Edmund K. Miller ACES (Applied Computational

Edmund K. Miller 3225 Colle Celestial Santo Fe, NM 87501 (505) 820-7371 (voice/fax) [email protected] (e-moil)

T

his column will appear just before our yearly meeting, being held in Montreal, Quebec, Canada. All reports indicate that this meeting should be the biggest ever, with nearly 1,300 papers scheduled for presentation over five days, ratherthan the usual four. This record paper count stems from not only AP-S submittals, but also the fact that all URSI Commissions will take part in this meeting. There will also be two full days of short courses, on Sunday, July 13, and Friday, July 18. I hope to see many of you there. Topics discussed in this column include a brief review of the March, 1997, ACES meeting, announcements of some available software, and some further comments regarding radiation from simple antennas.

ACES (Applied Computational Electromagnetics Society) 1997 meeting, held in Monterey, California ACES just concluded (as this column is being written) its 1997 meeting at its usual venue, the Naval Postgraduate School in Monterey, California. This was a record-setting meeting, too, with about 220 papers scheduled for presentation. Gratifyingly, this year’s meeting had relatively few “no-shows,” apparently as a result of requiring payment of the registration fee before a paper was accepted for inclusion in the digest and scheduled for presentation. It’s worth noting that over 250 papers were originally accepted, with at least part of the attrition due, evidently, to the advance-payment requirement. Another innovation that seemed to work well this year was imposition of an “excess-page charge,” on authors whose pagecount submittal exceeded a threshold of 16 pages. While a pagecharge policy hadbeen previously used, this year’s refinements now made it minimally confusing. An individual registrant was permitted a maximum of eight digest pages per paper, and a maximum of 16 total pages in the digest. If three or more papers were :ubmitted with a total page count exceeding 16 pages, or a single paper exceeding eight pages, a charge of $15/page was required for pages 17-xx or 9-xx to be published in the digest. This page-charge policy was implemented to give individual authors who submitted several acceptable papers an opportunity of having them all included in the meeting proceedings, without ACES experiencing unacceptable financial losses due to their prolificacy. However, because papers published in the proceedings can be of journal-article length, the meeting record can be a much more useful product than one havinga one- or a few-page limit. One unfortunate consequence of the larger number of presented papers atACESnow (the first-1985-meeting had 37

IEEE Antennas and Propagation Magazine,

papers) is that there are as many as four parallel sessions during the three days of paper presentations. That, of course, is still many fewer than the 16, or more, parallel sessions that can now occur at the combined AP-S/URSI/NEM ~neeting.For several years, an afternoon poster session, atwhich exhibitor demonstrations are also given, has been held at ACES, as one way to handle more papers. This session is rather similar to some European meetings I’ve attended, where wine and hors d’oeuvres are also served: possibly explaining its popularity, if nst for the presenters, at least for the attendees! There are also two full days Jf short courses given at ACES meetings, normally on Monday and Friday, with the formal sessions held on the intervening three days. This year the course topics included finite elements, ray lracing for mobile communications, the TLM (Transmission-Line Matrix) method, practical EMC/EMI design and modeling, genetic algorithms, FDTD, wavelengths, software forCEM, lybrid modeling, and radiation physics. Given that the quality and variety of the papers is good overall, the fewer parallel sessions and the very attractive venue in Monterey, the ACES meeting is on: worth considering.

Available CEM software Several CEM software packages are briefly described below. I had hoped to run some of them, so that I could provide a moredetailed review, and I still plan on doing so, but in the interests of timeliness, I will settle, for now, cmn these descriptions. The material that follows is excerpted fromrecentbrochures or user’s manuals. Please note that inclusion in this column is not intended as an endorsement of any of the mentioned software, being provided solely for reader information. Material enclosed by quotation marks is excerpted directly fromvendor brochures or other sources.

