3-element Coil-loaded Yagi for 40 Meters

The all time top 3 posts on this blog are designs for 40 meter wire yagis. In retrospect this is understandable. On 20 meter and above a rotatable yagi is within the reach of most hams. Below that it is not. Wire yagis are an economical and effective way to get a boost on 40 meters for DXing and contesting. From personal experience I know they can work very well indeed.

But now I am looking to join the minority with a 3-element rotatable yagi for 40 meters. The XM240 I have in storage is only part of my future plans. I also want something with better gain and performance across the band. I have the tower and the rotator to make this possible. Since a full size yagi is so challenging I am exploring 3-element yagis with shortened elements. The quest is to find how close we can come in performance. I am certainly not the first!

Selecting a shortening mechanism

There are a few ways to shorten dipoles and yagi elements. We can use one or more to meet our design objectives.

• Loading coils
• Capacity hats
• Linear loading
• Traps
• Bending the elements

When yagi elements are electrically shortened the antenna can be a nightmare to tune. It is no surprise that most hams who want such an antenna will opt to buy rather than design and build. There is something to be said for paying someone else for doing the heavy lifting.

On the other hand there may be a lingering suspicion that the compromises in a commercial design may be greater than advertised. Too often these products focus on low SWR rather than gain. The former is easier for the customer to observe, plus it makes operating more convenient.

This should not be taken as a smear against commercial products, many of which do measure up very well. In my quest for a larger rotatable yagi for 40 meters it is only natural that I would try to design something suitable before making the decision to buy or build, or to choose a full-size yagi. The knowledge gained is worthwhile no matter the outcome.

For example, the Cushcraft XM240 uses coils and capacity hats. Moxon rectangles bend the elements, and may even use loading coils. What they all have in common is that gain must be compromised, whether by inefficiency (loss) or reduced aperture. SWR bandwidth is often reduced as well because shorter elements can have lower radiation resistance.

The capacity hats in the XM240 are small and therefore have only a modest impact on shortening. Their advantage may be more about increasing element coupling to raise feed point impedance and improve F/B. But I haven't studies this closely other than simplified computer models. Those capacity hats are vulnerable when working on the antenna, so there had better be some performance benefit!

Loading coils must be high Q to keep loss low in a yagi, which means large, and large means increased wind and ice loading, and risk of breakage. Linear loading has similar efficiency challenges, and with greater vulnerability to ice. Traps are like coils with respect to loss, with the further disadvantage of not reducing element length all that much. Do it if you feel you must have a huge multi-band yagi (such as for 30 and 40). It will be challenging to design, build and tune. This won't be the first time I've linked to VE6WZ's site for high Q coil construction. Have a look if this style of yagi interests you since it's a critical component.

I chose to keep it simple: coils. With a target Q of 600 and elements 70% of full size it is possible to design an effective 3-element yagi for 40 meters that is reasonably rugged for the VE3 climate. It was for this purpose I earlier modelled elements of this type.

Modelling woes

Tapered elements are not well modelled with NEC2. The Leeson stepped diameter correction (SDC) in EZNEC deals with that nicely, but not when the element contains loads. EZNEC 6 is reported to correctly model such elements under certain constraints. Unfortunately the resulting model's correlation to reality is not always predictable. I've chosen to stick with version 5 for now.

Since NEC4 is not in my immediate future I modelled the element as constant diameter. This is sufficient to closely approach the true antenna pattern and impedance behaviour even though the length will be incorrect. As we'll see there is a way to translate the finished model into a working antenna by doing some work with the antenna in the air. Even with NEC4 there will be enough difference between the model and reality that a similar tuning procedure would be required.

Design procedure

Designing a 2-element yagi is straight-forward, even simple. All you do is make a resonant element for the design frequency and then place a copy of it next to it. You can adjust the element spacing to meet your objectives. If the performance is at the wrong frequency all you do is shift the resonant frequency of the parasitic element (reflector in this example). You then choose a feed system for the driven element, such as a beta match, and adjust for best SWR.

