Describes the capability and limitations of the antenna analysisprogram developed by Richmond of Ohio State for NASA. Shows the basicassumptions of the program, and its structure. Describes a supplementaryprogram to prepare data input. Includes a sample problem, withproblem parameters, data input and results output. Recommends theprogram as a check for other analysis programs, and for problems notallowed by the common MiniNEC, specifically, effect of insulation onwires, scatter patterns and echoing area.
FORWARD
In the early 1970's, J.H.Richmond of Ohio State University completed anantenna analysis program under a NASA contract. While this work influencedlater activity in the field, the program itself has been largelyneglected. The purpose of this paper is to invite attention to some of theuseful concepts in the program and the theory behind it, and to showsome of the type of results it produces.
BASIC ELEMENTS OF THE THIN⌐WIRE PROGRAM
The heart of the program is the "reaction concept" of V.H. Rumsey(1). This is based on the idea that any real-world measurement of theelectromagnetic field must include introduction of a probe into thefield. What is measured is not the field, but rather the reaction of thefield on the probe. The alternate term for reaction is coupling: the
author finds this easier to visualize.
For the Thin Wire program (2,3), the field is assumed to be thatproduced by current on the surface of a wire of constant diameter andstated conductivity. Errors are present if the wire diameter islarge, with appreciable circumferential current. Theobservation point is assumed to lie on the axis of the wire for the selfreaction, or on the axis of an adjacent wire for mutual reaction.Diameters and lengths may be independent for the two wires, buterrors will be introduced if segment lengths are greatly different.
To simplify computation, the currents are assumed to besinusoidal in form. The specific relation used is of the form:
where Z is position along the wire from segment end Z1 to End Z3, andP1,P2 are switches which cause the second term to be zero for Z1<Z<Z2,and the first term to be zero for Z2<Z<Z3. G is the complexpropagation constant, G=s(Mu*Epsilon)^1/2. D1 and D2 are the lengths from Z1 to Z2 and from Z2 to Z3.
If the lengths D1 and D2 are each a quarter wavelength, therelation is for a sinusoidal distribution along the entiresegment. Since the current on thin real wires is nearly but not exactlysinusoidal, use of segments as long as a half-wavelength will lead toanalysis errors, essentially of the same order as for the valuesdeveloped by Carter (4) for half-wave dipoles. Segment lengths of theorder of 0.25-0.3 wavelengths will lead to relatively small errors, ofthe magnitude of "two term" analyses of King (4). Note that very shortsegments will lead to a triangular current distribution. These factorsmay be contrasted to the assumptions for MiniNEC, a constant pulse overthe segment (except for a zero half pulse for end segments) or for NEC,of the form, constant + sine + cosine terms.
As usual with this type of antenna and field analysis, the formulationleads to an impedance value:
Em = In * Zmn
where the Zs are the self and mutual impedances of the segments, E is thevoltage impressed at one or more segments, and I are the segmentcurrents. Since reciprocity is assumed, the voltages may be theresponse to an incident electromagnetic field. Thusscattering and echo area problems may be handled by the same formulation.For simplicity, impressed voltages are based on the delta gap model,zero feed gap width with gap capacitance neglected.
Additionally, the impedance matrix may be modified to the form:
Zmm = Zmn + Z'mn + Z''mn
where Z' represents loading elements introduced into the array ofsegments. Usually these are lumped loads, so only the elements for m=nexist. The effect of conductor resistance is handled as a lumpedload. Z'' is a matrix representing the effect of insulation surroundingthe particular segment. Again for simplicity, approximations limit the
thickness of insulation to a few wire diameters for accurate calculation.
The current version of the program requires the insulation to be the same
thickness on all segments of the antenna, but this limitation is easily
removed, as is the current limitation of identical wire for all segments.
The environment around the antenna may be free space, or amedium of arbitrary dielectric constant and loss factor, forexample, sea water. However, there is no provision for an interfacebetween two environments, so a buried antenna must be well buried.The original program has no provisions for the presence ofearth, but the ideal earth situation is easily handled by specifying animage antenna.
The program features resulting from the above approach issummarized in Fig.1. Many of these are the identical to those of themore common programs mentioned above. A major difference is theavailability of the insulated wire routine (although this is includedin NEC3, still of restricted availability). The externalexcitation routines are available in NEC, but not in MiniNEC.
Limitations on problems imposed by the program are summarized inFig.2. These are not much different than for the commonly used programs.The use of sinusoidal current distribution does mean that somewhatlonger segments can be used than in MiniNEC, without serious loss inaccuracy. However, testing for convergence is recommended for eachnew antenna configuration, by increasing the number of segments.
Adler (5) has extended the program to include reflectioncoefficient approximation to a real earth. As in MiniNEC, his version uses
ideal earth directly under the antenna, i.e., the image technique.However, his version does not allow the multiple ground zones of MiniNECor NEC.
PROGRAM INPUT AND OUTPUT
The original Thin Wire program was written in the Fortran of the early1970s. Input was by punched cards, and output was to a line printer.Output was bare, a table of numbers only.
The author has retained the same input form for data, making use ofthe free form input and output features added to Fortran. This"Input Card Deck" is created by a separate BASIC program. This requestsnecessary inputs, translates these to card form, and writes the results toa disk file, to be called by the Fortran Program. A sample input fileis shown in Fig. 3. The corresponding header output is shown in Fig. 4.Comparison of the two clarifies the meaning of each item in the inputfile. Note the use of flags to specify the type of analysis and tocontrol its output.
