icara. induced-current analysis of reflector antennas

9
John L. Volakis ElectroScience Lab Elecrical Engineering Dept. The Ohio State University 1320 Kinnear Rd. Columbus, OH 43212 + I (614) 292-5846 Tel. + I (614) 292-7297 (Fax) volakis. 1 @osu.edu (e-mail) David B. Davidson Dept. E&E Engineering University of Stellenbosch Stellenbosch 7600, South Africa (+27) 21 808 4458 (+27) 21 808 4981 (Fax) [email protected] (e-mail) Foreword by the Editors This issue, we have yet another contribution from Spain: the fourth in just over a year! This paper discusses the practical appli- cation of Physical Optics to reflector antennas. The authors present the basic theory, supported by an extensive list of references, and then discuss a code, ICARA, which implements this. A student ver- sion of the code will be available. We thank the authors for their contribution. Whilst PO can give excellent results for this class of anten- nas, it has limitations for more general problems. As the authors note in their paper, the method assumes the surface current as a given, rather than solving for it rigorously, as in the MOM. It is interesting to note that the PO approximation is essentially the first term in the MFIE, and that PO has been combined with the MOM to form a useful hybrid method, as implemented in the code FEKO, for instance. Further discussion may be found in [l, Chap- ter 61. 1. D. B. Davidson, Computational Electromagnetics f o r RF and Microwave Engineering, Cambridge, UK, , Cambridge University Press, 2005. ICARA: Induced-Current Analysis of Reflector Antennas Jose A. Martinez Lorenzo, Antonio G. Pino, lsidro Vega, Marcos Arias, and Oscar Rubiiios Grupo de Antenas, Departamentode Teoria de la Sefial y Comunicaciones ETS lngenieros de Telecomunicacion, Universidadde Vigo Campus Universitario,3631 0 VIGO, Spain E-mail: [email protected] (A. G. Pino); [email protected] (J. A. Martinez); [email protected] (I. Vega); [email protected] (M. Arias); [email protected] (0. Rubiiios) Abstract The aim of this work is to present the lCARA (Induced-Current Analysis of Reflector Antennas) software, which is able to predict the behavior of reflector antennas using the Physical Optics method. The software offers different options for antenna configurations,single and array feed models, and far-field or aperture-field analysis. Keywords: Reflector antennas; reflector antenna blockage; antenna radiation patterns; physical optics; reflector antenna feeds. 92 /E€€ Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005

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Page 1: ICARA. Induced-Current Analysis of Reflector Antennas

John L. Volakis ElectroScience Lab Elecrical Engineering Dept. The Ohio State University 1320 Kinnear Rd. Columbus, OH 43212 + I (614) 292-5846 Tel. + I (614) 292-7297 (Fax) volakis. 1 @osu.edu (e-mail)

David B. Davidson Dept. E&E Engineering University of Stellenbosch Stellenbosch 7600, South Africa (+27) 21 808 4458 (+27) 21 808 4981 (Fax) [email protected] (e-mail)

Foreword by the Editors

This issue, we have yet another contribution from Spain: the fourth in just over a year! This paper discusses the practical appli- cation of Physical Optics to reflector antennas. The authors present the basic theory, supported by an extensive list of references, and then discuss a code, ICARA, which implements this. A student ver- sion of the code will be available. We thank the authors for their contribution.

Whilst PO can give excellent results for this class of anten- nas, it has limitations for more general problems. As the authors note in their paper, the method assumes the surface current as a

given, rather than solving for it rigorously, as in the MOM. It is interesting to note that the PO approximation is essentially the first term in the MFIE, and that PO has been combined with the MOM to form a useful hybrid method, as implemented in the code FEKO, for instance. Further discussion may be found in [l, Chap- ter 61.

1. D. B. Davidson, Computational Electromagnetics for RF and Microwave Engineering, Cambridge, U K , , Cambridge University Press, 2005.

