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Author Topic: Formulas for calculating Yagi dimensions  (Read 17837 times)

Posts: 7


« on: September 06, 2005, 03:57:49 AM »

Hello all,

If anyone has the formulas required to create yagi antennas of any frequncy, for any number of elements.

I want to build some 2 meter and 70cm antennas for satellite work, and want to learn how to make them.

I know there are lots of resources for these antennas, and software to build them. What I want is the formulas for myself so I can learn how they are designed.

Thanks in advance

Posts: 21758

« Reply #1 on: September 06, 2005, 08:17:32 AM »

Stick with the software, it's much better and still provides a great understanding of how beams are designed.

There aren't any "formulas" to do this correctly because everything in antenna design is interactive; so, changing one dimension per a formula results in the need to change other dimensions or parameters.  Instead of formulas, the programs use interactive algorithms that automatically make all the *other* changes properly, if you change one thing.  To do this using individual formulas results in a lot of working around in circles and never reaching the end result.

This is the reason that until modern programs were developed to model and predict beam antenna designs (and this started about 30 years ago, so the idea isn't so new), most beam antennas were developed using scale models and actually measuring (empirically) the results -- as opposed to "calculating" anything.  The very well physically modeled designs that evolved over years and years of antenna range experimentation are pretty much identical to the modern designs developed by modeling programs.  This is very evident when I compare my 9 element M2, developed by modeling software, to my old 8 element Telrex, which was developed in the mid-1950s on an antenna range.  The two designs are 45 years apart in age, and nearly identical in results, right down to element taper and spacing (as well as boom length).  Amazing how good those old "range modeled" designs were, if one had the time and access to an antenna range.

But it never happened using formulas.

There are some very basic "formula drafted" Yagi designs which are not optimized well but do work; Jim Lawson's (W2PV's) old Yagi handbook is a good reference for these.   The ARRL Handbooks and ARRL Antenna Books from the 1950s and 1960s (and maybe into the mid-1970s) also contain the "formulas."  But again, the end results are not well optimized, and the formulas were dropped from the books in favor of computer-modeled designs that work better.



Posts: 17411

« Reply #2 on: September 06, 2005, 02:20:13 PM »

I agree with Steve: there is no such thing as THE set of
formulas for a yagi.  Well, you can find some information
on 2-element yagis since there are fewer variables, but
even there the length and diameter of each element, plus
the spacing between them, all interact.  Then each person
may have different criteria whether they want a low SWR,
high front/back ratio, wide bandwidth, high gain, sharp
pattern, or other criteria.

First I'd recommend you read W4RNL's article on choosing
a 3-element yagi: he discusses a lot of the different
factors involved, and this will give you a very good
introduction to the topic.  Then browse the many different
antenna articles and designs on his web site - you may
find some that will work for you.

Then go to W9CF's site and try out his yagi modelling
applet.  This allows you to try out different yagi
designs and see the resulting horizontal and vertical
patterns, impedance, gain, etc.  (This doesn't compare
exactly to the results from some of the other antenna
modelling programs, but generally this is only a problem
when you are trying to design for a very high F/B ratio.)

If you spend some time experimenting with different
dimensions you will get an idea of the trade-offs and
interactions involved.

Posts: 7


« Reply #3 on: September 07, 2005, 03:32:49 AM »


I want to say thanks but you realy didn't help me. I guess what I should have said was I want to understand how to design an antenna. How do you calculate the spacing of elements, the lengths etc.

And Antenna modeling software does not tell me this stuff. I am a programmer so I understand how changing one thing will change other things.

If you don't know the math please do not respond. I do not need encouragement or discouragement. What I need is the Math, the procedures, and the science involved with building antennas, specificaly the Yagi.

I could even use the source code from some antenna modeling software, and I could figure it out myself.

Thanks anyway

Posts: 3151


« Reply #4 on: September 07, 2005, 05:50:39 AM »

You might want to look into the ARRL Continuing Education courses such as:

Antenna Design and Construction - EC-009


Antenna Modeling EC-004

Dennis KG4RUL

Posts: 492

« Reply #5 on: September 07, 2005, 06:27:03 AM »


What you're asking for is impossibly difficult because you have to start availing yourself of engineering sources, books, programs, internet resources and devoting yourself to intense and tedious study. No one can deliver it to you.

Posts: 17411

« Reply #6 on: September 07, 2005, 02:23:01 PM »

Perhaps part of the problem is that the actual design
process is NOT about calculating the spacing and element
lengths.  Rather, one CHOOSES a set of spacings and
element lengths/diameters, then models them to see whether
they give the desired pattern, gain, f/b ratio, impedance,
etc.  Then you tweak one or two values and try again.
Eventually you get a feeling for which adjustments make
the biggest difference in the design, and (hopefully)
find an antenna that meets your requirements.

If you want to understand the modelling process, I'd
suggest starting with W4RNL's website - he has a whole
section on modeling, including pointers to many sources
of programs (and source code in several languages).

Another good resource is W2PV's book, "Yagi Antenna
Design".  Dr. Lawson was one of the first to apply
computers to yagi modelling, and his book gives a lot
of background of how he did it.  (His models don't give
exactly the same results as the current NEC-based models,
but it should give you a good idea what is involved.)
This also includes methods for calculating tapered
elements, etc.

Basically, he divided each element up into a number of
segments.  He assumed a 1 amp current in the feedpoint
segment, and, using the mutual coupling between every
pair of segments (which depends on spacing, distance,
and orientation) he solved a big hairy matrix to find
the current flowing in each segment.  Given that, he
could then calculate the total field at any direction
from the antenna (far field) as the vector sum of the
currents in all the segments, with the relative distances
to each (and hence phase shifts) calculated relative
to the desired point in space.

On a more simple note, I have a spreadsheet that will
scale antennas for different frequencies and element
diameters, which I wrote based on W2PV's equations.
Basically, to scale an antenna the element spacings are
simply scaled by the frequency ratio.  For the element
lengths, I use his formulas to calculate the actual
reactance of each element at the original frequency,
then work backwards and find what length of the new
diameter element would give the same reactance at the
new frequency.  Rather than designing my own antennas
(since I haven't found a good antenna modelling program
yet that runs on my Macintosh) I generally find a W4RNL
design or one from another source that appears to meet
my needs and scale it for the desired frequency/element
diameter.  This spreadsheet isn't perfect: it doesn't
necessarily take into account capacitive coupling between
elements, for example, or metal boom effects, but I've
had pretty good luck with it so far.

The W9CF applet that I pointed to earlier includes a
brief discussion of the computational algorithm it uses.

Beyond this, you can search for information on the
Method of Moments calculations - that is the computation
core at the root of most modern modelling programs.

Posts: 82

« Reply #7 on: September 07, 2005, 03:38:11 PM »

Go to this link and give this a try.

various antenna designs to play around with; yagis, quagis, quads, gamma match. these calcs will get you in the ball park, but you will have to be creative. they are free downloads. also check Cushcraft. there site has manuals that you can model from on various beams.
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