August 1947 QST
Table
of Contents
These
articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list
of the QST articles I have already posted. All copyrights are 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 nobrainer. 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. 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 MatchedLine Coupling
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 difficulties.
The widespread use of 50 and 75ohm coaxial lines for feeding
amateurband antennas has introduced the amateur to some problems
that he was unprepared for through his experience with higherimpedance
tuned lines. The following discussion will cover only the coupling
of transmitters to a pure resistive load, such as is presented
by a properlymatched coaxial or parallelwire 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. 1  A load R is coupled to a tube through
circuits L_{p}C_{p} and L_{s}C_{s}.
R can be connected in parallel as shown, or in series.
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 Q_{p} and Q_{s} 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 k_{o} = 0.1 (a practical
value, remember) an antennacircuit Q of over 8 is required.
If the antennacircuit Q becomes too low, it will require a
higher value of k to reach k_{o}, and this may be a
physical impossibility. This is the condition generally described
as "it won't load up!"
Fig. 2  A parallel circuit, A, and a series
circuit, B. The series and parallel notations are derived from
the connection of the resistance.
The Q of the paralleltuned circuit in Fig. 2A 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. 2B, 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 75ohm line to feed a beam on 29 Mc., and the line is flat.
The 75ohm lines in Fig. 3 intersect the 29Mc. line at 740 μμfd.
for parallel tuning and at 7.4 μμfd. for series
tuning. Thus if one is to couple his 75ohm line to the final
tank he can connect the line as in Fig. 2A (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.
2B 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 300ohm loads, connected in series
or in parallel.
The curves of Fig. 3 are for an antennatank Q of 10, which
is the correct value for a plate tankcircuit Q of 12 and a
coupling factor of 0.09. Tighter coupling will allow the antennacircuit
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 LtoC ratio when coupling to flat lines.
To use the graph, find the intersection of the resistanceload
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" 75ohm coaxial line on 144 Mc. but the system
loads nicely when you put a 20μμfd. 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 300ohm 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 300ohm 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 coppertubing 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 LtoC ratio,
is generally necessary for coupling to lowimpedance lines.
When using a seriestuned 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 handcapacity effects are observed.
* Assistant Technical Editor, QST.
Posted January 25, 2016