ICARA: Induced-Current Analysis of Reflector Antennas

Jose A. Martinez Lorenzo, Antonio G. Pino, lsidro Vega, Marcos Arias, and Oscar Rubiiios

Grupo de Antenas, Departamento de Teoria de la Sefial y Comunicaciones ETS lngenieros de Telecomunicacion, Universidad de Vigo

Campus Universitario, 3631 0 VIGO, Spain E-mail: [email protected] (A. G. Pino); [email protected] (J. A. Martinez); [email protected] (I. Vega);

[email protected] (M. Arias); [email protected] (0. Rubiiios)

Abstract

The aim of this work is to present the lCARA (Induced-Current Analysis of Reflector Antennas) software, which is able to predict the behavior of reflector antennas using the Physical Optics method. The software offers different options for antenna configurations, single and array feed models, and far-field or aperture-field analysis.

Keywords: Reflector antennas; reflector antenna blockage; antenna radiation patterns; physical optics; reflector antenna feeds.

92 /E€€ Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005

Page 2: ICARA. Induced-Current Analysis of Reflector Antennas

I. Introduction

everal analytical techniques have been applied to calculate the S diffraction patterns of reflector antennas. Aperture-field integration or surface-current integration were first used for the main beam and the near-in sidelobes [ 1, 21. The Geometrical The- ory of Diffraction (GTD), developed by Keller [3], was then applied to reflector antenna analysis, in combination with Geomet- rical Optics (GO), in order to predict the far-out sidelobes and the backlobe. The problem with GTD is that it predicts singular values in the transition regions adjacent to the GO incident and reflection shadow boundaries. It also fails near the caustics of the diffracted rays. To overcome some of the problems of the GO+GTD method, some other techniques were also developed [4, 51, such as the Uniform Asymptotic Theory (UAT), the Uniform Theory of Dif- fraction (UTD), and the Equivalent Current Method (ECM).

Another technique that has been used for reflector or multi- reflector antenna analysis is Physical Optics (PO) [5, 61. This con- sists of considering a source that illuminates the reflector antenna surfaces, which then reradiates additional fields that superimpose with the original source fields, but do not change the original source currents. The problem simplifies to finding the induced cur- rents and calculating their radiation patterns. The PO method is able to predict the forward and backward radiation of a reflector antenna, and to also consider the blockage effects in the case of multi-reflector configurations.' The Physical Theory of Diffraction (PTD) [7] was formulated to correct the effects of the geometric discontinuities.

2. Formulation

2.1 Scattered Fields from a Perfect Electric Conductor (PEC), Physical Optics Approximation

The magnetic and electric fields scattered by a perfect elec- tric conductor (PEC) can be expressed as [8,9]

H S = - j [ T ( ( J ) x V G ( ; , ? ) ] dS',

4

where ?(7) is the current density over the surface. The unprimed

coordinates represent the observation points and the primed coor- dinates denote the source points, and G(F,T) is the Green's func-

tion, defined as

( 5 )

where R = IY - 71, I? = (7 - J ) / R , and the functions G1, G2 , and G3 are

-1 - jkR + k2R2 R3

G1 = ,

3 t 3 jkR - k2R2 G2 = R3

-1 - jkR R3

G , = - .

The first approximation consists of assuming that kR >> 1, which implies that the distance between the source and the obser- vation point is much greater than the wavelength, but it has no implications with regard to the size of the source. Therefore, the fields can be written as

R

A new approximation can be considered by taking into account the size of the surface (&). If we assume that the observation point is

in the far-field region of the surface ( R > 2 0 ; //1 ), Equations (7) and (8) are reduced to

r 7

To solve the previous integral equations numerically, we divide the surface into triangular patches. Each element, denoted with by index i , is considered to radiate in its far-field region. The observation points are denoted by the index k . Consequently, Equations (9) and (lo), applied to a single patch, can be written as

e-jklF-7/ - - j H i k =--

22 <k (3) y y' =-- .