PHLASH-EPM, Photonic, RF, Microwave & Antenna CAE, Version 2.1, from Toyon Research Corporation, 75 Aero Camino, Suite A, Goleta, CA 93 117-3139; Tel: (800) 742-2334 x127; Pax: (805) 685-8089; E-mail: [email protected]. PHLASH-EVTMis an integrated computer-aided engineering (CAE) tool that combines antennas, photonics, and electronics design in the same package. It allows assessing “...the overall effect of design changes to the photonic portion of the system by encompassing the entire system including antennas, and photonic, RF, and microwave components.” Rather than attempting to summarize the package, a good idea of what it does might instead be obtained from a partial listing of the table of contents in the User’s Guide, as follows:

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pointing device. It comes with a 40-page 8 . 5 “ x ll”, attractively produced manual. For pricing information and availability, contact Toyon Research Corporation using the information provided above.

“PHLASH-EPMBasics Creating a New System Saving a System Opening an Existing System Exiting PHLASH-EVTM

Xpafch (v. 2.4), an RCS predictioncode,and FISC (v. l.O), a multi-level, fast-multipole algorithm for scattering, on CDROM,fromDEMACO, Inc., 1430 Oak Court,Suite 303, Beavercreek, OH 45430; Tel: (937) 247-3719; Fax: (937) 427-3796, http://www.demaco.com/Xpatchcd; E-mail: [email protected]. According to the DEMACO brochure, Xpatch is a “general-purpose radar signature prediction

Setting up a System in PHLASH-EPM

... ANALYSIS DESCRIPTION Antenna Analysis Element Antenna Gain Source File Generation Source Impedance

code and environment for calculating high-frequency electromagnetic scattering.” It was developed under sponsorship of Wright Laboratory, Defense Advanced Research Projects Agency, and Naval Air Warfare Center. Purchasers of Xpatch must send a photocopy or fax of their DD2345 Militarily Critical Technical Data Agreement for approval by the Wright Laboratory sponsor.

Link Analysis Distortion Input, Output, and Load Impedance Noise Components Noise Figure Power Gain S-Parameters

The Xpatch package includes several modules, as follows: McImage, which overlays a CAD file with a predicted or measured S A R (Synthetic Aperture Radar) image; XpatchES, a synthetic-aperture-radarsimulation package; XEdge, a CAD visualization tool; Job Control, which controls lengthy executable runs across a heterogeneous network of SGIs and Suns; Cifer, a file translator package; McRange, which displays a CAD file with measured and predicted time-domain signatures; XYPlot & PSPlot plotting packages; XpatchF and XpatchT frequencyltime-domainRCS codes.

Combined Analysis Analysis Minimum Detectable Field Overall Power Gain Tuning Spurious-Free Dynamic Range Signal-to-Noise Ratio COMPONENT REFERENCE RF Sources Arbitrary Array Electrically Short Dipole Electrically Small Loop Fixed Thevenin Equivalent Frequency-Dependent Thevenin Equivalent General Antenna One-meter Dipole Thin Resonant Dipole

FISC computes RCS using a moment-method-type approach, where the target geometry is represented by a facet file. The target can be perfectly conducting, or described by an impedance boundary condition. The computational engine is based on a multi-level, fast-multipole algorithm. It’s stated that it will “Calculate the RCS of the VFY218 airplane at 1 GHz with 200,000 unknowns on a single-node SGI Power Challenge with 1 GB of memory,” but the time required todo this and the computational accuracy are not given. It’s also stated to have “Built-in bistatic approximation for multi-angle monostatic RCS, and built-in interpolation for multifrequency runs.” Finally, FISC includes dynamic-memory allocation and a GUI interface, and provides surface-current imaging using XEdge.

Photonic Components Laser Laser Diode Mach-Zendher Interferometer Optical Fiber Photodiode Detector

Purchasers of the XpatchlFISC CD receive:

Electronic, Microwave, and RF Components Lumped Elements Transmission Line Components Active Devices Other Components”

Executables for Sun Solaris 2.5 and SGI IRIX 3.516.2 (32 bit) User’s manuals in PostScriptTMand PDF formats 1 year of technical support.