A 3-element yagi is almost as easy. That is for one with full size elements. Add loads and it can become a chore.

Let's walk through the steps.

1. Model a resonant driven element of the desired length as a percentage of a full-size element. Place a coil at the mid-point. Adjust the coil value, not the element length to bring it to resonance at the selected centre frequency. I chose 7.1 MHz. Make sure the coil in the load table has the correct ESR (equivalent series resistance). Use the formula R = X / Q.
2. Make two copies of driven element. Place one behind (reflector) and one ahead (director) of the driven element. As a first step place the driven element slightly back from boom centre since this usually improves performance and allows room for a boom-to-mast clamp.
3. Next, shorten and lengthen the director and reflector, respectively, by about 6%. Do this even if the element contains a load, whether a coil, trap or capacity hat. check the gain and F/B over the desired frequency range. Don't worry yet whether that frequency range matches what you want. However be sure to keep the loads on all element the identical distance from the boom. This will come in handy later. It will help to model each half element as two wires with the inside wire a constant length and the load at the outside edge. The other wire is the one you adjust.
4. Adjust the length of one of the parasites until the F/B and gain are optimized, or at least as good as you make them. You'll know you're close if the performance is similar to that of full-sized yagis with the same number of elements and boom length that you can find in the ARRL Antenna Book and other texts.
5. We still have no matching network so the SWR will be quite poor. All you need right now is to get the feed point resistance (the R component of Z = R + jX) as high as possible while keeping the gain and F/B as good as possible. Remember to check this over the frequency range, not just one frequency. You want performance over the whole band! The process is iterative.
6. Move the resonant frequency of all the elements by the same percentage (that is, multiply length by the same number) to move the performance to the band or band segment of interest. Do it again if necessary.
7. Design and model the matching network and adjust the network and driven element to optimize the SWR curve. Perfection may not be possible, but if you paid attention in step 5 you ought to come close.
8. Save the model! Now, delete the driven element and one parasite. Place the source on the remaining element and measure the reactance at the centre frequency. Write down that number, or save this model as well. Open the full model and do the same for the other parasite.
9. Build the antenna. Use a tubing taper schedule for your robustness requirements. A fibreglass tube is a good choice to bridge the length of the large-diameter coil.
10. Assuming that the driven element is a split for dipole feed (e.g. beta match), adjust its length as a reflector. Raise it on the tower, preferably at least λ/2 height. Hook up your antenna analyzer and measure the reactance. Adjust element length when the (inductive, or positive) reactance matches that from step 8. Do the same but for the director dimensions.
11. Assemble the full antenna, with the reflector and director lengths per your measurements in the previous step.
12. Raise the antenna to its final position. Adjust the feed system to optimize the SWR. Get on the air and enjoy the product of your labour.

Now you know why the vast majority of hams buy rather than build yagis!

Since the antenna has a narrow bandwidth when gain is maximized I developed two alternatives: one with maximum gain and one with broad bandwidth. They make an interesting contrast. Since beauty is in the eye of the beholder you decide which is better.

Design A: maximum gain

My results, based on ~70% of full length 25 mm diameter elements on 40 meters, are as follows. Coils are 7.2 μH with a Q of 600 and ESR of 0.5 Ω, with centres 3.385 meters from boom centre.

• Reflector: L = 14.20 meters; X = +26.3 Ω
• Driven element: L = 13.92 meters; X = -11.5 Ω
• Director: L = 13.64 meters; X = -49.0 Ω

The actual centre frequency as measured by resonance is 7.140 MHz. That is why the parasite reactances are not of equal magnitude. Both parasites are ±38 Ω relative to the driven element.

An L-network feeds the driven element, but a beta match could be used by shortening the driven element (capacitive reactance). The L-network was selected so that it can be more easily tuned, and another reason as we will discover. The 2:1 SWR bandwidth is 100 kHz, from 7.0 to 7.1 MHz.

