40 Meter Wire Inverted Vee Reversible Moxon

My 40 meter rotatable reversible Moxon project is progressing well. However, it is not an antenna that most hams could contemplate building and raising. Recently a friend decided to build a fixed direction version of the antenna with inverted vee wire elements. It can be a good choice since it's lightweight and the two most important directions for contesting in this part of the world are northeast (Europe) and southwest (US). I therefore thought it worthwhile to spend some time evaluating its performance, in at least one configuration.

Years ago, I worked through the performance and construction of a variety of 40 meter wire yagis. This is an opportunity to add one more design concept to that old pile. I've avoided modelling this antenna in the past because the 90° corners are not accurately modelled with NEC2. It's close but it would require adjusting wire lengths after construction. NEC5 does better, and I will be using it throughout this article. It integrates very well with EZNEC.

Before we start, it may be helpful to mention general points about 2-element yagis with a reflector. These include wire yagis, Moxon rectangles and rotatable aluminum yagis, with loaded or full size elements.

• Maximum gain occurs below the lowest frequency within which the SWR and F/B are optimum. For most 40 meter antenna designs intended for CW use, the target frequency for maximum gain is typically between 6.950 and 6.975 MHz.
• Gain bandwidth is narrow. Although the maximum gain looks good -- typically around 7 dbi in free space -- gain in excess of, say, 6 dbi is typically less than 100 kHz on 40 meters. It is a pet peeve of mine that this is rarely mentioned when compared to yagis with 3 or more elements.
  
• Gain is reduced when the elements are not straight and parallel λ/2 lengths. This applies to Moxons, yagis with loaded elements (coils, capacitance hats, etc.) and elements with any bends. It is equally true of the antenna presented in this article.
  
• Inverted vees have a higher angle of radiation and greater ground loss than dipoles with the same peak height, including when they are incorporated into yagis. 
• 2-element yagis "see" the ground more strongly than yagis with more elements at the same height because there is more radiation directed up and down. A height of 20 meters for all parts of a 2-element 40 meter antenna reduces ground interaction to near negligible, but elements that bend downward, closer to ground, such as inverted vee elements, affect antenna performance.
  
• Copper wire elements have more loss than aluminum tubing. Depending on the antenna design, wire yagis have 0.2 to 0.3 db less gain due to resistance loss. The loss is higher at frequencies near maximum gain where the radiation resistance is especially low. For 2-element yagis with a reflector (including Moxons) that is at the bottom of the frequency range.
  
• Tuning of wire yagis is sensitive to wire gauge, material, insulation, proximity to obstructions and metal used for utilities and house infrastructure, and height of the element ends.

To simplify the design process I will begin with an ordinary Moxon rectangle in free space. It will be symmetric. which is necessary to reverse it and preserve performance. There is an implied switching system at each element centre, which will be described further below. Once that antenna model works as intended, the elements will be rotated to form inverted vees, and the required adjustments made. Only then will ground be added to the model. Proceeding in steps may take longer but typically leads to more predictable and better results.

Modelling the antenna with inverted vee elements and ground from the start complicates the process. Scaling elements that are not parallel to the X, Y or Z axis can make it difficult to maintain desired angles, lengths and see the impact of ground. Doing it is stages really takes no longer and we get to see the impact of bending the elements and the ground on performance. For a similar 40 meter wire "diamond" yagi, I wrote a spreadsheet to simplify the process. Here I'll do it differently, as will be described below.

The model at this point has the following parameters, which are in range of what is typical for Moxon rectangles:

• Boom length: 5.6 meters (0.13λ at 7.1 MHz)
• 12 AWG (2 mm) bare copper wire
• Element length: 15.04 meters
• Each right angle leg: 2.65 meters
• Gap between element ends: 30 cm
• Reflector element coil inductance: 1.25 μH
• Gain at 7.0 MHz: 6.33 dbi (free space), which falls to 4.6 dbi at 7.3 MHz
• F/B: 10.5 db at 7.0 MHz; 30 db at 7.1 MHz; 20 db at 7.2 MHz and 9.5 db at 7.3 MHz
  

The SWR is pretty good, but it could be better. I did a little optimization -- coil, boom length and element tip gap -- and I was able to lower the SWR slightly, at the expense of 0.1 db of gain. However, these changes are negligible and we can expect greater effects once the elements are folded into vees. The exercise was interesting but arguably inconsequential. Note that I calculated the SWR down to 6.95 MHz to highlight the impact of a low radiation resistance where gain is maximum.

