Gain, Beamwidth and Stacking of Yagis

Yagis

A rundown on these complex antennae.

 

There is a lot of conflicting information about yagis out there. I have spent a few years designing yagis, and doing the practical tests to resolve some of the confusing information. As this web site is about the UHF CB, the information about yagis on this page refers to yagis built for UHF CB, 477 MHz. I do not claim to be an authority on UHF yagis, but I have have done a lot of work in this area, and some my conclusions are based on practical tests.

This page is a long-term work in progress. It takes a long time to build a yagi, test it, build it again, test it again, etc,

and spend time with the family.


Firstly

 

In this article, I will be talking about yagis, and referencing practical tests that I conducted with my yagis. The reason I use my own yagis for testing is because that is what I have available. This is not intended to be a paper about how good my yagis are, just about yagis in general.


Basic Design

 

A yagi is made up of elements and a boom. The boom is the long pole down the guts. One of the elements is connected to the radio by the coax. This is called the 'driven element'. The rest of the elements are called 'parasitic elements'. The parasitic elements in front of the driven element are called the 'directors', and the elements behind the driven element are called the 'reflectors'. There is usually only one reflector, but there can be more. When an element is exactly the right length for the frequency it is being operated at, it is said to be 'resonant'.

 

The two basic types of yagi designs are narrow bandwidth and wide bandwidth. It is fairly easy to work out which one any yagi is just by looking at it.

 

The wide bandwidth yagi will have the director elements all the same distance apart, but the length of each element gets progressively shorter from the driven element towards the front of the yagi. The idea is, that the element in the middle is resonant at the centre frequency of the yagi, with the elements towards the back resonant at the lower frequencies, and the elements towards the front resonant at the higher frequencies. At any given frequency in the range of this yagi, at least one element is resonant, with all the other elements 'sort of' close to resonance.

 

The narrow bandwidth yagi has all the director elements the same length, but spaced increasingly further apart from the driven element towards the front. All the elements are resonant at the same frequency, and moving away from the resonant frequency results in all of the elements becoming 'less resonant', so the SWR gets real bad real quick if you go off frequency.

 

The (crude) pictures below are exaggerated so you can see what I mean.

 

The broad bandwidth yagi (below) operates over a wide frequency range.

The trade-off is gain, with a wide bandwidth antenna having less gain.

 

The narrow bandwidth yagi (below) has a high gain.

The trade-off is bandwidth, with a narrow bandwidth antenna only able to operate over a smaller frequency range.


Feedpoint Impedance / Matching (incomplete)

 

A standard dipole has in input impedance of 75 ohms. A folded dipole has a feedpoint impedance of 300 ohms. But these figures are only true when the dipole is in free space. As a part of a yagi, the feedpoint impedance is determined by the number of parasitic elements, and their distance from the driven element. In the presence of the reflector and directors, the feedpoint impedance goes down.

 

Most conventional matching methods just aren't suitable at UHF frequencies. The matching sections such as - gamma-match, T-match, delta-match, quad-match, etc., are too lossy at UHF frequencies.

 

This is what I'm talking about - look at the delta match on the UHF yagi in the picture below. It's as big as, if not bigger than, the driven element it's matching! Whether you're a scientific thinker or not, there has to be as much radiation coming out of the side of this yagi as there is coming out of the front. What a waste! And look how close it is to the reflector. This antenna can't be operating to it's full potential.


Gain

 

I don't think there is a formula to calculate the gain of the yagi. None that would be accurate by any stretch of the imagination, anyway. There are too many variables for this to be calculated by a simple equation. There is software out there that will model a yagi and calculate the gain, but I don't trust most yagi modelling software available to the public. More on yagi designing/modelling software later in this article.

 

Practical test.

I set up a dipole connected to a signal generator with 1dB stepped output, and an Icom IC-400PRO with external digital signal strength meter at about 50 metres away. I fed signal into the dipole until I got three readings on the signal meter of the Icom, a low signal, a medium signal, and a strong signal. I then replaced the dipole with the 22 element yagi, and the fed signal into the yagi until I got the same three readings on the Icom signal meter. I took the difference between the signal generator output required to get the same signal strength on the Icom meter and averaged the three readings. The difference represents the gain of the yagi over a dipole. Add 3dB to get dBi.