• Shunt, across the input port: 575 pf
• Series: 0.94 μH

The gain of this antenna is above 7 dbi from 7.0 to 7.2 MHz, reaching a peak of 7.5 dbi near 7.050 MHz. Gain sharply falls above 7.2 MHz and below 7.0 MHz. The narrow SWR bandwidth is due to the low radiation resistance, a consequence of using loaded elements. F/B follows a similar frequency profile. The charted performance appears later in this article.

In comparison to a full size 3-element yagi there is approximately 1.5 db less gain. There are several reasons for the lower gain:

• Shorter elements contribute about -0.3 db
• Coil loss varies by frequency between -0.3 and -0.6 db for coils with a Q of 600; loss rapidly rises as the Q declines, so don't skimp on the coils
• Up to -0.5 db due to the shorter boom length of 12 meters (40') versus 14.7 meters (48')

This amount of gain is about the best we can do for elements of this size and loading. You cannot do better with alternative loading schemes, including linear loading.

Design B: maximum bandwidth

In this design the elements use the same construction and spacing. The only difference is the total element length, which is achieved by changing the length beyond the coils.

• Reflector: L = 14.30 meters; X = +51.5 Ω
• Driven element: L = 13.92 meters; X = 0 Ω
• Director: L = 13.64 meters; X = -92.4 Ω

The reactances are with respect to the 7.14 MHz resonant frequency of the driven element. Notice the much wider and unequal tuning spread of the parasitic elements. The L-network to get the SWR curve below is as follows:

• Shunt, across the input port: 370 pf
• Series: 0.64 μH

The 2:1 SWR bandwidth is now a respectable 200 kHz, double that of the maximum gain design. It covers all the spectrum of interest for DXing and most contests. In Europe and other regions this is the entire band.

We pay the price with lower gain, averaging around -1 db. However, the gain remains good all the way to 7.3 MHz. The F/B is also quite good across the full band.

Performance comparison

The chart at right shows the gain and F/B of both designs alongside each other to ease comparison. These are for free space. The F/B will differ by several db over real ground. As for any horizontally-polarized antenna the elevation angle of peak gain and position of lobes and nulls is height dependent.

SWR curves of the yagi are virtually unchanged by the presence of ground when 20 meters or higher, and even a little lower. This is typical for yagis.

Notice that the maximum gain design (A) reverses direction above 7.250 MHz (negative F/B). Design B has usable gain and F/B across the band, although its matched SWR bandwidth is 200 kHz. That 200 kHz can be placed higher in the band for SSB enthusiasts by changing the L-network.

Q of the L-network coil is not critical since the power dissipated is very small. A loosely-wound coil of bare solid copper (approximate Q of 150) is sufficient. It must be bare to allow a movable tap for the purpose of tuning the network. The capacitor should be a high current (low ESR) transmit door knob or equivalent, or an air-core or vacuum variable. For an example see my earlier article on the L-network for my 80 meter tower vertical.

Tuning challenges

The driven element is resonant at 7.140 in both designs. If you use a beta match you will have to shorten the driven element to add capacitive reactance. However I am specifying an L-network (see explanation below). The design process discussed earlier includes a step where the driven element is used to find the actual lengths required for the reflector and director based on reactance. But the impedance of a simple dipole like this varies with height, in both the R and X components.

When the driven element is moved from free space to the real world the resonant frequency (where X=0) depends on height. Notice in the chart how the resonant frequency changes. You must account for this during tuning.

You should also use the coils of the parasitic elements on the driven element to find the correct length of the parasitic elements since if, like me, you cannot build a set of exactly matched coils there will be unit to unit variation. After tuning with those coils you can move them back where they belong.

Be sure to keep the leads from the analyzer to the feed point very short or the reactance of the parasites will deviate from what you measure. If you use a length of transmission line between analyzer and antenna it must be an exact multiple of λ/2, or you should use an analyzer that can automatically measure and compensate for the transmission line length.

The L-network does not have to be redesigned for every adjustment of the yagi's tuning. You can make modest changes by adjusting the shunt and series components. Tap the coil and, at least initially, use a variable capacitor.

