Tuesday, January 31, 2017

40 Meters 3-element Wide-band Wire Yagi

As I look forward to having a tall tower later this year I am talking to others while reviewing my objectives to make a final determination on what antennas to focus on first. This brought me back to 40 meters and wire yagis. I wrote several articles on this topic in 2015 and these remain among the most popular according to web site statistics and referrals from other sites.

This popularity is not too surprising to me since 40 meters is the first band for which an antenna with gain requires more effort than buying a small bundle of aluminum and tossing it up on a tower or roof. Whether you contest, DX and just want a reliable band for rag chewing through the downside of this solar cycle 40 meter antennas with gain are an asset.

Where I am and where I'm going

The XM240 currently up 21 meters atop the free-standing tower is adequate for short paths, including Europe and the US. The bandwidth is poor with respect to gain, F/B and match. Regarding the latter two the deficiency is readily apparent. Gain is not easy to assess without the ability to A-B test against another antenna of know characteristics. Nevertheless this is a perfectly fine antenna, even with its limitations, and I am happy with it.

A full size 3-element rotatable yagi up 43 meters, should the plan come to fruition, will do wonders for longer path DX and contesting, especially to snag rare multipliers and grab those rare and distant DXpeditions. For the high volume contest paths to the US and Europe it will help very little since those are well addressed by an antenna at half that height due to the typically higher radiation angle associated with those paths.

My tentative plan was to move the XM240 to the guyed tower when the tower is finally raised later this year, side mount it at a height of around 25 meters and make it fully rotatable (300°). However this introduces a problem. The US and Europe are in roughly opposite directions and the paths are frequently open at the same time. Rotation is impractical for switching between working those two paths during a contest.

This brought me back to the idea of a fixed, reversible yagi pointing northeast and southwest. If made of wire it can be built at low cost and would provide excellent diversity for contest and everyday operating. One disadvantage of that antenna is its narrow SWR bandwidth, although better than a short 2-element yagi like the XM240. If I were only interested in CW and digital modes that would be no problem. SSB coverage without matching and switching complications is desirable for contests.

The time had come to do some modelling.

Improving the 3-element wire yagi: coupled resonator

I will take the reversible 3-element yagi with inverted vee wire elements and try to improve it to meet my current needs. This is what I want to accomplish:
  • Keep the gain as high as possible, especially in the CW band segment
  • Low SWR across the band -- 7.0 to 7.3 MHz -- without switching or tuning
  • Instant switching between directions
  • Similar performance -- gain, F/B, match -- in both directions
This is a tall order. Per my earlier models on rotatable 40 meter yagis there are really only three methods of extending bandwidth:
  • Switched matching network, which adds complexity and operating inconvenience
  • Parasitically coupled resonator or a dual-driven element, both which add a fourth element
  • Spreading the resonance of the reflector and director, which lowers gain
I chose to go with the simplest solution: the parasitically coupled resonator. This is a popular technique for achieving a wideband 50 Ω match on multi-element HF yagis, such as the OWA series of designs by WA3FET. I previously used on to achieve a full band match on a 3-element yagi.

There is a substantial cost for the additional element -- money, wind load, weight -- on a 40 meter rotatable yagi, a cost that is almost entirely avoided with a fixed wire yagi. It was worth a shot. Let's review how I did.

Modelling procedure

To begin I used the exact dimensions of the director and reflector from earlier 3-element design. Recall that it is these elements, not the driven element, that determines gain and F/B and SWR bandwidth in a 3-element yagi. Eventually some change became necessary, which I will come to shortly.

The driven element and coupled resonator were initially separated by 1 meter per my modelling results from the full size yagi design with a coupled resonator. That antenna covered the entire 300 kHz of the 40 meter band with impressively low SWR. Rather than borrow one of WA3FET's designs I based mine on seeing them and combining that with what I know of yagis. I must have done something right!