 

Some people have tried to convince me that yagis do not work the same way when used as a receive antenna as they do when used as a transmit antenna, that a yagi only exhibits gain when transmitting. Poppycock. But let's prove it once and for all. I connected the Icom up to a dipole with a clear sight of channel 4 repeater. I noted the receive signal strength. I then replaced the dipole with the yagi, and noted the signal strength. I connected the Icom to the signal generator and noted the signal generator dB output needed to repeat the two signal strength readings. The difference between the two signal generator figures represents the gain of the yagi over a dipole. Add 3dB to get dBi.

As I suspected, the gain figure matches the figure derived from the transmit test above. So there's that myth put to bed.


Beamwidth

 

A yagi is commonly referred to as a 'beam' antenna. It gets this name because it concentrates it's transmit and receive energy in one direction. How narrow or wide that 'beam' is, is called it's 3dB beamwidth. It is also less commonly called the 'FWHM', which stands for full-width-half-maximum. Full width refers to the angle between both -3dB points, as opposed to the half-angle, which is rarely used, except in some software such as Yagi-Max. Half-maximum is the 3dB point. If you reduce your power by 3dB, that means you halve it. If you increase your power by 3dB, that means you double it.

What does 3dB beamwidth mean? Take a look at the chart below. It is the radiation pattern of a typical yagi. Ignore the fact that it is a VHF yagi. A yagi is a yagi. This one seems to have a lot of energy going out the back of the yagi, but that is not why we're looking at it. The inner circles mark how much lower in power the signal coming from the yagi is, at that angle. They are calibrated as -3dB, -6dB, -10dB, and so on. If you look at where the power from the yagi falls below -3dB, that is where it is halved, you will see that it is at 335 degrees and 25 degrees. The signal from this yagi falls by 3dB at 25 degrees either side of it's strongest point. Therefore, this yagi has a 3dB beamwidth of 50 degrees.

 

 

planes of polarisation

 

 

formulae

BWh/BWe=1+4.03306*EXP(-0.264152*Gain dBi)

or

A = Gain x Wavelength / (4 x Pi),

 

 

 

The chart below shows what beamwidth could be expected from a theoretically perfect yagi for various gains.

 

Gain

Beamwidth

0 dBi

360 deg

3 dBi

180 deg

6 dBi

90 deg

9 dBi

45 deg

12 dBi

22.5 deg

15 dBi

11.25 deg

18 dBi

5.125 deg

21 dBi

2.5625 deg

 

As we know, antennae aren't perfect, so a yagi with such gains won't have these beamwidths.


Stack Spacing. (incomplete)

 

What's the correct spacing when co-phasing your yagis? It seems there are as many different opinions on this as there are 'experts'. Most of these come from the amateur ('Ham') radio enthusiasts.

 

Firstly, there are the plain 'rules of thumb'. These rules are different whoever you speak to. One of these rules goes - half a wavelength, or five-eights of a wavelength, or one wavelength, etcetera. Another of these rules goes - one third of a boom length, or one boom length, etcetera. And yet another of these rules goes - two feet for each element, or six inches for each element.

 

These 'rules of thumb' are not very scientific, and because they vary so widely between different 'experts', none of them can be counted on to be accurate. Almost all of these rules have been arrived at by experimentation by amateur radio operators, and mostly from experiments in the HF band. Typically in the HF band, antennae are huge, and it is just not possible to experiment with huge spacings on huge antennae, in a suburban area. So for the most part, these 'rules of thumb' are just a 'best guess'. Ham radio operators come to most of their conclusions through experimentation. Results can be influenced by many different factors, and just because one spacing is performing better than the last spacing you tried, that doesn't mean that it is the correct spacing. Another experimenter may get totally different results, and that is where the variation of opinions comes from.

 

So, what do the commercial and professional antenna manufacturers say? I contacted a number of manufacturers, and once again, there is a wide variation of opinions. Firstly, co-phasing of yagis is not a common practice in the commercial field, so a lot of manufacturers did not have any spacing recommendations at all. The manufacturers that did have a recommendation for spacing of their yagis arrived at their recommendations through rudimentary experiments, just like the amateurs. Whatever seemed to work the best for their basic antenna designs in one experiment became the permanent recommendation for their antennae.

 

Well, that's no help to us, we want the truth. The scientific truth. OK, let's look at some formulae. Once again, there are many different formulae, mostly coming from, once again, amateur radio operators. I found several different formulae, some outright absurd which I will not even present here.