G(-,-) 4n I7-q

The Operators in Equations and (2) can be devel- The total fields produced by the entire surface are obtained by ' adding all the patches' contributions at the observation points: oped and the equations can be written as

/€€€Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005 93

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(14)

Equations (13) and (14) can be thought of as the discretized ver- sions of Equations (7) and (8), respectively. When the observation point is in the far-field region of the antenna, the electric and mag- netic fields can be written as a discretized version of Equations (9) and (10) in the following way:

r 7

Some integral equations, such as the EFIE or MFIE [ 10, 111, can be applied to obtain the current density, J(F'), which is not known a priori. However, for objects with a large electrical size

'and small local curvatures, the Physical Optics (PO) approximation provides an adequate estimation of such currents, with less com- putational cost. The PO approximation of the induced current is [8, 91

where Fin' (7) and li' are the incident magnetic field and the out-

ward unit vector normal to the surface, respectively, at 7 . The dis- tribution of the PO current across any triangular patch is assumed to be constant in magnitude and linear in phase, as described in [9]:

.-, J,,(J) = ~~,(a).~-ik(r-.d)-B, (18)

where is the center of the patch, and jji is the unit Poynting vector, which can be obtained by computing both the electric and magnetic incident fields at 8 . The solution of the integral expres- sions of Equations (1 1) and (12) for triangular patches with the distribution of Equation (18) is described in [9].

2.2 Fields Radiated by a Single Reflector

As we can see in Figure 1, the incident fields Hint, Einc are generated by the feed, characterized in general by the electric and magnetic sources M f e e d , Jfeed . Taking into account the PO

approximation, the value of the current, & , induced on the sur- face by the feed radiation can be obtained by Equation (17). The

scattered fields, ZM, i&, are then obtained by the radiation of

Jh in free space.

The back radiation and the spillover lobes are critical phenomena in reflector-antenna analysis. By adding the direct feed radiation to the scattered fields, both effects are taken into account.

94

2.3 Fields Radiated by a Dual Reflector

Figure 2 illustrates the procedure to obtain the radiated fields of dual-reflector antennas. The first step is to compute the PO cur-

rent, Ti, over the subreflector, produced by the feed. Equa- tions (1 l ) to (14) are then used to compute the radiated fields (pro-

duced by 7:) incident on the main reflector surface. The proce-

- s EM

- inc E

Figure 1. The single reflector analysis.

Figure 2. The dual reflector analysis. '

IEEE Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005

Page 4: ICARA. Induced-Current Analysis of Reflector Antennas

J feed

A7fied

A simpler model of the feed, referred as the cos-q [5 ] model, has been also considered to allow faster computation.of the source radiation. This is valid only when the first reflector surface is in the far-field region of the feed [12]. The magnetic field radi- ated by this feed model can be written analytically as

7; J,& J , , B Considered effects

- Yes

-

Yes

dure is valid when the distance between both surfaces is much greater than the wavelength, even if the main reflector is not in the far-field region of the subreflector.

- Yes - Only main reflector radiation. Yes Yes - Main reflector radiation,

spillover, and back lobes.

subreflector blockage.

spillover, back lobes, and subreflector blockage.

- Yes Yes Main reflector radiation and

Yes Yes Yes Main reflector radiation,

The current across the main reflector, & , is given again by the PO approximation, Equation (17). These currents are consid- ered to radiate in free space to generate the fields E& , E& .

An effect that must be also taken into account in dual-reflec- tor antennas is the blockage produced by the subreflector. One method to simulate it is based on geometrical considerations, by canceling the blocked surface current. The method adopted here is

based on the computation of the blockage current, T ~ J , induced

by the main-reflector radiation of & on the subreflector surface.

The current &B generates the fields g$,B, E$,B. The total fields produced by the antenna are then computed as

Different combinations of the radiating currents can be selected depending on the effects to be considered, as described in Tab’le 1.

2.4 Feed Models

To model the feed of the reflector antenna, we first consider the radiation of a circular source with an electric current distribu- tion with tapered amplitude and quadratic phase error, controlled by the parameters p and S, respectively:

J feed ( P ) = J o [ P + ( l - P ) c O s ( 3 ] e

where J,, is a constant current density, a is the radius of the circu- lar source, p is the radial coordinate at any point of the source, and g p is the unit polarization vector of the source. The radiation of Equation (2 1) is computed by discretizing the source into trian- gular patches and applying Equations (1 1) to (14) to obtain the

(for X-polarization), (22)

(for Y-polarization), (23)

where V is a constant voltage, (@,+,I-) are the spherical coordi- nates of the observation point referred to the feed reference system, and qx and qy are the parameters used to control the beamwidth

for the principal planes of the feed.