PHLASH-EVTMrequires an Intel 386DX or higher processor (486DX or higher is recommended), and a math coprocessor. It runs under Microsoft Windows 3 . 1 ~or later, running in 386 enhanced mode; Microsoft Windows NT version 3.51 or later; or Microsoft Windows 95. It requires 4 MB of memory (8 MB is recommended) for Windows 95 or Windows 3 . 1 and ~ 12 MB for Windows NT.A hard-disk space of nominally 8 MB is required, which may vary due to cluster size and disk compression. The program is provided on two 3.5” high-density floppies, and requires a VGA or higher-resolution monitor, with a Microsoft mouse or compatible a4

Hardware requirements include: Minimum of 64 MB or RAM Minimum of 200 MB hard-disk space R4000 or greater CPU(SG1) 3rd Party OpenGL Software (SUN)* ZX graphics card (SUN)** *Required for XEdge and McRange **Recommended for XEdge & McRange The XpatchlFISC CD ROM and license for 1-9 computers costs $490 each, with discounts offered for greater quantities. Note that

:EEE Antennas and Propagation Magazine, Vol. 39,No. 3, June 1997

all CDs are encrypted: the software will run only on computers having valid licensesas provided at the timeof purchase.

The MININEC Professional Series, MININEC for Windows, MININEC Professional, and MININEC Broadcast Professional, from EM Scientific, Inc., 2533 N. Carson Street, Suite 2107, Carson City, NV 89706-0147; Tel: (702) 888-9449; Fax: (702) 883-2384; http://www.sierraweb.codemsci/;E-mail: [email protected]. MININEC, sometimes incorrectly regarded as an offspring of NEC, has by now accumulated a long history. Its first public release was in 1982, when aBASIC version, developed for the Apple I1 computer, became available. This first version was 550 lines in length, and ran on a 64-kB computer. It was later transferred to the PC line, continuing to be written in BASIC. Otherversionsof MININEC becameavailable,some in translations to other languages, with one choice being FORTRAN. This latest version,from its originalauthors, is nowalso in FORTRAN. The three versions included in the MININEC Professional series share the same electric-field, integral-equation formulation, in mixed-potential form, and a Galerkin numerical treatment using piecewise-linear basis and weight functions. They run under the Microsoft Windows environment, using input-data screens having queued dialog boxes with spreadsheet-like data displays, and provide tabular and graphical output options. Options and capabilities include: Peak or RMS currents and chargeson wires Input impedance and admittance Near electric and magnetic fields Far-field patterns (dBi andelectric field) Effective height and current moments Multi-port (antenna-to-antenna) coupling 3D geometry display with rotation and zooming Mouse support 3D current and charge display, andlinear, polar and 3D pattern plots Various-format (linear, semi-log, log-log and Smith-chart) plots A variety of modeling constructs is offered: Straight, helix, arc and circular wires Wire meshes Frequency stepping Lumped-parameter impedance loading Transmission-line interconnects Free-space, perfect- and penetrable-ground planes(the latter using a reflection-coefficient approximation) Rotational symmetry Cartesian, cylindrical and geographic coordinate systems .Dimensions in MKS or English systems Required computer resources include a 3.5-inch disk drive, an IBMPC or compatible 386or 486 processor with a minimumof 2 MB of memory. A VGAor super VGA graphics cardis required, Windows 3.11, Winamouse is recommended,andaMicrosoft dows NT, or Windows 95 operation system. Capabilities offered by the three codesin the MININEC Professional series progressively increase, in order, from the Windows, to the Professional, to the Broadcast version, with the latter offering the broadest set of options. For example, it offers plane-wave illumination and RCS computation, and various options of interest


to radio-station designers. The corresponding number ofunknowns and wires handled are 800& 400, 2000 & 1000, and 4000 & 2000, Professional version is respectively. The user’smanualforthe quite extensive, almost 200 pages in length, providing a thorough discussion of the interfaceandtlackgroundtheory,andalarge number of representativeapplications.Therespectivecosts of thesethreeversionsare$125, $390, and$790,withdiscounts offered for quantitiesof 10 ormore:.

