September 1950 QST Article

## September 1950 QSTThese 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. |

Complete with all the nitty-gritty details and necessary formulas for designing an inductive loop coupler for a rotating antenna is this article by Mr. Robert Mumma. Such a device is useful when you desire a steerable antenna that prefers not to or cannot accommodate a section of coaxial cable interfacing the fixed mast to the rotating antenna. It is rare that such a requirement is found, since installing a set of limit switches to prevent the cable from wrapping itself around the mast is relatively simple to implement. However, if you want a system that continually rotates while searching for or broadcasting signals, then something like this is needed. A radar antenna is a prime example, as would a search and rescue operation using a directional antenna listening to distress calls be another. There is also a 'cool factor' that might cause you to build and install one.

A Coupling Method That Is Independent of the Matching System

By Robert E. Mumma, W8ORI

In the usual inductive coupling system for facilitating the rotation of beam antennas the output loop is part of the
driven element.^{1}

There are many times when it is not convenient to make the output loop a part of the antenna system - for instance, when
the" plumber's delight" type of beam is used. The coupling loop design to be described has been adapted so that the loops
can be inserted anywhere in a transmission line carrying r.f. power. It consists of a single-turn input or primary loop
and a single-turn output or secondary loop, shown as L_{p} and L_{s} in Fig. 1. Each loop is tuned with
a variable condenser. The transmission line from the transmitter is connected across the tuning condenser C_{p}
for the primary loop, and the transmission line to the antenna is connected across the tuning condenser C_{s} for
the secondary loop. In both cases a balanced type of transmission line is shown.

The design of this antenna coupling system is easily followed by means of an example. Suppose that the system is to be designed for your latest 20-meter three-element beam, which is tuned to 14.2 megacycles and is being fed with 300-ohm Twin-Lead. Experience has shown that a Q between 5 and 10 for the coupling loops will bring the dimensions within reason and make the tuning broad enough to cover the entire band. Since we must start with some number, let us assume that the Q is 5.

The equivalent circuit for each of the loops in Fig. 1 is shown in Fig. 2. L is the inductance of the loop, C is the capacitance of the tuning condenser, and R is the impedance of the transmission line, which is assumed to be a pure resistance.

(1)

When R is 300 ohms and Q is 5, X will be 60 ohms. The losses in the loop and in the condenser are assumed to be negligible
in comparison with the 300 ohms shunting the tuned circuit. With these loops tuned to resonance X_{L} and X_{C}
will both be 60 ohms. Then

(2)

and

(3)

Knowing the diameter of tubing available to make the loops, and the inductance desired, the diameter of the loops can
be determined from the nomogram^{2} shown in Fig. 3. If 1/4-inch diameter copper tubing is used, the diameter of
the loop will be found to be 11 inches.

In this case, 250-μμfd. variable condensers can be used to tune the loops. The voltage rating required will be determined by the impedance of the transmission line and the input power. With 500 watts of unmodulated r.f. power in a matched 300-ohm transmission line, the peak voltage across the condensers will be approximately 550 volts. The voltage across the condensers will rise to twice this value with 100 per cent modulation. Since the peak voltage may rise to several times this value during the tuning-up process, when standing waves appear on the transmission line, it will be well to make the initial tuning adjustments at reduced power.

The spacing between the loops for the maximum transfer of power can also be calculated, and the loops mounted permanently on stand-off insulators before the tuning operation. Letting k represent the coefficient of coupling for the maximum transfer of energy, it can be shown that

(4)

Q_{s} and Q_{p} are the Q's for the secondary and primary loops, respectively. Since the same type transmission
line is connected to both the primary and secondary loops and the loops themselves are the same, Q_{s} = Q_{p}.
Therefore

For the general case when any two inductances are coupled, let k represent the coefficient of coupling. Now

