1
], has the virtue that it
gives an unambiguous and generally optimal solution to the problem of how
to adjust a given matching network, and provides directional information
in relation to the adjustment of the network reactances. The system is
therefore vastly superior to the conventional SWR monitoring approach used
in manual impedance matching; and, being free from ambiguity, is the basis
for the design of maximally dependable automatic matching systems.
An attempt to popularise the R, G, φ
approach was made by Nigel Williams,
, in about 1980. Nigel designed and produced prototypes for a
multi-function bridge, which he called the "M50
", but the associated commercial project never came to
fruition. Many years after the event, he discussed his ideas with me
(DWK), and subsequently passed over his notes and documents so that I
could work them into a publishable form. The subsequent review and
updating ot the material however proved not to be straightforward. The
bridges were inaccurate due to lack of compensation for
current-transformer non-idealities and needed to be improved; and it
seemed that the audience for a set of articles about operations in the
Z-plane would be limited to those with a good grasp of traditional
circuit-analysis techniques. Hence I set out to do two things: The first,
which turned out to be a significant undertaking in its own right, was to
develop the background material needed for a good understanding of the
subject. The second was to review the subject of bridge design, with a
view to discovering best practice so that the Match Meter could be
To say that reviewing the subject of
current-transformer bridge design proved not to be a simple matter would
be something of an understatement. Here we enter a world fraught by lack
of experimental data, naive theory, unchecked calculations and defective
simulation models. It turned out that Nigel's bridges were fairly good
after all, at least in an overall scheme where published (and some
commercial) designs can turn out to have amplitude errors of 70% and phase
errors of -720°. It is no wonder that people complain that they can't get
their antennas to work over a wide range of frequencies. With monitoring
equipment like that who could?
So I ended up doing a great deal of work on
the theory and practice of bridge design and was subsequently able to
identify all of the significant sources of error. The approach I used is
this: I noted that bridges can be evaluated by choosing two independent
(or nearly independent) adjustable parameters of the bridge itself and
treating their deviations from the design values vs. frequency as
perturbations for the purpose of finding the phase and amplitude tracking
performance. The current transformer itself can be treated as a
transmission-line device, and compensations for its imperfections deduced
accordingly. When the problem is correctly understood, and the bridge is
properly compensated, it is easy to achieve amplitude tracking better than
0.3% and phase accuracy better than 0.2° over the 1.6 MHz to 30 MHz
range [see Evaluation &
optimisation of current transformer bridges
]. Such accuracy is not
needed for the purpose of setting-up radio stations, but since obtaining
it requires no exotic test equipment or laborious procedure, there seems
little point in not having it.
So here is my attempt at teaching AC theory,
measurement technique, electrical materials science, inductance and capacitance; and at
explaining how those ideas can be used to make radio stations work.
DWK June 2007, Feb. 2014.
D W Knight 2003 - 2014. N Williams
1983 and 2005.
asserts the right to be recognised as the principal author of
this work and is the person to whom all enquiries should be directed.
Nigel Williams died in June 2012.
My close friend Andy Cowley (M1EBV), who died on 23rd
2012, spent a great deal of time reading and commenting on the developing
articles and provided considerable assistance in library work and the loan
of test equipment and reference materials.
] "Automatic Tuning of Antennae
". M J Underhill [G3LHZ] and P A Lewis.
SERT Journal, Vol 8, Sept 1974, p183-184. Reprint of paper in Mullard
Research Labs Annual Review, 1973.