Antenna Farm – Article 17 – Dec 19, 2022

By Charles KC6UFM

Parasitic Elements: The Three and Four Element Yagi

Hello ECR Family, and welcome to The Antenna Farm. This is your friendly Antenna Farmer Charles, KC6UFM.

In Part 15 of The Antenna Farm, we looked at some of the theory of operation and history of the Yagi antenna, as well as some details on how dipoles work and radiate. Part 16 expanded our Yagi concept to a two-element design by adding either a DIR or REF to the basic dipole. This part will look at how the addition of more parasitic elements (DIR) impacts the operation and performance of the Yagi antenna and expand the forward lobe while reducing the side and back lobes.

It is assumed that you have read and—more importantly—understood the information presented in Parts 15 and 16. You may wish to have Parts 15 and 16 open in other windows so you can refer back to them from time to time.

Again, I would strongly encourage you to follow along and build these models in EZNEC or some other antenna modeling software.

For the expanded models in this article, we will be starting with the “standard” Yagi as described in Part 16, that is, a single DE with a single REF element. For the sake of simplicity, we will be adding only more DIR elements, though, as you learned in Part 16, you can manipulate the antenna impedance by selectively adding either REF or DIR elements as needed. Also, again to keep things simple, we will not make any attempts here to optimize the Yagi design, though you can tailor things like the forward gain, FB Ratio, and FS Ratio as needed for a specific installation by changing element length and the relative spacing between elements. Just remember that the Yagi cannot create energy…it can only focus it in different directions.

The Three Element Yagi

As expected, as you move lower in frequency, the size of the Yagi increases. For no other reason than practical limits of size, most Yagi antennas for use below about 20m will be either two or three elements. We have already looked at a two element Yagi with a DE and a single REF element in Part 16. Now, we’re going to add a DIR to that design to create a three element Yagi.

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Figure 1 shows the EZNEC inputs needed for this antenna. You will note that Wire 1 (the DE) is still 992mm long, Wire 2 (our REF) is 1017mm, and Wire 3 (the DIR) is 904mm. The spacing between the REF and DE as well as between the DE and DIR are all 257mm. The feed point (source) is still at the 50% point on Wire 1. In other words, this is exactly the same as the “Traditional” Yagi from Part 16 plus a DIR.

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Figure 2 is the basic view of our three element Yagi. Note that the DE (center element, Wire 1) has the feed point at its center, the REF (right-most element, Wire 2) is slightly longer than the DE, and the DIR (left-most element, Wire 3) is slightly shorter than the DE. You’ll recall that because of the interactions between the various EM fields, the direction of maximum radiation will be along a line starting at the REF and moving to the left, passing through the DE and on to the DIR.

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Figure 3 is the SWR plot of our new three element Yagi. You will note that the SWR is lower than that of the “Traditional” two element Yagi from Part 16, but there is now a slight curve being introduced to the plot. Recall that adding a DIR will cause the capacitive reactance to increase. In the “Traditional” two element Yagi, we had a complex impedance of 33.2 + j38.54 ohms. Looking in the lower left corner of Figure 3, you find that the complex impedance of our new three element Yagi is 21.72 – j3.534 ohms. In other words, the actual resistance fell by about a third, but the reactance shifted dramatically to the capacitive side. The net effect is that we have a somewhat lower resistance and the reactance is closer to j0 than with the “Traditional” two element design, so the SWR will appear lower with the three element antenna. This is a good thing! We can easily transform the lower resistance for matching purposes (50 ohm unbalanced feed line to a 22 ohm balanced antenna…a 2:1 balun would get us VERY close) and safely ignore the reactance for all practical uses. In fact, using such a balun would give us a theoretical SWR of about 1.19:1.

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Figure 4 is the view of our new antenna with current distribution curves added to the elements. This is effectively the same as the similar figures from Part 16 and is shown mostly so you can see a consistent progression of the designs.