Two additional far-field models, based on numerically defined pattems and arrays of cos- q elements, respectively, have also been considered.

3. Software Architecture

The architecture of the software is based on independent modules (see Figure 3). This section shows the general structure, as well as the function of each module in the simulation process. First of all, it is necessary to define the geometry to be analyzed (Geometric Module). The second step is to select the feed used to illuminate the antenna (Feed Module). Once the feed is defined, the Physical Optics stage computes the currents on the antenna surfaces (Physical Optics Module). The next step is to obtain the radiated fields (Analysis Module). The computed results are man- aged with the post-processing modules (Array Synthesis Module and Graphics Module). Finally, the selected geometry and the computed fields can be exported with the Output Module.

radiation over the first reflector surface, and Equations (1 5 ) and (16) for the far-field computations. Figure 3. The ZCARA main control window.

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Figure4

Figure 4. The geometric aided design window for a single or dual reflector.

3.1 Geometric Module

This module is used to iritroduce the geometry to be simu- lated. The selected geometry can be defined by a geometrically aided design tool, or it can be read from a file.

Figure4 illustrates the first case (Geometry Aided Design Window). The user defines the geometric parameters of the main reflector (focal length, offset height, dish size) and the subreflector if exists (magnification factor, eccentricity, inter-focal length, and tilt angle between the axes of the main reflector and the subreflec- tor). The program also presents other computed parameters, as seen in Figure4. The selected geometry is plotted in a Graphic Area (GA) of the window. The profile has a number of hotpoints, which can be moved with the mouse to redefine a new geometry. As a result, the parameters of the new configuration are updated over the corresponding boxes and the profile in the Graphic Area is refreshed. The number of patches of the discretization must be selected, too. The discretization algorithm of the main reflector is based on the projection of a discretized elliptical aperture over a parabolic surface, as described in [9]. The subreflector points are obtained as those corresponding to the main reflector by a ray- tracing scheme.

In the second case (Importing Surfaces Window), for each surface the user must select two files. The first file has the Cartesian coordinates of the surface points, and the second file has the indexing of the points that form each triangle. Moreover, it is necessary to introduce the feed location, as well as the target, to point the feed axis correctly. Once the files and the surface parameters have been introduced, the geometry, the feed point, and the target are plotted in the Graphic Area of the window to test if the geometry and its parameters were introduced correctly. This module provides an additional capability for analyzing arbitrary shapes, which can be generated by a shaping procedure or any other external program.

3.2 Feed Module

The software includes four different feed models. The first one is the disk of electric current, described in Equation (21). .The user selects the disk radius, a, the parameters p and S, the fre-

quency (or wavelength), and the polarizatkK The second feed model (Figure 5) is the cos- q model, described in Equations (22) and (23). The selected parameters for this case are the exponent, q, or the taper illumination at the reflector-edge direction. The third model consists of reading the CO-polar and cross-polar components of the feed pattern from a file. This is particularly useful for simu- lating the reflector antenna with a real feed with measured pat- terns, or those predicted by external software. In this case, the user introduces the name and the sampling parameters of the file. The directivity of the feed is computed by a brute-force integration of the power pattem, and it is then presented in the window. To per- form the calculation of the magnetic and electric radiated fields of the feed at any arbitrary location, such as the surface patches or the observation points, an interpolation scheme is applied. The two- dimensional interpolation implemented is linear in 4 and of sec- ond order in B . For these three feed models, a three-dimensional view of the density of the PO currents over the first surface is plotted as soon as any feed parameter is changed, to test the quality of the illumination of the reflector surface.

The last feed model is an array of cos-q elements (Fig- ure 5). The user can introduce, delete, and relocate the individual elements of the array. The Graphic Area shows the three-dimen- sional view of the illumination produced by the selected element. The contribution to the radiated field of the antenna due to each element of the array with unit excitation is computed separately and stored. Later, the user will be able to select the excitations on the Array Synthesis Module. The concept of a power matrix is used as in [ 131 for the radiated power considerations.

3.3 Physical Optics Module

The task of the PO module is to calculate all the set of cur- rents over the surfaces of the antenna, as described in Section 2. Once the computation is finished, a color map of the surface-cur- rent density is plotted. This is usually the most time consuming part of the analysis.

