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How to Prepare to Model Your AM Array

Practical Tips to Guide You When Considering the Use of Moment Method Modeling

We are now several months into the new AM technical rules that permit moment method modeling of eligible AM directional arrays.

The first model proofs were filed almost immediately after the February effective date, and many (if not all) of the stations that have filed are either operating under program test authority, an STA or a new license as a result of those filings.

These months have been a time of learning for engineers throughout our industry, from consulting engineering firms, all the way to station engineers doing the field work associated with the modeling. We are learning what works and what doesn’t, what policy decisions the FCC needs to make with regard to the new rules and specific solutions to special cases.

And so, with these months of experience behind us and many years of modeling in front of us, it occurred to me that perhaps this would be a good time to take a fresh and practical look at the modeling process.

In doing so, I would hope to help those contemplating this option to make the right, informed decision and get the horse before the cart as they start down the modeling path.


There are several precedents to employing the modeling option. Some of these are in the rules and have been well-publicized (and some have been well-misunderstood!) but I won’t belabor them here. Do keep in mind, however, that only series-fed arrays are eligible. If your array employs skirted or shunt-fed towers, forget it.

Disconnect lighting chokes and their tower-potential AC wiring before measurement. But beyond what’s in the rules are several key prerequisites that figure heavily into the cost/benefit analysis. I have learned the hard way to look at these first!

Item number one is the as-built tower geometry. The new rules require that a surveyor’s or engineer’s certificate be submitted showing the actual array geometry. While the rules don’t specify a tolerance, the Media Bureau seems to be using 1.5 electrical degrees as the cutoff point — if each tower in the array is inside a 1.5-degree circle centered on its design position, you’re good to go; if not, then your only option may be to redesign the pattern based on actual tower locations and go through the 301 application process. That adds a lot of time and expense to the process, and thus, is an important first step in the evaluation process.

So you’ve sent the surveyor out to provide you a sealed drawing of the array geometry and he hands you one showing the actual distances and bearings between array elements. How does one go about getting from there to the variance from the design location in terms of absolute distance? I’ve found that the easiest way is to convert to X-Y coordinates.

Start with the reference tower at X = 0, Y = 0 (0, 0). Then convert the design locations of all the other towers to X-Y coordinates. This is easy: X equals spacing between the towers times the cosine of the azimuth (direction angle between the towers) and Y equals spacing times the sine of the azimuth. A tower that is 75 electrical degrees in spacing and 40 degrees in azimuth from the reference tower would have coordinates 57.453, 48.209.

Next, convert the surveyor’s as-built tower locations to X-Y coordinates in the same way. You will have to convert from feet to electrical degrees and from surveyor angle units to clockwise azimuth reference to true north.

Then it’s a simple matter of determining the distance between the design and as-built coordinates. Find the difference in the X coordinates and the difference in the Y coordinates, and then take each difference as one leg of a right triangle per the Pythagorean theorem. Take the square root of the sum of the squares of the sides and you have your variance. Since we have calculated the variance in units of electrical degrees the answer can be used directly to determine if you are within the allowable tolerance.

If you do this for all the towers and find that each is within the 1.5-degree circle, you’re good to go. Otherwise, you have a decision to make whether to invest in a pattern redesign, allocation study and subsequent FCC filing or forget about the modeling option altogether.

Item number two is your sampling system. Many sampling systems are old and in unknown condition. Are your sample lines of equal length (within 1 electrical degree) and equal characteristic impedance (within 2 ohms)? If not, you will have to replace, adjust or repair them prior to employing the modeling option, and this can be a significant expense.

Photograph and otherwise document everything in the tower base region. As such, sweeping the sample lines should be done very early in the modeling process. Find the electrical length on the carrier frequency and determine the characteristic impedance of each line. If the lines meet the FCC criteria you can proceed with moment modeling. Otherwise, you have another decision to make: upgrade the sample system or forego the modeling option.


With those two “biggies” out of the way, the next step in the process is to measure the base impedance matrix. Using a bridge or network analyzer, measure the base impedance of each tower with all the other towers both open at the base and shorted.

If the towers are all relatively short (less than 100 electrical degrees or so), you can forego the short-circuit measurements. Otherwise, carefully measure each base impedance in turn and record the results.

Your notes should also include a notation of the type of bridge or analyzer used and whether the reactance values are corrected or uncorrected if you do not use a network analyzer.

There are a lot of caveats in this impedance measurement process. Most folks will measure at the ATU output because it is likely the last place in each tower’s transmission path that you can open the circuit and connect a bridge or analyzer. But there are some issues with this location.

In every case there is a finite (and often measurable) amount of series inductance in the feed tubing between the ATU output and the tower. This must be accounted for.

There is also a finite (and usually unmeasurable) amount of shunt capacitance to ground from the feed tubing, bowl insulator and internal ATU “plumbing” between the measurement point and the ATU output. Depending on the impedance of the tower, this may be significant and we may have to account for it in a nodal analysis supplement to the antenna model.

In many installations there will be other current paths that may have to be disconnected or accounted for. Static drain chokes should be disconnected, as should lighting chokes and their associated tower-potential AC wiring (to eliminate the capacitive coupling back to the choke through the wire insulation). Sample line isocoils must also be disconnected on the tower side.

Yet another “stray” path that must be eliminated in loop-sampled towers is the sample line that often parallels the feed tubing from tower to ATU.

Next, short across the base insulator with several low-inductance straps and measure again at the ATU output. The residual reactance will be the series inductive reactance of the feed tubing.

With a tape measure, determine the height of the tower base pier above ground. Measure the height of the base insulator and obtain any and all other information you can about it. Measure the tower face width and note the number of sides. If the tower base section tapers, measure the face width at the base, the face width at the top end of the taper and the length of the taper. Note the location where the feed tubing connects to the tower itself. Take a photo of each tower base, including base pier, insulator and feed tubing. Also photograph the location where the bridge or analyzer was connected.

The more information you can give to the engineer doing the model, the better the model will be. He will likely construct not only a calibrated tower model but also a couple of circuit models accounting for the series and (estimated) shunt reactances in the base region, including base insulator, Austin transformer, lighting choke, static drains, isocoils and isocouplers.

With good and complete measurement data the engineer can quickly construct and calibrate the model to determine whether the array can likely be adjusted to the model parameters with the existing phasing and coupling system, or whether modifications will be necessary.

In some cases — and this is something I found out in the second array that I modeled — it may be necessary to change from base to loop sampling.

In the months since the new modeling rules went into effect, we have learned that the modeling process isn’t a simple matter of “just do it.” Rather it is an information-gathering and decision-making process that in some (most) cases will lead to a successful filing. In those cases, folks are finding out that it is well worth the time and effort.

Cris Alexander is director of engineering at Crawford Broadcasting Co.

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