(5)

where M is the mutual inductance between the two loops, L_{p} is the inductance of the primary loop, and L_{s}
is the inductance of the secondary loop. Since the inductances of these two loops are equal, this equation reduces to

The spacing between the loops can be determined, in terms of the mutual inductance, from the following formula:^{2}

M = 1.27ND (6)

where M is the mutual inductance in micro-henrys, D is the diameter of the loops in inches, and N is a factor depending on the diameter of the loops and the spacing between the loops. Solving for N,

From Fig. 4 it will be noted that the value 0.00966 for N corresponds, with sufficient accuracy for these calculations,
to a ratio of 0.28 for r_{2}/r_{1}. The diagram in Fig. 4 is a vertical section through the two coupling
loops, with r_{2} being the vertical distance or spacing between the loops and r_{1} the diagonal distance
from one side of the lower loop to the opposite side of the upper loop. If Y is used to represent the ratio r_{2}/r_{1},
then

Using the value 0.28 that has just been determined for Y, and 11 inches for the diameter of the loops, D, the spacing
between the loops, r_{2}, can be found:

**Construction and Tuning **

All of the data are now available to make an efficient set of coupling loops for 20 meters, when using a 300-ohm transmission line. The copper tubing should be formed into as perfect a circle as possible, with the ends approximately one inch apart. The variable condensers should be connected to the open ends of each of the loops with as short leads as possible, because these leads are part of the inductance. The condensers should be mounted in weatherproof containers that will permit adjustment after the condensers are mounted. This can be accomplished by slotting the condenser shaft and leaving a hole large enough for a screwdriver opposite the end of the shaft. This hole can be covered with waterproof tape after each adjustment.

A simple weatherproof cover can be made by mounting the variable condenser on a screw cap that fits a glass jar large
enough to accommodate the condenser.^{3} The glass jar can be removed when adjusting the condenser, then replaced
and sealed with a rubber ring under the lid after the adjustments are completed. This type of weatherproof covering can
be mounted on the beam structure by fastening a bracket to the lid. Regardless of the type of covering used, all steel parts
should be painted to prevent rust.

The writer's installation, using metal cans to cover the condensers, is shown in one of the photographs. It will be noticed that a set of 10-meter coupling loops is mounted coaxially with the 20-meter loops. Because of the difference in frequency, these two sets of loops operate independently of each other.

Before installing the system in a transmission line, be sure that the antenna has first been matched to the line. The tuning procedure consists of tuning the secondary loop for maximum current in the transmission line to the antenna, and tuning the primary loop to eliminate standing waves on the transmission line back to the transmitter. If the spacing between the loops is correct, it will be possible to adjust the condensers so that the s.w.r. on the line to the transmitter is minimum at the same time that maximum current flows in the line to the antenna. This will not be possible if the loops are too close together or too far apart.

The current indicator for the transmission line to the antenna is shown at I in Fig. 1, and consists of a short length of transmission line with one end shorted and a dial lamp connected across the other end. The length of this coupling loop will depend on the current required for the lamp and the power delivered by the transmitter. The indicator can be fastened to the transmission line with short lengths of adhesive tape, and removed after the adjustments are made.

In tuning the primary loop for minimum standing waves on the transmission line, a twin-lamp indicator, shown as SW in Fig. 1, is probably the easiest to use. The only precaution that should be followed is to keep the twin-lamp at least three feet away from the coupling loops. Also, if the section of transmission line on which the twin-lamp is mounted is closer than 1/4 wave-length to the antenna, the line should be perpendicular to the antenna. The primary and secondary loops both may have to be tuned several times before the correct adjustment is achieved, since any great change in capacity required to tune one loop will affect the tuning of the other loop.

It might be well to point out that if the length of the driven element is not such as to be resonant at the operating frequency, it may not be possible to match the line to the antenna properly. When this is the case it may not be possible to tune the loops correctly, because of the reflected reactance.