3.4 Analysis Module

This module computes the fields produced by the antenna at a set of observation points selected by. the user. The observation points can be in the far-field region or in the aperture region. The user can also select the different effects to be considered, as shown in Table 1. In the far-field computation (Figure 6a), the user selects the type of pattem (4 cuts, 8 cuts, or two-dimensional patterns in the U-V domain), as well as the number of observation points. In the aperture-field computation (Figure 6b), the user can select the observation points along any of the principal axis or across any of the principal planes of the antenna.

3.5 Graphics Module

The Graphics Module (Figure 7) is used to represent all of the computations of the analysis and design process. Thus, the selected geometry, the illuminated surfaces, and the computed fields can be represented in this window. For the representation of the two-dimensional cuts of the computed fields, the module shows the value of the maximum and minimum values of the co-

96 IEEE Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005

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Figure 5. The cos- q and array feed models.

Figure 7. The PO current density for the dual reflector exam- ple.

Figure 9. A three-dimensional representation of the co-polar pattern for the dual reflector example.

5

-5

-10

-15

-20

-25

-30

-35

4 5

2 Y

z Figure 11. The scattered field on the offset plane for the dual reflector example. , Figure 10. The aperture field for the dual reflector example.

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Figure 6a. The Physical Optics analysis window for the far field.

Frequency Disk Diameter (2a ) P

Figure 6b. The Physical Optics analysis window for the aper- ture field.

8.4 GHz 0.11826 m

1

polar and cross-polar components. Moreover, two cursors are plotted in the window, to track the data points while the computed values are shown. Different representations are available for the representation of the field in three dimensions: a contour plot, a Cartesian plot, a'polar plot, and a spherical plot. In all cases, it is possible to select the co-polar or cross-polar component, as well as the phase or magnitude, to be plotted. All the figures can be exported to a file and saved in a . J P G or . BMP format.

S

3.6 Array Synthesis Module

0

This module allows for changing,the excitation of each array element. The window shows the pattern obtained with any excita- tion vector selected by the user. The resulting pattern can be saved for further plotting in the Graphics Module.

3.7 Output Module

The Output Module is used to export the design data to archives. The geometry can be saved in ASCII files containing the nodes and triangles of the discretization process. The computed field can be saved in standard ASCII files containing the magni- tude and phase of the co-polar and cross-polar components of the electric field. Besides this, the user can use the Project Manager to save the actual state of the simulation to a file with an internal format, . ica, which can be reloaded in later sessions.

98

Table 2. The Gregorian antenna geometry.

1.375 m

Eccentrici 0.45 m

Table 3. The feed parameters.

Configuration I Dual G r e g z a q I Polarization I LinearX I

4. Application Examples

In this section, we present the results of two reflector antenna configurations analyzed with the ICARA software in order to show its capabilities. As we will show, the ICARA results agree well with those obtained with a well-recognized code such as Grasp8-se (Version 8.2.5).

4.1 Gregorian Dual-Reflector Antenna

The selected geometry is the same as that plotted in Figure 4, and the parameters are summarized in the Table 2. In this example, we have selected a feed model of the type "disk of electric cur- rent," with the parameters described in Table 3. These ensure a taper illumination of -12 dB at the subreflector edge direction.

The PO current density over both surfaces is shown in Fig- ure 7. Figure 8 shows the antenna's far-field pattern in the eleva- tion plane ( 4 = 0") for B between -35" and 5 " . Good agreement with the Grasp8-se results is shown in the figure. To compute the radiation patterns, the spillover and subreflector blockage effects were been taken into account. For the Grasp8-se results, a Gaussian-beam feed model was used, with the same illumination level of -12dB at the subreflector edge direction. Figure 9 shows a three-dimensional representation of the co-polar pattern. Fig- ure 10 shows the co-polar field magnitude computed by ICARA at the aperture defined at z = 0.5 m. It is possible to identify an upper zone at the aperture dominated by the main reflector-surface radia- tion, and a lower region dominated by the spillover contribution, this last region showing a null corresponding to the subreflector- blockage effect. Figure 11 presents the co-polar field magnitude, sampled at the offset plane ( y = 0), showing the different effects such as the main-reflector scattered wave, spillover, subreflector blockage, and the back lobes of the antenna.

