A 40-Meter Star

L. B. Cebik, W4RNL

The horizontally oriented 1-wavelength square loop is a fairly standard low-HF amateur antenna. It lends itself to use with parallel feedline for multi-band application. However, a 1-wavelength loop tends to radiate broadside to the loop. Therefore, the antenna tends to provide better performance on bands above the lowest.

The Standard Square and the 4-Pointed Star Loops

The need for a longer circumference is often at odds with amateurs who have only limited space for wire antennas on the lower HF bands. However, one way to increase the circumference of a loop without increasing its footprint is to draw in the 4 sides of the loop toward the center. The result is a 4-pointed star configuration. Fig. 1 shows the difference between the standard and star loops, as viewed from above (or below, as the case may be).

Fig. 1 also provides us with a key to the main dimensions of the loop and the star. The length of a side for a square horizontally oriented loop is also the length of one side of its footprint. For the 40-meter (7.15 MHz) test case, each side of the loop is about 36.2' long for a near resonant loop. This provides an antenna and a footprint circumference of 144.8' or about 1.05 wavelengths at 7.15 MHz for a near-resonant loop. On the right side of Fig. 1 is the star. Here, we must distinguish between the wire length and the footprint. For a near resonant loop, we require a footprint side dimension of about 31.9', which results in a footprint circumference of 127.6'. This dimension set is actually smaller than for the square loop. However, as shown in the sketch, each wire is stretched inward toward the center. We cannot make the wire touch at the center, but we can come in rather close. The most radically inset case that I have so far explored positions the apex of each angle formed from the side wires at 1.75' from the antenna center. This yields a distance of about 3.5' between opposing points. The resulting wire length for each side of each point in the star is about 21.35'. The total wire circumference thus becomes about 170.8' or close to 1.25 wavelengths.

We can compare the potential performance of the two configurations on 40 meters via the following table of modeled results.

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
              Square and Star Loop Performance at 7.15 MHz

Antenna Height 50'.  Antenna Wire AWG #12 copper.  "Insets" refers to the
distance of the limit of the star side inset point from the exact center
of the array.

                      Gain       El. Angle        Feed Z
                      dBi        Degrees          R +/-jX Ohms
Square                5.54       47               157.5 - j 6.3
Star: 1.75' insets    5.50       39                65.7 + j 9.0
Star: 2.0' insets     5.50       39                66.8 + j12.0
Star: 3.0' insets     5.50       40                71.1 - j 0.6
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Several aspects of the tabular data are significant. First, the 40-meter gain of the two versions of the loop is virtually the same. However, the elevation angle of maximum radiation is considerably lower in the star version. Fig. 2 graphically illustrates these matters by showing the two azimuth patterns, each at is respective TO angle, to exactly overlay each other. However, the elevation pattern of the star along the axis of maximum radiation has a noticeably lower angle of maximum radiation (take-off or TO angle).

Second, if operation is contemplated only on 40 meters, then the impedance of the star configuration is suitable for a coaxial cable as the feedline Either 50-Ohm or 75-Ohm cable will do. For similar operation, the square configuration would require either the use of a parallel feedline or the use of a 4:1 balun with a 50-Ohm coaxial cable feedline.

Third, the star configuration is not especially sensitive to just how far toward the array center we push the insets. The distances from center shown may be doubled to see how far apart we may place the inner points of the star. There is considerable room for variation before we lose our advantage over the square loop in terms of TO angle. However, note that the 3.0' inset has bumped the TO angle upward one notch. As we further move the inner start points away from center, the antenna slowly returns to the characteristics of a simple square loop.

The principle behind the star is an attempt to increase its wire circumference length without increasing its footprint. The 0.2- wavelength increase, while not giving us the almost pure edge-wise radiation of a 2-wavelength loop, does raise the entire wire length in the star loop to 1.25 wavelengths. That much length is sufficient to lower the 40-meter radiation angle by a noticeable amount.

The Square Loop as a Multi-Band Wire Antenna

The square loop allows us to feed the antenna on higher bands, relative to the base-line 40-meter band to which we have cut it. We can summarize the performance with the following tabulated samples for the HF bands.
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
                    40-Meter Square Loop Performance

Antenna Height:  50'.  Antenna Wire AWG #12 copper.

Freq.      Gain       TO angle   Feed Z           Pattern Shape
MHz        dBi        Degrees    R+/-jX Ohms
7.15       5.5        47          160 - j    6    Oval
10.125     4.8        32         3060 + j 3140*   Almost square
14.1       8.5        19          275 + j  120    4-leaf clover
18.1       7.2        16         1035 + j 1480*   wobbly oval
21.1       8.7        13          255 + j   55    4 main lobes, 60
                                                  degrees off axis
24.95      8.0        11         1230 - j 1380*   6 near-equal lobes
28.1       10.8       10          265 + j  115    4 lobes 45 degrees
                                                  off axis
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

With exceptions, the patterns generally are strongest in a line through the feedpoint and the corresponding center point of the wire opposite. We may call this the main axis of the antenna. On two bands of high interest, however, the patterns depart from the noted tendency.

