VA2GU PHASING ANTENNAS(dec. 2010)


This text file is a companion to the ARRAY PHASING program developped by VA2GU; you will find below the 10 steps used in the design of your multi element dream array of phasing antennas.

The 6 programs referred to in this article are:


1. VA2GU ARRAY PHASING1.XLS
is a spreadsheet file that will give you the driving impedances of each element in an array of up to 5 elements.
In the process, it will also produce the mutual impedances of pairs of elements, using two independent methods.
The inputs required are the self impedance of each element, the coupled impedances of pairs of elements and the design current magnitude and phase of each element, that you obtained from modeling the array.


2. VA2GU ARRAY PHASING2.XLS
is a spreadsheet file that will convert polar (46.8, -27.2*) values to/from cartesian (rectangular 41.6-j23.4) values. These values may be for impedance, voltage, current or what have you.
This file will also calculate the parallel equivalent of two imaginary numbers (like 2 parallel complex impedances).


3. VA2GU ARRAY PHASING.XLS
is a spreadsheet integrating VA2GU ARRAY PHASING1 and 2.

4. PHASE MUTUAL Zij.TIF
is a tag image file that you find in all litterature including ON4UN and ARRL Antenna books. It gives you on the Y axis, the mutual impedance value AND SIGN of two elements, when spaced by the value on the X axis.
This is what you use to chose the sign of the mutual impedances obtained from the spreadsheet above.


5. LAWLUM.XLS
is a spreadsheet program developped by Robye Lawlum and is used to find the L network components required to match all the elements' feedlines ends; these components give you a same voltage value at those points allowing you to "short" out all those ends to connect a single feeder. Rob has generously provided his program to John ON4UN and is provided as part of ON4UN LOW BAND DXING CD-ROM software. This program is not available on this site for obvious reasons.

6. TLCALC1.xls
TRANSMISSION LINE CALCULATOR is a spreadsheet that calculates virtually all transmissions lines parameters. It is being used here to find stub lengths for L and C in our array phasing components; it is a relatively inexpensive and very available component replacements for actual L and C. The link to get that program:
http://www.qsl.net/aa3rl/tlcalc1.html
This page is published by Mike Banz, AA3RL as a service to the Amateur Radio community and makes it available freely.


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All my research has pointed to the absence of practical information and programs for generalized horizontal array phasing.
Almost all of the published works, articles and programs available are for nearly idealized array of elements having the same self impedance and are directed in majority to vertical arrays.
My 20 degree sloping location 1200 feet from sea water, required the use of horizontal arrays because it provides lower radiation angles than vertical arrays; but this takes exception from my CVA closed vertical array, requiring no radials..
The VA2GU ARRAY PHASING SPREADSHEET CAN BE USED FOR HORIZONTAL, VERTICAL, OR ANY PHASED ARRAYS, USING NON-IDENTICAL ELEMENTS' SELF IMPEDANCES, as well as for those "idealized" arrays,

The ARRAY PHASING spreadsheets are automating the calculation of the driving impedances and network components required, when phasing up to 5 elements of any vertical, horizontal or any other types of arrays that can be put up with or without artificial ground.

In addition, ARRAY PHASING provides 2 methods of proofing your phasing measurements and calculations, gives the parallel value of 2 complex  numbers (2 parallel impedances) and provides conversions of polar to/from cartesian (rectangular) values. This information will also be used in the design of your array.

You can appreciate the power of such a spreadsheet program if you ever had to find the square root of imaginary numbers (never mind squaring, multiplying or dividing them) and having to convert cartesian to/from polar values.
It's fine to manually do it once or twice (I had to do it to proof my spreadsheet formulas) and you probably can find one or two sets of values per day, hoping not to make a math error in the manual calculations.
But imagine phasing 2, 3, 4 or even 5 elements and having to do the math a dozen times every day for a week or three, while erecting/phasing the array!!! The spreadsheet does it without error, in the time it takes to input the raw data.

This spreadsheet was not invented by VA2GU, but has been derived from a considerable research on array phasing matters, including but not limited to the theoretical works, papers and proceedings of Dr. John Krauss W8JI (sk), Balanis and several other authors on array phasing.