Overall, the measured performance is about what one can expect from a wire Moxon. Making it symmetric and reversible has little impact. That's good.

I split the elements at the centre to make it easy to fold them into a vee shape. It is not my intent to try every possible interior angle, settling on 120° as the most common choice and one with typically good performance. Angles of 90° and less are strongly discouraged for any inverted vee or yagi made from them since the fields between element legs increasingly cancel. The interior angle will be less than you expect due to wire sag, so keep that in mind when you lay out the antenna on your property.

The lower radiation resistance reduces gain and can make matching to 50 Ω more difficult. This is a Moxon so we don't want a matching network at all!

The first change was to rotate the elements by 30°. There are significant differences. First, the SWR curve improved slightly. However, as expected, the operating range shifted upward by about 50 kHz. Also expected, the gain and F/B declined. At the bottom of its range, which shifted upward to 7.05 MHz, gain fell to 6.05 dbi, a reduction of about 0.3 db. F/B bandwidth remains wide, typical for a Moxon, but it never gets as good as for the rectangle. (You can scroll down if you want to see the performance comparison in a chart.)

A slight gain improvement of 0.05 db was achieved by decreasing the coil inductance to 1.2 μH, at the expense of a slightly worse SWR. Increasing the coil to 1.3 μH did the opposite, decreasing gain by 0.05 db and improving the minimum SWR to almost 1.0. Leaving it at 1.25 μH seems to be a good compromise. That said, environmental interactions will likely have a greater impact than small adjustments such as this.

Scaling a Moxon rectangle is not trivial. Each dimension has a unique role, and those roles must be respected when the scaling is performed. Yes, you could simply scale every dimension but the results might not be what you expect. Consider these points:

• The gap between element ends is critical to the Moxon rectangle's unique performance. I try to keep this dimension constant once I've decided on the geometry for a particular frequency. Small changes are okay but there can be surprises.
  
• Radiation is from the long parallel sides of the rectangle. Longer is therefore better. The fields of the symmetric and opposite inward legs largely cancel. Proper scaling requires that the ratio of their lengths is kept constant, but doing so requires changes to the boom length, element tip gap or both. Again, small changes usually have small consequences.
• The wire gauge also must be scaled for an accurate result. However, for small changes the effect of wire diameter is negligible and can be ignored.
  

For this design I kept the gap of the Moxon rectangle (gray) constant (green circle): 30 cm. Note that the scaling options have been exaggerated in the diagram. All show an increase in the size (lower frequency), but the opposite scaling should be obvious. Since this antenna is a reversible Moxon with symmetric (identical) elements, one scaling calculation applies to both elements.

In option A (red) the boom length changes but not the rectangle's long sides. In option B (blue) all dimensions are scaled equally. Both change the basic geometry of the rectangle, which can be detrimental when referenced to a fixed frequency. My preferred option is C (orange) since the boom length and inward legs are kept constant. 

All that said, it is reasonable to argue that this is much ado about nothing since the scaling factor in this case is small and therefore so is the potential performance impact. In practice the scaling option is more likely to be driven by construction and environment constraints, and that's perfectly fine.

You could bend the long sides inward as I did for the 2-element diamond vee yagi that I referenced earlier but that, too, alters performance, and not for the better. It is an option that may be appealing when the dimensions must be adjusted once the antenna is in place. The boom length may be more difficult to change.

Shifting the antenna's frequency range downward by 50 kHz requires lengthening the element by approximately 0.8%. The length was therefore added to the long sides. Adding 1% is even better since we are not changing the lengths of the inward legs; that is, the wire length changes are made in the long sides. 

The long side half-elements were increased from 7.52 to 7.59 m. A small increase of the reflector coil inductance to 1.3 μH slightly improved the free space SWR and put the frequency range where I wanted it, and equal to that of the horizontal (conventional) wire Moxon.

Gain and F/B of the inverted vee Moxon are lower. The gain reduction was expected but I was unsure how the F/B would be affected. The SWR bandwidth is roughly equivalent, which is one of the main attractions of the Moxon rectangle.