For output, the author has added explanatory statements to theoriginal Fortran code. The same technique was used by Adler. Theoriginal form is simply too abbreviated and condensed to beuseful.
An example of output when current listing is specified is shown in Fig.5. Both per-unit and absolute current is shown, the first as magnitude andangle, the second as real and imaginary components. Both are shownfor each segment end. The efficiency, power and drive point impedance shownin this figure are always output, even though current output is notspecified. The near field values are calculated and output only ifspecified. A program loop may be added to the main program if near-field
values are needed at a number of points. Such calculations are expected to
become more important, as restrictions on field intensity for health
reasons occur.
Output with far-field calculations specified is shown inFig.6. There is complete freedom in specifying calculation angles. Foreach one, the horizontal and vertical field components are shown,and the total field intensity. Values may be saved for use in aseparate plot program. Adler outputsreal and imaginary field components,and provides a plot program.
Output with the two types of scatter calculation are shown inFig. 7. Cross sections and scattered field intensities are shown asappropriate for back⌐scattering or bi⌐static scattering. Note that theinduced current in the antenna may also be output by specifying currentprint with external excitation.
Since the impedance matrix is calculated, its values may be outputto give the self and mutual impedances of the various segments.Fig 8 shows such an output table for a dipole with four segments. Sincethe matrix is stored in half-diagonal form to save memory, thefirst four lines in the table are the values for Z11 to Z14, the nextthree are for Z22 to Z24 and so on. For simplicity in use, this optionwas written as a separate version of the Thin Wire program.
The same technique can be used with the more common antennaanalysis programs. However, in the case of MiniNEC, note that theinternal matrix must be multiplied by a quantity jM before values areoutput.
EXAMPLES OF PROGRAM CAPABILITY
Since much of the Thin Wire program capability is the same as forother programs, only two features are reviewed here.
Fig. 9 shows the effect of adding insulation around a dipole (6). As iseasily visualized from the concepts of antenna inductance andcapacitance, adding a dielectric at the wire surface will reduce theresonant frequency, of the order of the original frequency divided by thesquare root of the insulation dielectric constant for infinitelythick insulation. At the same time, the radiation resistance willdecrease, by the same order. These effects are very evident in the datahere. Further runs are necessary to show the other effect of dielectriccoatings, reduction in the SWR bandwidth of the antenna.
The magnitude of change with thin coatings is often less than thatproduced by other factors, such as presence of the earth, or objects inthe near field. However, the performance of antennas such as theYagi are very sensitive to changes in the parasitic elements, so use of theThin Wire analysis can save test and adjustment time.
Fig. 10 shows the self impedance of a two-segment dipole as a functionof segment length and angle between segments. This is the "Inverted Vee"antenna problem. The same table can be developed with the other commonanalysis program, but the accuracy with MiniNEC will be poor. This tablecan be extended further, with some loss in accuracy due departure fromsinusoidal current distribution in real-world antennas. Results with NECshould be somewhat more accurate.
In view of the known difference between MiniNEC and NEC for sometypes of antennas, an important factor is comparison of outputs. Fig11 shows the results of such a comparison, for an array of twoidentical square loops fed at a corner, the diamond version of the"quad" antenna. The thin wire and NEC results agree to about 0.4percent in frequency for the condition of zero reactance, whereasthe MiniNEC results differ from both by some 5 percent. Completecross⌐comparison remains to be done.
OBTAINING THE PROGRAMS
The original thin wire program is available as a paper copy inFortran as
The accompanying report is available as NASA CR-2396, available indepository libraries. The Adler version is from The Naval Postgraduate School
Library, Code 0212, Monterrey, CA 93940 (the NTIS number is not known).
SUMMARY
Experience with the Thin Wire program so far shows that its mainvalue is in the capability that other available programs do no have.The most important is the insulated wire condition. The program is alsouseful as a check of the results of the more common MiniNEC.
It is a fast program, and is relatively easy to use. It seems tohave sufficient accuracy for general use, but more checks against antennameasurements and comparisons with other programs is needed before thiscould be recommended as general practice.
REFERENCES
(1) Reaction Concept in Electromagnetic Theory, V. H. Rumsey,Phys. Rev., n6, v94. Also in Computational Electromagnetics, IEEEPress, NY.
(2) Computer Program for Thin-Wire Structures in a HomogeneousConducting Medium, J. H. Richmond, Ohio State University, Columbus,Ohio, 1974.
(3) Radiation and Scattering by Thin-Wire Structures in the ComplexFrequency Domain, J. H. Richmond, Ohio State University, Columbus,Ohio. A Summary is in Computational Electromagnetics, IEEE Press, NY.
(4) See the development in John D. Kraus, Antennas, 2nd ed,McGraw⌐Hill, NY, 1988.
(5) "ASAP" Antennas-Scatters Analysis Program: a User⌐Oriented Thin WireAntenna Computer Code, Richard W. Adler, Naval Postgraduate SchoolReport NPS⌐62AB770801, Monterrey, CA
(6) R. P. Haviland, Insulated Antennas, Communications Quarterly,v3, n1, Winter 1993