Interface programs for the NEC-code series. The following twoproductsareinterfaceprogramsfor NEC. Theyare intended to make the problem of preparing input data and checking its accuracy, and examining and V Isualizing the output, more userfriendly than the basicNEC package. NEC-Win Pro and GNEC, from Nittany Scientific, Inc., 1700 Airline Highway, Suite 361, Hollister, CA 95023-5621; Tel:/Fax: (408) 623-0573; http://www.nittany-scientific.com;Email: salesanittany-scientific.cclm. Thefollowingdescriptive comments are excerpted from the WWW page given above and a product brochure. NEC-Win Pro wasdesignedto facilitate thedesignand analysis process by providing an easy-to-use toolfor antenna modelers, being targeted originally to NEC-2. A goal was to provide the weddesignerwith an intuitive ,;raphical interface that assists in modelpreparation,and in presentationandinterpretationofthe results. It offers features like three-dimensional visualization; realtime rotate, pan, and zoom with th: mouse to let the user see more views of the design interactively. Spreadsheet-style data entry of the wire coordinates is used, together with copy, cut, and paste commands, to make it simpler to place data information into commercial spreadsheet programs, tonm formulas and variables.

NEC- Win Pro enables display of radiation patterns on-screen, or printing them in full color for presentations or review. Alternatively, the screen, or a portion of it, can be saved as a bitmap file, to place into a word-processing program as a graphic element. Also “included with NEC- Win Pro is a modified NEC2 core, which has been optimized for the 32-bit operating system. The core supports DMA (dynamic memory allocation) and is capable of calculating the results for thousands of segments.” System requirements include: DOS-system computer with anIntel or compatible 80486DX 33 MHz microprocessor or greater A hard disk drive, a mouse, and 1.4 a MB floppy drive Microsoft Windows Version 3.I or later. 12 MB of available hard disk space for program files 8 MB of RAM VGA or SVGA monitor capable of 256 colors Although NEC- Win Pro will run on Windows 3 . 1 ~systems, the developers“highlyrecommend” ihat theprogrambeused on a Windows 95 or NT system. The ideal minimum system would consist of a Pentium computer with 12 MB RAM, running Windows 95 or NT.

The WWW page has a nice windowthat provides a dynamic The window demonstration of how NEC-W,’n Pro works. (Figure 1) that would be seen by the user is reproduced on the WWW page, with the various selection buttons providing links that emulate the function of each. This gives the prospective purchaser

Vol. 39, No. 3, June 1997

85

Spreadsheet-style entry of description parameters Automatic guideline check to alert the user to accuracy-degrading conditions Comma-delimited data output (optional) for easy importation to other programs Intelligent determination of memory use,so that disk use as virtual RAM only occurs if all available memory has been used Dimensioned to analyze antennas with more than 3,000 segments and 1,000 wires Can read and write NEC-format files Operates as a single, integrated program in which NEC-Xis embedded

. NEC-WIN Example 5 E l e m e n t LPDA in ~ r e espace T a u = 0 . 9 0 F r e q u e n ~ yRange 3 0 0 - 4 0 0 MHz

o o .a7 o .a00406 -.z43 a . 1 7 2 8 , 2 4 3 a . a a m z 2 3 5 . 3 z m - . 2 1 ~ 7 o . 3 z m ,2187 o . o o o m 4 5 . 4 m z 8 8 - . 1 9 6 8 3 n . 4 6 8 z 8 8, 1 9 6 8 3 o .a00322 5 3 , 5 9 4 2 5 3 2- . 1 7 7 1 4 7 0 , 5 9 4 2 5 9 2, 1 7 7 1 4 7 0 .Oil0322 1 3 7

