Method of Moment Proofs


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I must admit that several years ago when the method-of-moments proof concept began to be seriously considered by the FCC, both Don Markley and I had some reservations about its use. The objections were not based on any problem with the theory, but rather concerns about how to independently verify the performance of an array licensed by this method. Were adjacent stations really being protected or would such proofs ultimately become a dry-lab exercise?

The requirement of the reference field strength measurements described in the rules, combined with our firm actually performing some of the proofs, have allayed my original fears. This valuable tool has become yet another available to the broadcast engineer. Like any tool, though, there are certain applications where another tool is more appropriate. Think of the traditional proof as a set of slip-joint pliers and the moment method proof as a ratcheting combination wrench. The pliers will usually loosen any nut, however, the wrench is a more specific and elegant solution. With increased specificity, however, comes the potential for exclusion in certain circumstances.

Except for some verification measurements, a MoM proof eliminates the ongoing monitor point checks.

Except for some verification measurements, a MoM proof eliminates the ongoing monitor point checks.


At the heart of the moment method proof is a computer model using an appropriate software package. There are several different ports of the code. The ports of the code vary in their user interface and usable platform. In some cases, there are PC executables, while in others the FORTRAN source code must be adapted and compiled. Regardless of the particular flavor, the goal of the computer modeling is to mathematically define the array adjustment error, and eliminate the human opinion or subjectivity component.

The moment method proof, however, is not applicable in all cases or array designs. For instance, arrays utilizing top-loading, sectionalized elements, or folded unipoles (i.e. skirted towers) must go the traditional route. In addition, shunt-fed elements also preclude the use of the method of moments. Therefore, the use of this process is more or less limited to the run of the mill "traditional" designs.

It would be logical to assume the towers in any given array are actually at the locations relative to the reference point as specified in the authorization. Often, however, the distances and orientations may not completely agree. Variances typically result from survey error, clerical error, or insufficient accuracy in techniques, and in the cases other than clerical are typically limited to older construction. Since the MoM proof is based on modeling rather than a plethora of ostensibly verifiable and repeatable field strength measurements, it is necessary to use the actual spacing and azimuths between the constituent elements in the model. As a result, a stamped survey by a registered land surveyor in your jurisdiction will be required. This survey must be an as-built version, and not the one utilized to lay out the locations during construction.

Once the as-built locations are known, a suitable model of the array can be constructed. In constructing the model, a simpler set of parameters that meets the minimum FCC requirements and does not violate internal program constraints is ideal. Early on in working with the software, one mistake that is commonly made is to make the model much more complex than it should or needs to be. An overly complex model, when it comes time to vary the parameters to match the measured impedance values, will become unwieldy, require excessive time for convergence, and ultimately not yield more accurate results. A kiss is always a good thing.

-- continued on page 2



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