4.2 Single Paraboloid Fed by an Array

The following example consists of a parabolic surface fed by an array of seven elements. We selected this geometry, which is

IEEE Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005

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Table 4. The location of the feed array elements (dimensions in the same proposed in [13], in order to compare our results with wavelengths). those previously published.

The reflector had a circular aperture diameter of 108.152, a focal length of 94.872, and an offset height of 70.942, where A is the wavelength. The location of each array element is shown in Table 4. All the elements had linear horizontal polarization, and they were pointed to a common target at (66.192, 0, -83.322). f ie element radiation was modeled with a cos-q feed, with qx = 2.8 and qy = 3.6. The operating frequency was 300 MHz.

Elements Method [I31 ICARA ~~~

1 - 46.48 dBi 46.53 dBi OD 48.61 dBi 48.63 dBi

CFM 48.04 dE3i 48.03 di3i 7

Table 5. The reference and computed gains. Figure 12 shows the radiation pattern of the antenna when it

was fed only by the central element. By using the Array Synthesis I I Number of [ Optimization [ Gain Gain Window tool, shown in the figure, we changed the excitation vec- tor of the array to fit the Optimum Directivity (OD) and the Con- jugate Field Matching (CFM) conditions described in [13]. The directivity results for these cases are shown in Table 5, compared to those obtained in [ 131.

5. Conclusions,

The ICARA software for the analysis of reflector antennas has been presented. It has a fi-iendly graphical interface for the design of single- or dual-reflector antennas, for both the analysis procedure and to show the graphical results. Various feed models can be selected to illuminate the surface. Some of them are valid only when the surface is in the far field of the source, but there is also a suitable option for the cases when this is not true. Besides this, a feed array can be considered, and the software contains a tool for defining the excitation vector and watching, at the same time, the final composite pattern of the antenna. Typical reflector antenna effects, such as blockage and spillover, can be taken into account. The software is able to import numerical data for the reflector surface and the radiation pattems of the feed, in order to perform simulations of real measured surfaces and feeds. ICARA is a useful tool for reflector-antenna engineering, and also for educa- tional purposes. A student version will be downloadable from http://www.com.uvigo.es/ant.

-35 -30 -25 -20 -15 -10 -5 0 5 e

Figure 8. The far-field pattern in the elevation plane for the dual reflector example.

6. Acknowledgements

This work was supported by FEDER-CICYT (TIC2001- 3330) and Xunta de Galicia (PGIDIT02PXIC322 1PN).

7. References

1. S. Silver, Microwave Antenna Theory and Design, New York, McGraw-Hill, 1949.

2. J. H. Kauffman, W. F. Croswell, and L. J. Powers, “Analysis of Radiation Pattems of Reflector Antennas,” IEEE Transactions on Antennas and Propagation, AP-24, January 1976, pp. 53-65.

3. J. B. Keller, “Geometrical Theory of Diffraction,” J. Optics Soc. Amer., 52, 1962, pp. 116-130.

Flgguw 12

Figure 12. The co-polar field of the single reflector example when fed only by the central element.

IEEE Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005

4. R. G. Kouyoumjian and P. Pathak, “A Uniform Geometrical Theory of Dieaction for an Edge of a Perfectly Conducting Sur- face,” Proc. IEEE, 62, 11, November 1974, pp. 1448-1461.

99

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5. Y. T. Lo and S. W. Lee. Antenna Handbook, Theory Applica- tions and Design, New York, Van Nostrand Reinhold Company rnc, 1988.

6. L. Dim and T. Milligan, Antenna Engineering Using Physical Optics, Practical CAD Techniques and Software, Nonvood, MA, Artech House, 1996.

7. P. U. Ufimtsev, “Elementary Edge Waves and the Physical n e - ory of Diffraction,” Electromagnetics, 11, 1991, pp. 125-160.

8. C. A. Balanis, Antenna Theory: Analysis and Design, Second Edition, New York, John Wiley & Sons, 1997.

9. A. Marcos Arias Acuiia, J. Oscar Rubiiios Lbpez, Ifiigo Cuiiias Gbmez, and Antonio Garcia Pino, “Electromagnetic Scattering of Reflector Antennas by Fast Physical Optics Algorithms,” Recent Res. Devel. Magnetics, 1,2000, pp. 43-63.