z

o

Sigma = 0 . 1 6

-.a7

EZNEC pro requires a PC-compatible with 80386 with a coprocessor, 80486, or Pentium processor; 3 MB available extended RAM; and EGA, VGA or SVGA graphics. Printers such as the HP DeskJet and LaserJet and compatible printers are supported, as are Epson-compatible dot-matrix printers. EZNECpuo is a DOS application and will run under DOS, Windows 3.xx, Windows 95, or Windows NT, and does not require a compiler. Figure 1. The NEC-Win Pro demonstration window. Prices for these programs are: a “try before you buy” opportunity to see how NEC-Win Pro works. NEC-Win Puo is available from Nittany Scientific for $425.00. The complete package consists o f The software The NEC- WinPro Users Manual, Data Entry Manual, and NECWin Basic Insert Manual One hour of technical support. Note that there is a less-comprehensive version, NEC-Win Basic, also available, that sells for $75. Another product offered by Nittany Scientific, due for release in May 1997, is GNEC. This extends the capabilities of NEC-Win Pro to NEC-3 and NEC-4. Because these versions of NEC are limited-distribution, GNEC will only be available to licensed users.

EZNEC pro Antenna Modeling Software, Roy Lewallen, PO Box 6658, Beaverton, OR 97007; Tel: (503) 646-2885; Fax: (503) 671-9046; E-mail [email protected]. Roy Lewellan (W7EL) has produced a series of packages based on NEC and MININEC, initially directed primarily towards the hm-radio operator community, but evolving into more-general modeling tools. At the recent ACES meeting, Roy announced his EZNEC pro software, consisting of EZNEC/4 and EZNEC-M, as extensions to his previous EZNEC program. EZNEC/4 is designed as an interface to NEC-4, which is provided with it as EZCALC4, a specially compiled version of NEC-4. The complete package is available only to those who are confirmed as registered NEC-4 licensees. EZNEC/4 permits the user to enter the antenna description via a spreadsheet-like entry, as previously released in its EZNEC predecessor, or it can directly read the NEC description files. The calculating engine used is user-selected from either a user-supplied NEC-4, EZCALC4, or the internal NEC-2. For those not able to obtain NEC-4, EZNEC-M v. 2.0 is available as an alternative, for which the only calculating engine is NEC-2, but both packages are otherwise identical. A few of the features included in EZNECpro are: 86

EZNEC/4 New program Upgrade from EZNEC-M v. I Upgrade from EZNEC EZNEC-M V . 2 New program Upgrade from EZNEC-M v. I Upgrade from EZNEC

$600

$450 $550

$425 $250 $375

Still MoreDiscussion of Radiation Physics Periodically over the past several columns, the question “Why does an antenna radiate?” has been considered. The discussion that follows continues that theme. First, I should note that there will be a special session at the Montreal meeting on this question as well. This will be Session 105, scheduled for Thursday afternoon in the Salon Richelieu, where 10 papers are to be presented. Many years ago, in the summer of 1986, shortly after the Macintosh computer became available, I was fascinated to learn of an intriguing diskette of EM-related programs developed at Starford University, by Profess Blas Cabrera and his students, for use in teaching undergraduate fields. I subsequently described a module from that diskette, Radiation, in the April, 1986, “PCs for AP.” Since I imagine that few current readers of the Magazine remember, or even saw, that column, and because it’s so relevant to the present discussion, I thought that it would be appropriate to revisit Prof. Cabrera’s program. The Radiation module from which the results below were generated is available for $59 as “Physics Simulations 11” from Intellimation Library for the Macintosh, Dept. SSCH, 130 Cremona Drive, PO Box 1922, Santa Barbara, CA 93116-1922; Tel: (800) 346-8355; Fax: (850) 968-8899. (Besides the Radiation module, this disk also contains several other fields programs.) The program uses the “kink model” to develop a sequence of 32 plots or frames of the electric field about a point charge, as it undergoes five selectable kinds of motiordacceleration:


Vol. 39, No. 3, June 1997

Instantaneous (impulse) Constant Oscillatory Circular Square Afier the 32 frames havebeengenerated, the results are then played back as a “film loop” or movie, where the playback speed is user-controlled. Representative frames from each of the acceleration types are shown below in Figures 2 and 3. It’s clear from these results that wriggling field lines are produced as a result of wriggling the charge’s position. These wriggles propagate outward as a transverse field, making a clear connection with charge acceleration as a source of far-field radiation. These results are not selfconsistent, from the viewpoint that the energy required to cause the charge motion is not considered, nor are possible relativistic effects. These results possess one significantdifference,compared to the fields of, for example, a center-fed dipole antenna consisting of a perfect electric conductor. For the dipole, charge neutrality is the usual condition, and the radiation field is comprised of closed E-

Figure The &field lines about a Point chargeundergoing oscillatorymotion (a), as obtainedfromCabrera’s Radiation program. The peak charge speed is 0 . 5 ~ where ’ c is the speed of light.

Figure 2b. The E-field lines about a point charge moving at a circularpath, as obtainedfrom constantspeedaround Cabrera’s Radiation program. The speed of the charge has a constant valueof 0.5c, where c is the speed of light.

IEEE Propagation Magazine, Antennas and

Figure 2c. The E-field lines abclut a point charge moving at constantspeedaround a squarepath, as obtainedfrom Cabrera’s Radiation program. T’he speed of the charge has a constant Of 0*5c’where is the ’peed Of light.

Figure 3a. E-field lines about a charge undergoing continuous acceleration, as obtained from Cabrera’s Radiation program. Thechargestartsfromrestand reaches a maximumspeed of 0.5~.

Figure 3b.E-field lines about :I chargeundergoingimpulse acceleration, as obtained from Cabrera’s Radiation program. The charge starts from rest and reaches a maximum speed of 0.5~.

Vol. 39, No. 3, June a7 1997

arises wherever a partial, or complete, charge reflection occurs. But a reflection is, in turn, associated with a spatial impedance variation, which is indeed a physically relevant engineering concept. Therefore, it seems reasonable to seek a quantitative connection between acceleration and spatial impedance variations, as a means to better understand radiation. These observations are relevant to a discussion in a recent column, where the log(kL)dependence of the power radiated by a NEC-modeled dipole, having a maximum current magnitude of one amp, was demonstrated. This effect was attributed to a “travelingwave” or ‘‘damping’’ radiation, occurring along the length of the dipole. This implies that there must be some sort of continuous reflection process going on, as the currenticharge wave propagates down the dipole. 3e-3

Figure 4a. The source current due to Gaussian-pulse excitation of a long wire. The early-time part of the radiated field is primarily due to charge acceleration, caused by the excitationsetting charge into motion on the wire. The later-time radiated field is associatedwith apartial reflection of theoutwardpropagating currentlcharge wave.

-

-

fn

Maxllreall, Bicone

= 1.689 x btaxflreall, Const-Radius Dipole

n

I 4

-2e-3

8 3

!= Z

a Q

I le-3 I-

z

W 0:

e

2 V Oe+O

0 20 40 60 80 100 1 3 DISTANCE FROM SOURCE (WAVELENGTHS)

Figure 5a. The magnitude of the real part of the peak-current values, as a function of position, on 1,200-wavelength constantradius (heavy line) and conical monopole (light line) antennas. An increased decay of the constant-radius-antenna current is evident, apparently due to its z-dependentwaveimpedance. This, in turn, must account for the length-dependent radiated power of this antenna.

.

