Antenna Farm – Article 16 – Nov 7, 2022

By Charles KC6UFM

Parasitic Elements: The Two 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. This part will look at how the addition of parasitic elements (DIR and REF) impact the operation and performance of the Yagi antenna.

It is assumed that you have read and—more importantly—understood the information presented in Part 15. You may wish to have Part 15 open in another window so you can refer back to that from time to time.

As you learned in Part 15, a Yagi antenna is a simple dipole with some “special” elements added to create a directional radiation pattern. The Yagi takes the classic dipole figure-8 pattern and forces the maximum radiation into an end-fire (that is, parallel to the boom holding the elements and perpendicular to the elements themselves) pattern. You’ll recall this is because the energy radiated by the driven element (DE) is absorbed by the parasitic elements, and then is re-radiated by the parasitics with the spacing creating an out-of-phase situation. When all the radiated energy from the several elements is combined (using vector analysis and math that you probably don’t want to know), the energy is focused in one direction.

A single element Yagi isn’t a Yagi at all…it’s a simple dipole, and that was looked at in detail in Parts 15, 6, and 7. In this part, we will look at the simplest possible actual Yagi, that is, an antenna with just two elements.

 Figure 1 (Click here for full size image)

The “Traditional” Two-Element Yagi

Traditionally, two-element Yagis consist of a DE plus a REF…

Figure 1 shows the info needed to create this simple antenna model in EZNEC. You will note that a second wire has been added. This new wire (Wire 2) is slightly longer than the DE we used in Part 15 for the dipole. While the DE (Wire 1) remains at 972 mm, the new REF is 1017 mm. This means that the REF is about 4.5% longer than the DE. The REF is spaced 257 mm (about 0.125 wavelengths) behind the DE. Both of these values fit with the general dimensions for a basic Yagi.

 Figure 2 (Click here for full size image)

Figure 2 shows what this new, two-element Yagi looks like. You can see that the source remains at the center of the DE and the slightly longer REF is positioned behind (to the right of) the DE.

 Figure 3 (Click here for full size image)

Figure 3 is the SWR sweep of the two-element Yagi. You will note almost immediately that the SWR of this two-element antenna is higher than that of the simple dipole in Part 15. Of far more importance right now are the impedance values in the lower left corner of the figure. You will see that the complex impedance of the antenna has changed from the 74.43 + j8.85 ohms of the dipole to 33.2 + j38.54 ohms. You’ll note that the resistive component has dropped by more than half, and the inductive reactance has increased by more than four fold. All of this by the addition of just one parasitic element!

 Figure 4 (Click here for full size image)

Now, in Figure 4, we see the current distribution on the elements of our antenna. The current on Wire 1 (our DE) is identical to that on the simple dipole. But look closely at the current on our REF element (Wire 2) and you will see that it drops to zero and then rises again slightly at the ends of the wire. This is because of the phase delay created by the spacing between the DE and REF as well as the extra length of the REF. Remember that only the DE has energy applied to it from the source (transmitter). The current in the REF is also slightly lower than the DE because the current here is being induced by the DE instead of being applied directly.

 Figure 5 (Click here for full size image)

Finally, in Figure 5, we get to the real meat and potatoes of all this…the radiation pattern. It’s easy to see that the two-element Yagi has forced far more energy out of the end of the array in a direction of a line running from the REF to the DE. While the simple dipole had a maximum gain of 3.12 dBi (in two directions), the Yagi has a “Forward Gain” of 6.25 dBi and the gain off the back of the antenna (the FB Ratio) is -11 dB. While not fully developed in this design, you can see the beginnings of FS Ratio as well.

As I said earlier, traditionally, we design Yagi antennas by starting with a dipole DE and then adding a REF, and finally adding some DIR elements to that. I’ve never really been all that big on tradition, though.

There is no reason at all why you can’t start with a DE and then add a DIR…

 Figure 6 (Click here for full size image)

The “Alternative” Two-Element Yagi

Figure 6 shows you the EZNEC input for a Yagi with a DE plus a single DIR (Wire 2). You will note that the DIR is 904 mm long, about 7% shorter than the DE. Again, it is spaced 257 mm in front of (to the left) the DE. This is, essentially, the same as the traditional design just flipped around.

 Figure 7 (Click here for full size image)

In Figure 7 you can see what this alternative Yagi design looks like. This time, you can see that Wire 2 (our DIR) is in front of the DE (Wire 1) and that the source hasn’t moved from the center of the DE.

 Figure 8 (Click here for full size image)

Figure 8 is the SWR sweep for the alternative Yagi. This time, however, there is not as large of a shift to the SWR from the simple dipole. The complex impedance of the alternative Yagi is 28.99 – j8.885 ohms. Now, put down the mic and listen. This is important, and 2m FM will be open to Europe again soon…the solar cycle is yet young! Again, the resistive component of the complex impedance fell by about half, just like with the traditional Yagi, but the reactive part has kept a similar absolute value as the dipole, but it has changed from inductive (a plus sign) to a capacitive (minus sign) value.

This leads us to two general concepts of Yagi design:

(1) Adding a REF will decrease resistance and increase inductive reactance.

(2) Adding a DIR will decrease resistance and increase capacitive reactance.

You can use these concepts as you design your Yagi to get the overall feed point impedance as close to a pure resistance as possible. Don’t worry about the exact value of the resistance, just try to get rid of as much of the reactance as possible…we can always transform the resistance later.

 Figure 9 (Click here for full size image)

Next, in Figure 9 we see the current distribution on the elements of the alternative Yagi. Again, you see that nice, smooth current on the DE (Wire 1) and a very slightly distorted curve on Wire 2, the DIR. This time, the current on the DIR is cut off suddenly at the end. Similar to the traditional Yagi, it is this distortion and phase shift that leads to the directivity of the Yagi.

 Figure 10 (Click here for full size image)

Lastly, the far field pattern of the alternative Yagi is shown in Figure 10. There are no huge differences in the patterns of the traditional and alternative Yagi antennas, and what few differences there are lie in the side lobes. The bottom line is that, for all practical purposes, they can be seen as the same. This means that if you are building a two-element Yagi, you can select to use either a REF or a DIR as needed to make matching easier.

There are two big take-aways I want you to understand in this article, and those are:

(1) How the addition of elements impacts the pattern of the Yagi antenna.

(2) How you can impact the antenna impedance by the selective addition of DIR and REF elements.

To wrap up the two-element Yagi, if you are following along and building the models in EZNEC (or whatever), I encourage you to “play” with things a little. Try changing the length of the DIR and REF elements and see what impact this has on the SWR and pattern. Try shifting the spacing around a bit, and see what happens. I would, however, strongly suggest that you change only ONE parameter at a time so you can more clearly see the impact of the change in the model. If you are careful and, perhaps, document what you are changing and what the effect is, you’ll be surprised how much you can learn by just “playing” with the parameters.

In the next Antenna Farm article, we’re going to continue in this vein and look at three and four element Yagi designs so you can learn how these changes impact the overall performance of the antenna.

Take Care & 73