The transmission line may be matched to the antenna using any of the standard methods. The delta match is too well known to require description here, but the author believes that better use of the "T" match could be made if it is considered as a folded dipole. It is doubtful if an impedance transformation greater than four to one can be obtained with a "T" match using the same diameter conductor as the radiator and spaced not more than four inches from it, regardless of how long it is made. More satisfactory results can be had by using a smaller conductor for the "T," and making it roughly 1/16 wavelength long. The match can then be achieved by adjusting the spacing between the "T" and the radiator. The "T" match for the radiator in my 20-meter three-element close-spaced beam is 10 feet long and uses tubing 3/16 inch in diameter.

The spacing is 4 1/4 inches (center to center) from the radiator, which is 1 1/8 inches in diameter.

Loops for other frequencies and other transmission-line impedances can be made by using these same equations. If a Q of 5 is used for calculating a set of loops for 10 meters the system will tune broadly enough to cover the entire 10-meter band without serious standing waves appearing on the transmission line, providing the antenna itself is flat over such a range. The higher the Q's of these loops, the more sharply they will tune, and also the farther apart they will have to be spaced to prevent overcoupling.

While the above calculations are based on the use of a balanced type of transmission line, it should not make any difference whether the center of the loop is at ground potential, as it is with a balanced transmission line, or whether one end of the loop is at ground potential, as it is with a coaxial line.

With low-impedance lines a Q of 2 or 3 should be tried, in order to keep the dimensions of the loops and the capacities of the condensers within reason. The lower Q will require closer spacing, as the calculations will show.

Also, it is possible that a certain amount of impedance matching can be done by connecting transmission lines of different characteristic impedance across the primary and secondary loops, respectively, and calculating the spacing between the loops on the basis of the resulting Q's. The difference in Q between the primary and secondary loops will be taken into consideration when using equation (4).

As a matter of interest, the calculated values for loops of 1/4-inch tubing to be used at various frequencies with various line impedances are listed in Table I.

**The W8ORI Dual Beam **

For those who may want the information, a sketch of the author's dual beam is given in Fig. 5. There are three elements on 20 meters and four elements on 10, with all elements in the same plane. In both beams the reflector is 0.15 wavelength from the driven element and the director is 0.1 wavelength from the driven element (actually, the spacing for the 20-meter reflector is a little short). The parasitic-element lengths were set by formula, while the driven elements were adjusted to obtain a flat transmission line. It will be noticed that the 20-meter driven element is approximately 12 inches longer, and the 10-meter driven element 6 inches longer, than the lengths given by the usual formula. This may result from the fact that the two driven elements are located so close to each other, although the tuning of one has no appreciable effect on the tuning of the other.

The 20-meter elements consist of a 12-foot section of aluminum tubing 1 1/8 inches in diameter with a 12-foot section of 1-inch aluminum tubing telescoped into each end. The 10-meter elements consist of a 12-foot section of brass tubing 5/8 inch in diameter with a 3-foot section of 1/2-inch brass tubing telescoped into each end.

The delta and "T" matching sections for the 10- and 20-meter beams, respectively, are made of 3/16-inch copper tubing and extend toward the rear of the antenna. In connection with the earlier remarks about "T" matching, it may be of interest to mention that in the first attempt at matching the 20-meter beam the "T" section was about 11 feet long and was spaced 3 inches (center to center) from the driven element. The twin-lamp showed that the match was poor, regardless of adjustments to the length of the "T'' section. The spacing was then changed and by experiment it was found that a center-to-center spacing of 4 1/4 inches gave a good match. The length of the "T'' was not at all critical, but the spacing was.

1 Taich, "Do It Inductively," Sept., 1947, QST; "Inductive Coupling to Rotary Beams," Technical Topics, March, 1948, QST.

2 From "Radio Engineer's Handbook" by F. E. Terman, 1943. Courtesy of McGraw-Hill Book Co.

3 This arrangement has been used by W8TDY.

Posted June 17, 2016