Fig. 3 shows the azimuth patterns of the square loop on 15 and 10 meters, with the axis presumed to run vertically on the page. The 15-meter pattern forms a sort of butterfly, with small lobes along the antenna axis. However, the strongest lobes are angled to the sides by about 60 degrees. The 10-meter pattern has only 4 notable lobes, each about 45 degrees off axis.

We may also note in passing the starred entries in the feedpoint impedance (Feed Z) column. Each of the non-harmonic bands presents an impedance where the resistance and the reactive components are both above 1000 Ohms. Without careful attention to the characteristic impedance and length of the parallel feedline used, the impedance at the antenna tuner terminals may fall outside the range of values that it can match.

The 4-Pointed Star Loop as a Multi-Band Antenna

We may perform the same modeling experiment with the 4-pointed star loop to evaluate its potential as a multi-band antenna for 40-10 meters. The results appear in the following table.
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
                     40-Meter Star Loop Performance

Antenna Height:  50'.  Antenna Wire AWG #12 copper.

Freq.      Gain       TO angle   Feed Z           Pattern Shape
MHz        dBi        Degrees    R+/-jX Ohms
7.15       5.5        39           65 + j   10    Oval
10.125     6.7        26         6820 - j 7650*   Diamond
14.1       9.3        19          540 + j 1850*   4-leaf clover
18.1       6.9        16          925 + j   75    Broad beam:  F-B 5.2 dB
21.1       6.2        13          945 - j 1270*   Broad beam:  F-B 1.3 dB
24.95      6.8        11           55 + j  340    Broad beam:  F-B 2.5 dB
28.1       6.9        10          715 - j  670    Triple forward lobes
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

For the entries called "Broad beam," the direction of maximum gain is toward the side of the star containing the feedpoints. If we overlay the outline of the antenna on top of the azimuth patterns in Fig. 4, the feedpoint will be above the plot center line across the page.

The patterns show one potential advantage of the star as a multi-band antenna. On all bands, there is a main lobe along the antenna axis through the feedpoint. Hence, the user is always aware of the direction of strongest signal. (30 meters is the one exception, but the main lobe to the reverse of the feedpoint side is only 0.7 dB stronger than on the feedpoint side, a difference that will not be detectable in operation.) Although the beam action--that is, having a small front-to-back ratio--is small, the reliability of having the main lobe along the same axis on every band used is a distinct plus.

There are three bands on which the reactance rises above 1000 Ohms. However, only on 30 meters are the values for both resistance and reactance so high as to create a very distinct problem for matching the feedline termination to the transceiver 50-Ohm system.

Why?

The distinctness of the square loop and the star loop patterns should arouse some curiosity as to the reason for the differences. Fig 5 provides a partial answer.

The upper diagrams compare the relative current magnitude distribution of the two loops on 40 meters. The current on the star remains higher further outward toward the array corners than on the square loop, and this phenomenon plays a role in lowering the elevation angle of maximum radiation (the take-off or TO angle). Otherwise, the gain and pattern shape of the 2 versions of the loop are the same.

The 15-meter case is especially interesting. For the star loop, the current magnitude peaks and valleys appear in close proximity along the outward star-point wires. Hence, the currents (or, more properly, the fields that result) tend to simply add to or subtract from each other-- with due place given to the phase of each current magnitude sampled. However, in the square loop, we have current magnitude peaks more linearly separated from each other, with distinct peaks at the four corners of the array. The result is the 6-lobes pattern, with the largest lobes at a considerable angle from the axis of the antenna.

These brief notes suggest that for some users of square loops, modification to a star design may be useful. The array dimensions for 40 meters will easily scale to 80 and 160 meters, although most users will have difficulty in scaling the height as well as the wire length. Since we are only approximating resonance on the lowest band of use and presuming parallel feedline to an antenna tuner, fussiness with dimensions seems out of place. Since the wire of the antenna has a small diameter relative to a wave length, any 50-Ohm resonance on the lowest band of use is likely to be a very narrow-band phenomenon.

Nonetheless, for the loop-user who wishes a lower TO angle on the lowest band of use and a pattern that has a maximum along the axis of the antenna on every band used, the 4-point star is viable alternative to the standard square loop. The cost is less than 20% more wire, which is likely to be the cheapest part of the antenna anyway. The star loop is not an answer to every loop problem. However, it does show that it pays to explore different wire geometries to see whether they have any potential for use.



Updated 04-13-2003. � L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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