• Adjusting the coil shifts the frequency of minimum SWR, thus shifting the 2:1 SWR points 
• Adjusting the capacitor changes the SWR near its minimum point; however it does little at the band edges where the SWR creeps toward 2

To reiterate, this is not a general rule. They are only valid for small changes to the network.

More bandwidth

To improve the SWR across a larger swath of the band, in particular for design A, there are a few possible solutions:

• Remote tuning of the L-network
• Coupled resonator
• Dual-driven elements

The first is most convenient with a simple switch to move the low SWR region higher in the band. This is easier with design B since the impedance is less variable in the SSB segment. A couple of SPST can suffice to switch a capacitor and coil tap. This works less well for design B because the impedance varies quickly above 7.150 MHz. I was able to get a 2:1 SWR bandwidth that only covered about 70 to 80 kHz below 7.2 MHz.

The coupled resonator works well with full size elements as we've seen before. It does poorly with design A since the radiation resistance is low. Perhaps if I'd kept trying I'd have had more luck. Even so an L-network would still be required to raise the feed point impedance to 50 Ω. When I placed the couple resonator close to the driven element the impedance was difficult to control. At wider spacing it began to act as a director and fouled the performance no matter how I adjusted the real director. Trial and error has its limits.

Dual-driven elements work well in a similarly sized antenna: the M² 40MDDLL. I tried a few variations of this type. I had no more luck than with the coupled resonator and put it aside, at least for now.

Interaction management

Interaction between antennas is a product of nearness, orientation and resonance. It can be a performance destroyer. Loaded antennas often have an advantage in this regard since the loads typically alter antenna resonance on harmonics. This is important since most of the HF bands are harmonically related. On 40 meters the major concern is with 15 meters, the third harmonic.

Both versions of this antenna do not resonate on 15 meters. The raw SWR profile shows one resonance at around 25 MHz. With the L-network in place there is only a weak resonance near 23 MHz. This makes these 40 meter yagis more friendly to stacking arrangements.

However, since the model does not account for element taper the real antenna will be different. For example, my simple model of the Cushcraft XM240 shows a shallow resonance around 20 MHz, with a potential for some interaction on 15 meters. In practice the actual resonance is in the vicinity of 18 to 19 MHz, as reported by those who've measured it. Therefore until this antenna is built and measured there is reason to be cautious.

The other aspect of interaction is of concern to contesters operating SO2R or multi-op. When two or more receivers are simultaneously used a transmitted signal, or its harmonics, can interfere with reception or cause IMD due to overload. There are several filtering techniques to address the problem. The feed point matching network on the antenna can supplement, but not replace, the filters.

The above chart shows the SWR of design A (design B is almost identical) without a matching network. There is a resonance near 25 MHz, far from 15 meters and close to 12 meters. Now look what happens when the L-network is inserted.

The resonance has moved downward and is greatly attenuated. The L-network helps protect the rig connected to the yagi from overload from transmitters on other bands. Harmonics form the 40 meter rig are suppressed and so will help protect rigs on higher bands.

The difference is that the shunt element in a beta match is an inductor while in the L-network I've specified it's a capacitor. The series element is also the opposite. An L-network of this type is a modest low-pass filter. It can be easier to adjust than a beta match when a low loss, high voltage variable capacitor is used in the shunt. In either case you must use a good common mode choke or you'll lose this benefit.

Conclusion

The coil-loaded designs in this article are viable if imperfect alternatives. Are they worth the trouble? Maybe. There is no simple answer. Certainly it is a fantastic learning experience. But that learning comes at a steep price.

Most hams would sooner choose a commercial design such as the M² 40MDDLL. I don't like the linear loading design because of its mechanical complexity and susceptibility to ice loading (more surface for ice to accumulate on). The price is reasonable for an antenna of its size. It has found favour with many hams.

Some would choose to take the step up to a full size 3-element yagi for its simplicity and better gain, or stick with a small 2-element yagi and its performance limitations. A full size 40 meter yagi is more economical to build than buy and is easier to tune that a yagi with loaded elements. But it is awfully large. Cranes are often used to raise and maintain these monsters.

I have many months to consider my options. This design and comparison to alternatives are food for thought.