 

Formula 1

S=51/BW

or

D=(51/BW)*Y

 

@120, S=0.425waves=267mm

@90deg, S=0.566waves=356mm

@30deg, S=1.7waves=1067mm

 

Formula 2

D=Y/(2*sin(BW/2))

 

@120deg, D=362mm

@90deg, D=444mm

@30deg, D=1213mm

 

or

 

S=1/(2*sin(BW/2))

 

@120deg, S= 0.577waves=362mm

@90deg, S=0.707waves=444mm

@30deg, S=1.932waves==1213mm

 

where:

Y is wavelength, in millimetres. The wavelength of 477MHz is 629mm.

BW is 3dB beamwidth, in degrees.

D is the resultant spacing, in millimetres.

S is the resultant spacing, in wavelengths.

-----------------------------------------------------------------

 

At the risk of creating just another 'rule of thumb', or another 'absurd' formula, I decided to have a practical test using my setup, and compare my results with the formulae. So, as this site is about UHF CB, and specifically about UHF CB repeaters, so all we want to know is - what spacing will give me the maximum power into the local repeater? My setup consists of two co-phased 22 element yagis, individually SWR'd using a tuned length of RG59 feeder, and a 1086 power divider, and stack separation of 1200mm. I wanted to see if I could improve my signal into the repeaters.

 

This experiment needed line-of-sight to work. I could have used the gain test setup, but I wanted a real world test. I have line-of-sight to channel 4 repeater, so the test was conducted by recording the received signal strength of channel 4 repeater. My Icom IC-400PRO has an external digital signal strength meter that reads from 200 at minimum to 1500 at maximum signal. As I knew that the strong signal I would be receiving would swamp the Icom receiver, thereby masking differences in readings, I used fixed in-line attenuators to reduce the signal at the radio, hopefully to make the differences more exaggerated. You can see in the following charts how close to maximum signal strength the readings are.

 

The following chart show the signal strength received at various spacings, with various attenuators in-line.

Signal strengths fluctuated, as they do, so are averaged over 15 seconds and rounded to the nearest 5.

 

 

Spacing (mm)

500

600

700

900

1000

1100

1200

1800

Attenuation

(dB)

 

 

 

 

 

 

 

 

 

0

 

1385

1385

1390

1400

1400

1400

1380

1420

-6

 

1240

1240

1260

1260

1260

1260

1260

1290

-12

 

1140

1145

1145

1150

1155

1145

1145

1165

-18

 

995

1000

1000

1015

1020

1000

1000

1030

 

 

 

 

 

 

 

 

 

 

SWR

 

1:1.38

 

 

1:1.32

 

 

1:1.30

1:1.29

 

As I suspected, the high signal strength from channel 4 pretty much swamped the readings, masking any difference that changing the spacing might make. If the test were conducted to a distant station, I am sure that there would have been very clear differences in the different spacings. BUT, however, I did not build this setup for long-haul communication, I built it to pump a massive signal in to the local repeater. Anyway, even though the readings are very close to each other, it does look like the wider spacings result in higher gain than the narrower spacings. I was not able to go any wider than 1.8m because the driven element feeder cables would not reach any further.

 

This test however did demonstrate that formula No.2 seems to be on the money.


Co-phasing.

 

Formulae.

 

Practical test.

I use a power divider manufactured by 1086 Chris. He tells me that whatever the SWR of the antennae connected to it, the output will always be 50 ohms. As I understand phasing harnesses, they just transform impedances, so that claim doesn't sound true. Bad impedance in, bad impedance out. So, let's put Chris' claim to the test.

 

I made two new driven elements identical to the existing ones, for the two co-phased 22 element yagis. This time I used RG-58 feeder cables about two and a half metres long, instead of the tuned length RG-59 feeders. With an individual antenna using RG-58 as the feeder, there is an impedance mismatch, and a bad SWR. In this instance, about 2. I ran another spacing check with the new driven elements. I could have tested wider spacings than 1800mm because of the longer feeders, but because of limitations of time, patience, and mechanical considerations, I decided to just duplicate the previous spacing test.

 

The following chart show the signal strength received at various spacings, with various attenuators in-line.

Signal strengths fluctuated, as they do, so are averaged over 15 seconds and rounded to the nearest 5.