References, manuals, software programs, practical results and spreadsheet program from W1MK (Robye Lawlum), ON4UN Low Band DXing, ARRL Antenna Book, N6BV writing for the ARRL, AA3RL Transmission Line Calculator, Seeds Solutions Coax Matching and Logisoft Advanced Calculator were consulted and some are being used; I must also mention the invaluable practical articles from Forrest Gehrke K2BT.

Many other hams web sites were visited and their published articles in Ham Radio, QST, Antennex and other periodicals were read to make sense of the electromagnetic theory available to date.
It has not always been "friendly" readings and many publications have very limited practical applications; so you have to know enough not to use some of those articles in a general approach to array phasing.
But in the end, the final results have made those many research hours well worth the efforts. Have fun and see you on the air, mostly CW naturally.

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10 STEPS FOR THE DESIGN OF ANY 2 TO 5 ELEMENTS PHASED ARRAY.


1. Select your desired beam direction, array gain and front to rear for the physical antenna location selected.

2. Select the array that will provide those characteristics, c/w a first cut element dimensions and spacing.

3. ESTIMATE the height of your array over ACTUAL ground.

NOTE:
If no artificial ground, such as ground screen, ground plane or radials are used, be aware that your actual antenna height will be different in winter/summer (wet/dry ground). In my case, the array is located on top of a hill peak with practically no soil (max 12" in some locations) and granite rock forming the actual ground. Winter to summer electromagnetic ground varies by over 20 feet; the antennas here are higher in summer by that amount with the result that i have to provide two sets of phasing network components for the phased arrays erected.

4. Model the array for current magnitude and phase, element dimensions and spacing.

5. Erect each array element and using a VNA, PRECISELY measure the self impedance, to confirm the model results.
Rerun the model if necessary with new ground heights and other "estimated inputs" to reflect your actual array.
The precision of these initial readings are necessary, if you are to get the correct values of network that will give you the desired current mag. and phase (and produce the designed gain and directivity pattern).

NOTES:

Autek and MFJ cannot be used since they lack the precision in R AND Xj values.
I must say that Autek's VA1 may do the job. I did not have the instrument at phasing time, but have since used it and am very impressed with its precision, small size and convenient battery. (VA1 is smaller than the MFJ's battery pack!!!!and cheaper than the MFJ to boot!).

I was using my Autek to get me in the ball park and to regularly make a rough check of where i was when running the VNA program, but the RF1 was useless in providing the precise data required in the spreadsheets. I know of the MFJ and it suffers the same limitations. As previously stated, the Autek VA1 may prove an inexpensive approach (199 US$). The VNA I used, is from Array Solutions, model nr 2180; the AIM 4170 would also do.
http://aim4150.proboards.com/index.cgi?board=analyzer
Other VNA's I'm aware of, would probably do the job, but i do not have personal experience and cannot vouch for them.

When putting up multi elements, the self impedance of each element must be mesured without any other element "present", or up. You can actually open the base of other verticals and/or open circuit the center feed point of dipoles or loops (but without coax connected to that feed point, because that coax may convert an open end to other than open circuit at the antenna). Best is to lay other elements flat on the ground.

6. Erect 2 elements and measure their coupled impedance and make a table of values for each pair of elements in the array, with other elements "not present" i.e. take them down. See notes on the spreadsheet "VA2GU ARRAY PHASING1".

7. From "VA2GU ARRAY PHASING1" spreadsheet, select the mutual impedances sign and relative magnitude for each element per PHASE MUTUAL Zij.TIF file (see note below), reinput it in the proper space on the spreadsheet and use the resulting drive impedances.
These values will be used in the next 2 steps to calculate the phasing network components that will produce the designed current magnitudes and phases in each element of your array.

ARRAY PHASING spreadsheets provide several ways to confirm that your measurements were accurate and were inputted correctly.

NOTES:
Mutual impedance sign + or -? Since we have to extract the square root of a complex number, the result is either positive or negative. You have to select the proper sign, from the mutual phasing curves (PHASE MUTUAL Zij.TIF) that have been derived mathematically in the litterature.