The reason for the gain reduction in free space is dominated by field cancellation due to the bending of the elements. That is expected behaviour for inverted vees. There is a small but negligible increase of wire loss. I did not delve deeper into the calculation to determine why the F/B declined. It has approximately the same shape across 40 meters but with lower numbers.

The differences are not huge. Gain of the inverted vee wire Moxon increases towards the top of the band but is otherwise within 0.5 db of the horizontal wire version. F/B is even closer except for 100 kHz mid-band where the horizontal wire Moxon excels.

Out of interest, I added figures for the rotatable reversible Moxon that I am currently building (T-hat in the charts). Its gain compares favourably while the F/B is little better than the wire inverted vee Moxon. This is despite the negligible wire loss of aluminum tubes. Performance of the rotatable reversible Moxon is also somewhat reduced by the large T-shaped capacitance hats that keeps the elements short in comparison to the copper wire Moxon antennas modelled here. 

The SWR curves for all 3 antennas are close enough that I did not bother to plot them.

Those performance figures are for free space. When placed above real ground, the impact will be about the same for the rotatable Moxon and the horizontal wire Moxon. However, that is not the case for the one with wire inverted vees. 

The elevation plot compares the wire reversible Moxons at a height of 20 meters (λ/2), which is a good height for a 40 meter yagi. They are more similar than might be expected from the free space figures. Ground in these models is EZNEC medium ground.

Expect the relative performance of the inverted vee Moxon to decrease at lower heights and to approach that of the horizontal rectangle at greater heights as the influence of ground increases or decreases, respectively.

Let's move on to several construction details. These are suggestions rather than rules so feel free to improvise. First up is the boom. 

If the antenna is mounted on a tower, the approximately 5.6 meter long boom could cause problematic interaction with other antennas on the tower. A non-conductive boom is preferable but difficult to make strong enough, even with a rope truss. A stiff fibreglass joint between aluminum tubes will halve the conductor sizes and greatly reduce interactions with all but 6 meter antennas. Alternatively (as one friend of mine has done), use a short aluminum boom with ABS tips (or other non-conductive materials.

The second item is tying down the ends of the inverted vee elements. Although the antenna is mechanically complex compared to a conventional wire yagi, there is at least one method that is quite simple. A rope connects insulators at the element tips. The outward tension of tie-down ropes from the rectangle corners stabilizes the geometry and is as strong as the ground anchors. Trees or other convenient supports can be used to keep the ropes out of harm's way.

Finally, there is the switching system. A total of 3 DPDT relays are required, one on the boom and one at each element. SPDT relays cannot be used since both conductors of each coax section must be switched. The boom relay switches the 50 Ω feed line to what is the driven element for the selected direction. The default direction for the Moxon should be the one that is used the most. The lengths of the coax to the elements are not critical and do not need to be equal. The element relays select a series coil (to make the element a reflector) or the 50 Ω coax to the boom relay. 

Coil Q is not critical since its inductance is small. Even so use a coil design program such as K6STI's Coil to ensure a Q of at least 300. That's a reasonable design objective. For example, a coil that is 1.5" long, 1.5" diameter, 7 turns and 10 AWG copper wire, with 1" leads, has an inductance of 1.3 μH and a Q over 400. It should be enclosed to prevent rain and ice from affecting its characteristics.

In the default direction all relays are idle, using the NC (normally closed) positions. When the antenna is reversed, all the relays are energized so that the NO (normally open) positions are used. The control cable may be able to use the common ground (coax shield and/or tower), depending on how your station is wired. It can be dispensed with entirely using a bias-T circuit. Be sure to use relays adequate to the power level in use and never hot switch the relays.

A common mode choke can be integrated in the enclosure for the boom relay, or you can place one at each feed point on the short connecting coax runs to each element. The former should work well since the less than 3 meters of connecting coax is likely to have a high common mode impedance at 7 MHz.

I hope that this article has given you a few ideas to consider should you want a reasonably simple antenna with gain for 40 meters. As I mentioned at the beginning of the article, a friend of mine is building this antenna and I am curious to learn how well it works. The boom and switching system are installed but he might have difficulty fitting the wires within the property lines.