 

 

Spacing (mm)

800

1000

1200

1500

1800

 

 

 

Attenuation

(dB)

 

 

 

 

 

 

 

 

 

0

 

1380

1405

1400

1415

1420

 

 

 

-6

 

1230

1255

1260

1275

1280

 

 

 

-12

 

1130

1150

1155

1165

1170

 

 

 

-18

 

980

1015

1015

1030

1045

 

 

 

 

 

 

 

 

 

 

 

 

 

SWR

 

1:1.05

 

1:1.06

1:1.10

 

 

 

 

 

So, again it looks like the wider spacing increases the gain, but the real surprise, for me anyway, is the SWR. It seems that 1086's claim is correct. His power divider does make bad SWR's good. The SWR is much better with two bad SWR antennae than with the individually tuned good SWR antennae. Go figure.

 

When I have manufactured co-phased pairs of yagis in the past, I have used tuned lengths of RG-58 terminated into a single connector in a 'Y' style. I wanted to see how this compared with 1086 Chris' power divider.

 

The following chart show the signal strength received with different co-phasing methods, with various attenuators in-line.

Signal strengths fluctuated, as they do, so are averaged over 15 seconds and rounded to the nearest 5.

 

Phasing

Type

1086

P.D.

Y

Cable

Final

Attenuation

(dB)

 

 

 

 

0

 

1420

1415

1415

-6

 

1280

1280

1255

-12

 

1170

1175

1150

-18

 

1045

1050

1020

 

 

 

 

 

SWR

 

1:1.10

1:1.51

1:1.15

 

And yet another surprise. There was not really any difference in performance of the antenna array, but the SWR is markedly different. Although 1.5 is not a bad SWR, 1.1 is a lot better, and these tests were done at 4 watts. The SWR gets worse as the input power increases, so at 25 watts, the SWR of the 'Y' cable would be closer to 2.0. So, my decision was to go with the 1086 power divider, for the lower SWR at the radio.

(oh, did I say 25 watts? Not me, your honour, I meant 5 watts...)

 

After all testing was done, I increased the antennae height another 1.5 metres, tidied up the cabling, and took the final readings. There is a slight change in readings, but it is most probably just because the antennae is up a little higher, and clearer of effects from the roof and other antennae, but I am happy with the performance. Final calculations indicate that I am getting about 1 to 1.5 dB better performance. That doesn't sound like  much of an improvement for a solid 8 hours on the roof, but considering that co-phasing increases the gain by a maximum of 3dB, an extra 1dB is a 30 percent increase (on the increase).


The Quagi

 

If you have done any research on the internet, you will no doubt have come across a supposedly fantastic antenna called the 'Quagi'. The defining physical feature of the quagi is that the driven element, and usually the reflector, are square. The builders of these antennae claim they are the best antenna in the world. The most outstanding electrical feature, it is claimed, is the fact that you can connect it directly to RG-58 coax. No tuning or matching needed. In straight gain tests, these antennae are claimed to out-perform any regular yagi. So, why are they so good?

 

It's all in the feeding. Firstly, from all the research I have done, they have only been compared to yagis that use the archaic and lossy matching sections that I describe above. I have shown in my own experiments that if you can 'ram' power into the antenna, it will appear to perform better.

 

A case in point. I built a yagi which used a balun transformer to match the driven element to the 50 ohm coax. The SWR was great. The gain, however, was mediocre. Certainly not the gain I was expecting. I then removed the matching section and connected the 50 ohm coax directly to the driven element. The SWR was up near 2, but the gain had increased markedly. In reality, the gain of the antenna had not changed, but the amount of power making it to the driven element had increased. The loss from the bad SWR was less than the loss from the balun. I think that the quagi builders are mistaking gain for ERP (Effective Radiated Power).

 

In a yagi, the feedpoint impedance is determined by the nearby elements. The closer the driven element is to the first few parasitic elements, the lower the feedpoint impedance will be. And the further away the driven element is from the first few parasitic elements, the higher the feedpoint impedance will be. So, if you mutilate the driven element so that much of it is far away from the directors, and as a result the directors have less influence on the driven element, you can get the feedpoint impedance to 50 ohms. But there is always a trade-off.

 

As the builders of these quagis have only tested them against yagis with lossy impedance matches, I think that if you put one up against a yagi that is better built, you will find that they are not a great as their exponents claim they are. Besides, with over half of the driven element outside the 'line of elements', what would the radiation pattern look like? Pretty ugly is my guess. Of all the research I have done on quagis, I have not found anyone who has done a radiation pattern test on a quagi.

 

The Quagi. The square driven element is mostly outside the 'line of elements'.


Software (incomplete)

 

I have tested:

 

 

NEC

 

quick-yagi

 

yagi-max

 


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