10. R. F. Harrington, Field Computation by Moment Method, New York, IEEE Press, 1993.

11. F. Obelleiro, J. M. Taboada, J. L. Rodriguez, J. M. Bertolo, “HEMCUVI: A Software Package for the Electromagnetic Analy- sis and Design of Radiating Systems On Board Real Platforms,” IEEE Antennas and Propagation Magazine, 44, 5 , October 2002, pp. 44-6 1.

12. Y. Rahmat-Samii and W.A. Imbriale, “Anomalous Results from PO Applied to Reflector Antennas: The Importance of Near Field Computations,” IEEE International Symposium on Antennas and Propagation Digest, 2, June 21-26, 1998, pp. 816-819.

13. P. T. Lam, S.-W. Lee, D. C. D. Chang, and K. C. Lang, “Directivity Optimization of a Reflector Antenna with Cluster Feeds: A Closed-Form Solution,” IEEE Transactions on Antennas and Propagation, AP-33, 11, November 1985, pp. 1163-1174. @

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Eator‘s Comments Continuedfrom page 56

In its simplest mode, the fingerprint reader can be configured to replace the need to enter multiple usernames and passwords, including a system-level password for booting up the system. Thus, when an application prompts you for a password, you can swipe your finger across the fingerprint reader, and then choose the appropriate usemame/password combination (or combinations of other text, including name and address) from a popup widow. This doesn’t represent a possible security problem, because the IBM/Lenovo Embedded Security Subsystem stores the authentica- tion information separately in hardware in encrypted form. In its most secure mode, the fingerprint reader provides true two-factor authentication. You can configure the notebook to require both a successful fingerprint swipe and the entry of a pass-phrase to gain access to the computer, or to selected folders or files. The Embed- ded Security System can also be configured to provide on-the-fly hardware encryption and decryption of folders or files, including your whole “c:\” drive. If you make proper use of the security built into this notebook, your information is probably as safe as it can be on a notebook computer, period. The implementation is about as unobtrusive to normal operation as possible, and the hardware- based encryption seems to have minimal impact on performance.

If you carry data on a notebook computer the compromise of which could be damaging to you or your company, read that last paragraph again. This is serious, well-implemented security.

There are also a number of other features on the ThinkF’ad T series of notebooks that make it obvious that a great deal of good design and experience in using notebook computers has been involved. There is an Active Protection System for the hard drive. This senses rapid changes in acceleration (for example, when the notebook is dropped), and very quickly stops the hard drive and parks the heads to reduce the possibility of a hard-disk crash. There is also an improved shock-absorbing hard-disk mounting system. There is rescue and recovery software that goes significantly beyond what is included in Windows X P Professional. It provides restoration to previously saved system images, including data and applications. It also includes diagnostic and repair software that can help recover a crashed system even i f you can’t get the oper- ating system to boot (fortunately, I haven’t had to try this, but I’ve read through the specifications and instructions).

I’m convinced the built-in spatial-diversity antenna system is one of the best WiFi systems currently available on a notebook. I have often been able to connect in fringe-signal situations when those using other WiFi systems have not. The T42 series also includes Bluetooth connectivity, although I have not had any rea- son to try this. One feature that can be really useful is a built-in LED light at the top edge of the display. It provides keyboard illu- mination for situations where you have the display brightness tumed down and the ambient light level is low (e.g., on airplane flights where everyone else is sleeping and you don’t want to tum on the overhead light).

I want a notebook computer with a full-size keyboard that I can easily carry in my briefcase, without having to compromise on capabilities. The T series is the best combination of features and compromises I’ve found for this. The footprint is about 9.75 in by 12.25 in by about 1 in thick (with the 14.1 in display), and weighs about 4.5 lbs with the optical drive installed. The screen is avail- able with available resolutions of 1024 x 768 and 1400 x 1050 in 14.1’ in and 15.0 in sizes, and 1600 x 1200 in the 15.0 in size. The

Continued on page I05

100 /€E€ Antennas and Propagation Magazine, Vol. 47, No. 2, April 2005