I placed these two elements -- which together comprise the driven element system -- symmetrically around the centre of the boom to best preserve equal performance in the forward and reverse directions. True symmetry is however only possible if the driven element and coupled resonator are reversed along with the director and reflector, and I chose not to do this to keep the design relatively uncomplicated. There is therefore some asymmetry in performance.

Modelling a coupled resonator requires some care since it is only a short distance from the driven element with respected to wavelength: 1 meter = 0.024λ. Segment lengths in both elements must be made as equal as possible, even as the lengths are adjusted during modelling, or there will be significant errors. A short 1 segment centre 10 cm long wire is inserted in all elements to minimize NEC2 inaccuracy due to the angle between element legs and to facilitate insertion of source and loads.

When I started modelling this antenna I expected that it would be more difficult to achieve a broadband match as easily as with the full-size yagi. This is indeed what occurred. The reasons include:
  • Thinner conductors make for inherently higher Q antennas
  • Bending dipole elements into a vee lowers the radiation resistance, both increasing loss and constraining the current range in the driven element and couple resonator, which in turn affects the feed point impedance
Without a firm theoretical knowledge of what should happen I ran a series of modelling experiments to see how far I could push and prod the antenna towards my performance objectives. I used the current and net reactance to adjust each subsequent run. Ultimately I had a reasonable design with a great SWR and acceptable gain and F/B.

As it turned out that model was wrong. Checking the antenna with the average gain test in EZNEC I discovered that I needed to double the number of segments to coax NEC2 to generate more realistic results. The final model has about 40 segments per half leg, with some variation to equalize segment lengths in all elements.

The net gain is reduced by approximately -0.3 db due to copper conductor loss (AWG 12). The driven element and coupled resonator separation finally settled at 1 meter, exactly where I started. As far as I could discover this distance, while not overly critical, seemed to give the best results. Unfortunately this turned out to be large enough to make performance asymmetrical between forward and reverse directions.

Achieving nearly full band matching with an SWR below 2 required spreading the tuning of the director and reflector. To do this the director was shortened a small amount and the inductor load on the reflector was increased. The reduction in gain of about -0.2 to -0.3 db was, in my judgment, a good trade off. See the above EZNEC SWR chart of the yagi in the forward direction.

However performance is worse in the reverse direction so if you build this antenna you would have to pick your favourite direction and orient your driven element and coupled resonator accordingly. SWR bandwidth is reduced by ~30 to 50 kHz. A static or switchable L-network can help to improve the match, in both directions. I experimented with this but I am not prepared to make a firm recommendation on which is best. There is enough doubt in the quality of the modelled impedance that I would first build and tune the antenna, and only then measure the feed point impedance and build an L-network to transform it to 50 Ω with, hopefully, a far improved SWR.

Calibrating reality to the model

Wire gauge, insulation and other modelling inaccuracies make it vital to calibrate construction of the yagi. You cannot simply cut wires to the lengths found in the model and expect to achieve the modelled behaviour. For a simple dipole or vertical making an adjustment after construction is easy. Not so in this antenna unless you have a great deal of time on your hands.

Perhaps the simplest method of calibration is to build and tune one element so that its resonant frequency is identical to that in the model. In this wire yagi the best element for doing this is the director/reflector elements (excluding the reflector coil) since its tuning is critical to gain and F/B performance and any matching issues can be dealt with in the driven element and coupled resonator which are within reach of the tower.

To do that the modelled resonant frequency must be known. I deleted all of the wires from model other than the director and measured its impedance in free space and at several heights. In free space it is 56 Ω at 7.375 MHz. At the reference 25 meter height it is 48 Ω, also at 7.375 MHz. However at other heights the resonant frequency is different: 7.425 MHz at 20 meters and 7.350 MHz at 30 meters. For other heights you should run a model first. Remember to put the element under enough tension to remove sag that would reduce the interior angle and raise its resonant frequency.