3

-

e

0

’

-

Figure 4b. The broadside farfield, due to Gaussian-pulseexcitation of a long wire. The early-time partof the radiatedfield is primarily due to charge acceleration, caused by the excitation setting charge into motion on the wire. The later-time radiated field is associatedwithapartialreflection of theoutwardpropagating currenffchargewave. field lines, which are “shed” by the antenna as the oppositely propagating currenucharge waves pass each other at the dipole’s center. The single-charge source, shown here, cannot produce such closed field lines, but does nevertheless radiate, through its transverse-field components. From an engineering perspective, accelerated charge is not a quantity normally dealt with when solving for the fields of perfect conductors, treated as boundary-value problems. It’s fairly obvious where passive (as opposed to active, caused by applied fields) charge acceleration must occur, however, as this phenomenon

aa

20 40 60 80 100 120 POSITION FROM SOURCE (WAVELENGTHS) 0

Figure 5b. The magnitude of the imaginary part of the peakcurrent values, as in Figure 521.


Vol. 39,No. 3, June 1997

Some insight into this process can be achieved from examining the Gaussian-pulse response of a long wire (Miller and Landt [l]), for which a typical result is shown in Figure 4a. There, we observe that the initial source-region current closely follows the time variation of the applied Gaussian excitation, but then exhibits a long-lived, lower-amplitude undershoot. Since this undershoot occurs before the launched pulse could have reflected from the end of the wire, it can only have been caused by a continuous, partial reflection of the outward-propagating wave. This shows that there was a corresponding acceleration ofthe reflected charge, thus apparently explaining the log(kL) radiated-power dependence. For comparison, the broadside far field is shown in Figure 4b, hrther confirming that reflected charge is the cause of the radiation that follows the initial pulse due to the exciting voltage. The results in Figure 4 also seem consistent with the analysis presented byAnderson [2], who derived an approximate expression for the wave impedance of aninfinite wire of radius a as

which is a constant, independent of position [3]. This being the case, the current on a long conical antenna should differ from the slowly decaying current on the constant-radius antenna. In order to examine this proposition, NEC vas usedtomodel 1,200-wavelength CR-monopole and 1,200-wavelength monoconeantennas, producing the results shown in Figure 5 . The CR antenna has a radius of 0.001 wavelength, while the conical antenna has a feedpoint radius of 0.001 and end radius of 0.01 wavelength, respectively. Plotted in Figure 5 are the magnitudes of the current peaks as a function of position, for the CR and conical monopoles. The real part of the CR current is seen to be more highly attenuated than that for the bicone, but there is less difference between the smaller imaginary parts. Although not conclusive, these results seem consistent with the expeclation that a spatial-impedance dependence will result in a decaying current amplitude, due to reflection.

References 1. E. K. Miller and J. A. Landt, ‘‘Direct Time-Domain Techniques for Transient Radiation and Scattering from Wires,” Proceedings of the IEEE, 68, 1980, pp. 1396-1423.

This demonstrates a slow dependence of the wave impedance with distance, z, from the source, i.e. a spatial-impedance variation that would produce a wave reflection. This result for a constant-radius (CR) wire suggests examining the behavior of a conical structure, the wave impedance of

2. J. B. Anderson, “Admittance of Infinite and Finite Cylindrical Metallic Antenna,” Radio Science, 3, 6, 1968, pp. 607-621. 3. C. A. Balanis, Antenna Theo~y:Analysis and Design, New York, Harper and Row, 1982, p. 327. .E

VERTEX COMMUNICATIONS CORPORATION A leader in the development and manufacture of satellite communication earth station antennas for operation in the domestic, international, and military markets, has immediate opening for an

Advanced RF Design and Development Engineer Responsible for the development of components for waveguide feed systems as used in reflector type antenna systems. The successful candidate must demonstrate detailed experience in the technology of low-loss waveguide polarizer networks, feed hcrns, and shaped reflector apertures, and will assume immediate responsibility for enginelsring activities related to the design, development, and test of such specific antenna feed systems and associated waveguide components. A university PhD or Masters engineering clegree in microwave antenna theory and electromagnetics is preferred.

VERTEX offers an excellent salary and benefit program. For consideration, onl:! qualified applicants should apply directly to: Human Resources Manager VERTEX COMMUNICATIONS CORPORATION 2600 N. Longview Street Kilgore, Texas 75662 EOE M l F l H N [email protected]

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