August 1947 QST
Wax nostalgic about and learn from the history of early electronics. See articles
QST, published December 1915 - present (visit ARRL
for info). All copyrights hereby acknowledged.
An ample supply of surplus coaxial cable
after the end of World War II provided an inexpensive and easy to use form
of transmission line. Not having to worry about cable routing and unintentional
radiation makes transitions through walls, running along metal surfaces, and routing
high power transmission lines near habitable areas a no-brainer. Issues like power
handling, bend radius, and higher attenuation need more attention during the installation
design phase, but that pales in comparison to coaxial cable's advantages. In this
1947 issue of the ARRL's QST magazine,
author Byron Goodman addresses some of the issues Hams accustomed to using flat
transmission lines (conductor pairs separated by an insulator).
Coupling to Flat Lines - Circuit Considerations for Matched-Line
Fig. 1 - A load R is coupled to a tube through circuits
LpCp and LsCs. R can be connected in
parallel as shown, or in series.
By Byron Goodman,* W1DX
Here is a story full of useful information for the operator who has been having
trouble coupling to a "flat" line. It explains why some lines to require very tight
coupling and why some don't, and it tells how to insure that you will have no coupling
The widespread use of 50- and 75-ohm coaxial lines for feeding amateur-band antennas
has introduced the amateur to some problems that he was unprepared for through his
experience with higher-impedance tuned lines. The following discussion will cover
only the coupling of transmitters to a pure resistive load, such as is presented
by a properly-matched coaxial or parallel-wire transmission line. It must be remembered
that whether or not the line is matched - and hence presents a resistive load at
the transmitter end - is dependent entirely upon the load at the antenna end, and
no amount of adjustment at the transmitter end will correct for an unmatched condition.
The condition of match at the antenna end results in no standing waves on the line,
and the line is called a "flat" or untuned line. It is perfectly possible to put
power into a line that isn't "flat," as is done with any tuned line, but there seem
to be some misconceptions about coupling into untuned lines.
In the past, many amateurs have acquired a "flat" line and then blithely connected
the transmitter end of the line to a few turns jammed into the transmitter tank
coil. Sometimes it "loaded" and more often it didn't. The poor results were usually
blamed on the flat line, but so were the good results, and it may be difficult to
reconcile the different results. A little discussion of coupled circuits may clear
up some of the questions.
Fig. 2 - A parallel circuit, A, and a series circuit, B.
The series and parallel notations are derived from the connection of the resistance.
Normally we couple two resonant circuits, as in Fig. 1, at the value of
coupling called "optimum," which is the amount of coupling obtained just before
the tuning starts to broaden out and interlock. The coupling is a factor depending
on the mechanical relation of the coils in the two circuits under consideration,
and approaches a maximum value of 1. In practice, however, a value of 0.1 is readily
obtainable and anything above about 0.3 becomes difficult with adjacent coils. With
overwound or interwound coils, values up to 0.7 can be obtained. The value of optimum
coupling is given by the relation
where Qp and Qs are the primary- and secondary- circuit
Qs, respectively. Since we normally design our plate tank circuits with a Q of about
12 (see ARRL Handbook), Equation 1 above shows that, for ko = 0.1 (a
practical value, remember) an antenna-circuit Q of over 8 is required. If the antenna-circuit
Q becomes too low, it will require a higher value of k to reach ko, and
this may be a physical impossibility. This is the condition generally described
as "it won't load up!"
The Q of the parallel-tuned circuit in Fig. 2-A at resonance is given by
Q = 2πfCR
where R is the resistance in parallel with the tuned circuit.
When the resistance R is in series with the tuned circuit, as in Fig. 2-B,
the equation becomes
If a value of Q = 10 is assumed, and values of C calculated from Equations 2
and 3 for various frequencies and values of resistances, a family of curves is obtained
as in Fig. 3. Inspection of these curves will show the best way to couple one's
flat line to the transmitter. Suppose, for example, one is using a 75-ohm line to
feed a beam on 29 Mc., and the line is flat. The 75-ohm lines in Fig. 3 intersect
the 29-Mc. line at 740 μμfd. for parallel tuning and at 7.4 μμfd.
for series tuning. Thus if one is to couple his 75-ohm line to the final tank he
can connect the line as in Fig. 2-A (the resistance R represents the line)
and use a capacity of 740 μμfd. and the small coil necessary to resonate at
29 Mc. (a very small coil, in this case!), or he can use the series circuit of Fig.
2-B and a capacity of 7.4 μμfd., with the correspondingly larger coil required
to resonate to 29 Mc. with 7.4 μμfd.
Fig. 3 - The capacity necessary for a tank Q of 10 with
50-, 75- or 300-ohm loads, connected in series or in parallel.
The curves of Fig. 3 are for an antenna-tank Q of 10, which is the correct
value for a plate tank-circuit Q of 12 and a coupling factor of 0.09. Tighter coupling
will allow the antenna-circuit Q to be reduced, and less C will be required for
the parallel circuit and more for the series circuit. An antenna - it should be
"line" - that "won't load" is the result of not having adequate Q in the antenna
coupling circuit, and the curves of Fig. 3 can be used as a starting point
for determining the proper circuit and the approximate L-to-C ratio when coupling
to flat lines. To use the graph, find the intersection of the resistance-load line
with the operating frequency for both series and parallel tuning. This will give
two values of capacity. Select the more reasonable value of capacity of the two,
and build a coil that will resonate with this capacity to the operating frequency.
Then connect them to the line and you will have no trouble "loading" the transmitter.
If the condenser for series tuning is selected, then the antenna line must be connected
in series, of course.
A glance at Fig. 3 will also show that if you are using, for example, a
"flat" 75-ohm coaxial line on 144 Mc. but the system loads nicely when you put a
20-μμfd. tuning condenser across the antenna coil, you don't have a flat line!
If the line were flat, about 150 μμfd. would be required for parallel tuning,
and your results would indicate that your line is presenting a much higher load
than 75 ohms to the antenna coupling circuit or that the coupling factor is high.
The chart also shows that at 50 Mc. a 300-ohm line requires about 1.0 μμfd.
for series tuning or 100 μμfd. for parallel tuning. Since the normal reaction
is not to use a coil large enough to resonate to 50 Mc. with 1 μμfd. for series
tuning, or to use as much as 100 μμfd. for parallel tuning, it is easy to
see why 300-ohm lines "won't take the soup" at 50 Mc., and one usually ends up by
jamming a large coupling coil in the final amplifier tank when this type of line
is used. A small copper-tubing coil of 1 or 2 turns and a larger condenser for parallel
tuning would make the line "load" as it should.
It is hoped that, with the aid of the chart, more amateurs will realize that
series tuning, with the proper L-to-C ratio, is generally necessary for coupling
to low-impedance lines. When using a series-tuned circuit with coaxial line, it
is advisable to connect the rotor of the condenser to the outer conductor of the
coaxial line. This junction can then be grounded, if any hand-capacity effects are
* Assistant Technical Editor, QST.
Posted June 16, 2022
(updated from original post on