Once the element is built and tuned to the corresponding modelled resonant frequency the other elements can be scaled accordingly. In my model the total element lengths are as follows:
  • Director and reflector: 19.56 meters, with a 1.95 μH centre coil switched in for the reflector
  • Driven element: 20.72 meters
  • Coupled resonator: 20.79 meters
The interior angle of the inverted vee elements is 120°, just as it was in all the other 40 meter wire yagis I've modelled on this blog.

The angle can be reduced if that's desirable or necessary in smaller areas. Should that be done the above measurements are no longer valid. The revised antenna would need to modelled, not simply scaled. It is not a trivial task to come up with a optimized design for these variations. So be prepared to do some work. Do not expect that you can go ahead and build the antenna per my measurements and then merely cut and trim to get similar performance.

Comparison to other yagis

I took several yagis from previous design articles to compare these wide band wire inverted vee yagis.
  • XM240 (proxy design since NEC2 cannot accurately model this antenna)
  • 3-element reversible inverted vee wire yagi
  • 3-element full-size yagi
  • 3-element full-size yagi with a coupled resonator
All antennas were modelled at an apex height of 25 meters over medium EZNEC ground [0.005, 13], including conductor loss. All the models were improved from their original appearance in this blog to ensure that gain errors due to segmentation problems are correct to ±0.2 db.
I plotted the actual maximum forward gain without regard to elevation angle rather than the 10° I used previously for general DX usage. From my QTH Europe and the US paths are typically associated with higher elevation angles. Since the antenna apex heights are the same (average height of inverted vee elements is lower) the maximum gain is within a narrow range of elevation angles -- 21° to 24° -- tending lower as frequency increases, as expected.

Bandwidth for 2:1 SWR ranges from approximately 150 kHz for the XM240 proxy, 200 kHz for the 3-element yagis, 250 kHz for the inverted vee yagi with a coupled resonator and more than 300 kHz for the full-size yagi with a coupled resonator.

There are a few things that jump out of these charts. One is the different behaviour of 2 and 3-element yagis. This was expected and is typical. The other is how the varieties of 3-element yagi behave at the upper end of their usable range. What is different is how their performance diverges.

Some of that performance can be recaptured by shifting the frequency range of the array upward, at the expense of some gain and F/B at the bottom of the band. Since I'm primarily a CW enthusiast I choose not to make that compromise. You might choose differently.

The wire yagis have lower gain, which is expected. This is due to conductor losses and the vee shape (typically -0.3 db) and the lower average height. Yet for most of the range the gain difference is quite small, coming in at around 0.5 db. The gain loss is greater at the top of the band. As already mentioned this can be corrected, with trade-off at the bottom of the band.

In every case the 2-element yagi is a poor performer in comparison to the simplest 3-element yagi. That does not make the XM240 a bad antenna, just one with the inherent limitations for any antenna of this type. It is still far superior to a rotatable dipole or fixed inverted vee, and without excess requirements for a rotator and tower.

Will it be built?

Short answer: I don't know. First the tower must be built and something put up at the top, 43 meters up and more. It is possible that if I feel the pressure of time I will instead do something different on 40 meters for at least the rest of 2017. In this same my fallback option for the top of the guyed tower is the XM240, if I run into difficulty putting up a full size yagi this year.

Even if I build a wire yagi it may be the 3-element design I based this one on, just for the symmetry and easier construction and tuning. Unlike in that article, since I will only have the one tall tower this wire antenna will require a more conventional, although it will not be a continuous conductor to avoid interactions with other yagis on the tower. There are a few ways to accomplish this feat despite its great length (48' or 14.5 meters).

Stacking with the top yagi is on the agenda. Again, that will depend on time. Once the top antenna is selected I will model the antennas to determine whether stacking can be beneficial. It often isn't for yagis this close together -- 18 meters or 0.4λ.

Not matter what I need diversity on 40 meters and that calls for more than one antenna.

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