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Figure 5 is what you’ve been waiting for…the far field plot. If you compare this back to the “Traditional” two element design, you’ll see that the addition of the DIR has extended our forward lobe to 7.15 dBi of gain. This is a jump of nearly a full dB of forward gain, but the real advantage is in the side and back lobes…the FB Ratio went from about -12 dB all the way to -22 dB, and the FS Ratio went from -16 dB to -19 dB! All of a sudden, with just one additional element, that annoying buzz from the power lines across town just fell off by half (or more) of its strength. Again, remember that Forward Gain is rarely the real reason to having a Yagi.

The Four Element Yagi

Above the 20m band, Yagi antennas with four or more elements (sometimes a LOT more!) are practical. The general myth—er, I mean rule—of thumb, however, is that more than about 15 total elements puts you into the territory of diminishing returns on the investment. We’ll talk about this more later in the construction article, but just know that this is the classic “Old Wife’s Tale” and is based on bad assumptions.

For now, however, we’re going to look at a four element Yagi. This is nothing more than the three element design above with the addition of one more DIR. Again, we’re not going to do any optimization and just look at what happens (and why it happens) when we add an extra element.

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Figure 6 shows the EZNEC input screens for our four element antenna. The only change here is the addition of a second DIR (Wire 4) that is identical to the existing DIR (Wire3) in length and is spaced 257mm forward of the first DIR. Just as an FYI, elements are usually labeled with their type (DIR or REF) and a sequential number starting at the DE. So we now have an antenna with a DE (Wire 1), a single REF (Wire 2) termed REF1, and two DIR elements defined as DIR1 (Wire 3) and DIR2 (Wire 4).

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Figure 7 is the view of the four element Yagi. Just like the three element design, the radiation will run from REF1 (Wire 2) through the DE (Wire1), DIR1 (Wire3), and on to DIR2 (Wire4). It’s worth noting that the overall length of the antenna (from REF1 to DIR2) is only 771mm (about 31 inches). In other words, this antenna could use a yard stick as a boom and have some room left over!

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Figure 8 is our SWR plot. This time, you see that the SWR has jumped up, and the reason why is the shift in the antenna impedance. In the lower left corner, you’ll see that our complex impedance has become 13.06 + j8.536 ohms. The falling resistance causes most of the SWR, but again, we aren’t worried about that since we can transform the resistance as needed. The potential problem is that our reactance has become inductive again and the absolute value has increased slightly. But don’t worry…we’re going to look at a bit of magic later called the Gamma Match that will solve all of these issues.

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Figure 9 is our current distribution. Look closely at the current on our new DIR2…note that it is higher than the induced current in DIR1. This is because DIR1 is getting current ONLY from the DE, but DIR2 is getting current from the DE and from DIR1. This interaction tends to pull the pattern from the side lobes into the forward lobe, but does let some “leakage” get to the back lobe. We’ll see that in just a moment.

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Lastly, Figure 10 is the Far Field Pattern plot. Note how the forward gain has increased to 8.36 dBi, nearly 1.5 dB higher than the three element design. Also, the FS Ratio has jumped from -19 dB for three elements to almost -26 dB with four elements! Our FB Ratio has, however, gone from -22 dB to “only” -12.5 dB. Again, this design is NOT optimized for anything in particular, but you should see now that you can indeed make a design that has either maximum forward gain, maximum FS Ratio, or maximum FB Ratio. Usually, you can get only one of these to a maximum at a time. From a purely theoretical point of view, a four element Yagi could be designed to give a maximum forward gain of about 14 dBi, OR have a maximum FS Ratio of around -36 dB, OR a maximum FB Ratio of about -32 dB. These are done by shifting the lengths of the DIR and REF elements and/or the relative spacing of the several elements. The trick here is figure out what your particular needs are and then to design to those needs. I’ll say it again, but high forward gain is usually not the best reason for having a Yagi.

Once more, if you are following along and “building” these antennas in EZNEC or some other antenna design/analysis software, play with things a little. Change the lengths and spacing of the parasitic elements and see what happens. You’ll be surprised how quickly you begin to learn to have an almost “gut feeling” about what changes will do and how they can be used to fit your needs.

In the next Antenna Farm article, we’re going to take a look at common construction concepts, including matching, for Yagi antennas. We will also briefly consider other directional antennas that may, in some cases, present a better solution than a Yagi.

Take Care & 73