Formulas for calculating Yagi dimensions

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george oakes:
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

Steve Katz:
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.


Dale Hunt:
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.

george oakes:

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

Dennis Zabawa:
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


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