The curves are two damped sinus integral curve, where both the real and imag. parts (resistance and reactance) go through the zero axis, as a factor of spacing in wavelength between pairs of elements. It extends to infinity, but practically past a half wave spacing, the coupling becomes very small; BUT IT IS VERY IMPORTANT THAT YOU SELECT THE PROPER SIGN, IN ACCORDANCE WITH THE CURVES TO OBTAIN THE PROPER VALUE OF DRIVING IMPEDANCE FROM THE SPREADSHEET. THE SPREADSHEET WILL NOT DO THAT FOR YOU.
This coupled impedance is a key factor in obtaining the proper mutual impedance and as a derivative, the correct drive impedance.
So listen well here: past a half wave spacing, and even at half wave spacing, the coupling becomes very small. But the coupling will always be inductive, i.e. the proximite of another element will always add to the inductance of the element studied. As a result, the reactance value of a given element will always get greater as it is coupled to another element.

8. With the results of previous step, find the current magnitude/phase at the phasing box end of the coax feeding each element. Such a program is bundled with ON4UN book. You might have to actually pick the corresponding VOLTAGE (rather than current) magnitude and phase for use in the next steps.

NOTE:
Your elements are going to be fed with lengths of coax, long enough to reach the phasing box. Those lengths of coax and their Z can be anything you want; but you have to find out what the current (voltage) and phase will be at the end of each of those lengths; in the phasing box. These values are required to find the LC phasing components required to produce such currents(voltages)/phases from a common feedline.

9. Using W1MK's LAWLUM.XLS spreadsheet found on CD-ROM bundled with ON4UN Low Band DXing book, find the actual phasing LC network values.
These LC components are used to match each individual element voltage/phase obtained in the previous step, to the voltage/phase of the element with zero phase angle (the one you selected as the reference element). This program will also give you the end impedance at the output of the network components of each element at this common point;

NOTE
This common point is one of same voltage and phase, allowing you to physically tie those outputs.
But the resulting combined impedance will be the value of combining up to five impedances in parallel (if you have 5 el. array).
In order to produce the elements' current magnitudes and phases, you have to insert the necessary L/C network components for each element. You may even have to add another L/C where all the elements join, to give you the feeder impedance required.
From that point on to the TX, you will be able to use any length of feeder, because the final total array impedance will be that feeder Z.

10. Now find the parallel equivalent Z of all those impedances, with the VA2GU ARRAY PHASING2 spreadsheet program and find the LC components required to match your transmitter feedline (to convert that parallel equivalent Z to the Z of your common feedline to the tx), using LAWLUM.XLS program.

NOTES:
You might have to play with different lengths and/or types of coax, if the LC values obtained are not practical. This will require you to rerun
steps 8 and 9 above till you are happy with the results.

For caps and inductances, you can replace actual components with suitable length of coax (stubs) having open or closed ends, (and even wind simple coils), to prove your design. It's cheaper and easier to get another piece of coax when your calculations show you need different values of L/C.  This is where I use the TLCALC1.xls spreadsheet.

After your design is stable, go ahead and spend the money if you want and get "neat" and "real" components. This is liable to impress your wife or ham friends (if you need that kind of encouragement..... :).

Now, you're going to want to measure the magnitude and phase in the elements of your array, to confirm your calculations and prove your design. A simple circuit using a ferrite core, will show you those values at the other end of a length of coax on a multi trace scope.
Such a circuit is shown in ON4UN's book; i have used a mat'l 43 core, with 3/8" dia. hole. I wind ten turns of small gauge wire and run the antenna wire through the doughnut hole, for the primary. I made all lengths of coax equal or multiples of one wave, so I dont have to worry about coax phasing errors.
I have terminated both ends of the coax with the characteristic Z of the coax. I used 100 ohms coax RG62, but terminated it with 75 ohms non inductive R. Calibration of all core/coax circuits were done by putting all the cores through the same element and looking at all the scope channels for the same readings.


Most importantly, go have a blast!  (okay there are 12 steps, but 10 sounded so good!)

Good luck to those who dare to try and let me know how it works; well, i'm sure to hear you!
ROY, VA2GU

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