460 IEEE TRANSACTIONS ON BROADCASTING, VOL. 44, NO. 4, DECEMBER 1998

ON THE RLSA ANTENNA OPTIMUM D

Konstantinos Kechagias, Elias Vafiadis, Member, IEEE, and Joh alos, Senior Member, IEEE Radiocommunications Lab., Department of Physics, Aristotle University of Thessaloniki,

Thessaloniln GR-540 06, Greece

Abstract An optimal design for RLSA (radial line slot array) antenna useful for IDBS reception is presented. Classical geometries and structures given in the literature are first used. I t is €ound that in some cases these are not suitable. So, optimization techniques by using the right objective functions have been applied. Two different methods were developed and three antennas were designed. Numerical results and comparisons with other similar antennas give the advantages of our design.

I. Introduction Satellite communications have a tremendous

growth during the last decade. Only in .Europe satellite TV channels, broadcasting in 24 languages, have increased from 48 to 265. I t is expected by 2005 that more than 1200 TV channels miill be brought into action. According to a recent study[ 11, a large amount of the above will come from DBS (Direct Broadcast from Satellite).

DBS can be received via small aperture antennas with less than 35dBi gain. Various types of appropriate antennas, including p,srabolic reflectors, microstrip arrays and radial line d o t arrays (RLSA) have been proposed. Parabolic reflectors are the most widely used. However more compact, with low profile and less demanding mounting, easy installation and rigid construction antennas are desirable. Mircostrip antennas posses the above characteristics, but their efficiency and cost is inadequate.

A good alternative solution could be a slot antenna array. Such an array is the RLSA antenna which initially has been proposed by M. Ando et. a1.[2, 61. I t belongs to a class of annular slotted radial waveguide antenna. The first study of such a n antenna, operating in Ku-band, has been given by Goebels and Kelly[7], and later by Savov and Hiristov[8]. A recent work by Davis and Bialkowski[S] reports experimental investigation for a n RLSA antenna, which is being developed in Australia. Their study has shown a high radiation efficiency as well as an excellent suitability for DBS reception.

In the design of a n antenna for a predetermined structure, the best possible performance should be achieved. The above leads to the problem of performance optimization. The field of global numerical optimization has gained a great advance

during the last decade[l0, 111. However a few studies, concerning optimal antenna synthesis, have implemented such methods[l2, 131.

In this paper the problem of the optimal design of RLSA antennas is addressed. The synthesis is performed via simulating annealing or enumeration of all possible configurations. The structure of the antennas as well as the underlying assumptions are similar to that proposed in [2, 31. Single or double layer antennas are presented and slot positioning along spiral or annular rings will be examined.

11. Study of Ando et. al. Geometry The structure of the antennas, which is presented

in Figs. l(a) and 2(a), is that proposed by M. Ando et.a1.[2, 31. The two layer antenna consists of a twofold waveguide, which is formed by three equally spaced, parallel and concentric plates. The single layer one involves a radial cavity. The power flow in these antennas is presented in Figs. l(c) and 2(c). The signal is fed into the antenna a t the center of the rear side, through a coaxial cable probe, formed from the extension of the cable’s center conductor. The field produced in the structure excites a slot array on the top plate, which in turn radiates in free space.

In the two layer antenna a radially outward wave is created. This is reflected at the outer perimeter from a bifurcation, consisting of two metallic rings inclined by 450 and is transferred to the upper waveguide. For analysis purposes only the inward (for the double layer antenna) or the outward (for the single layer) traveling mode is taken into account. In order to ensure this condition, in double layer antenna an absorber is placed at the axis of the upper waveguide while placement of a n absorbing material in the perimeter of the single layer antenna is not so important. That is because the power that reaches there is negligible.

I n both types, underneath the slot array, a slow wave structure is implemented, by means of two sheets of dielectric material. This configuration has chosen as a trade-off between the wavelength reduction and overall dielectric losses. One of the materials has a relatively high dielectric constant, E ~ ,

which yields to a significant wavelength reduction, but also to a slightly increased loss. The other one has both lower dielectric constant, E ~ , and losses. These

Publisher Item Identifier S 0018-93 16(98)09559-6 0018-9316/98$10.00 0 1998 IEEE

characteristics are common to low cost and commercially available materials.

. .

( 4 (3) ( 4 Fig. 1 The two layer RLSA antenna. (a) Structure, (b) Slot

Aperture, (c) Power Flow

(a) (b> ( 4 Fig. 2 The Single layer RLSA antenna (a)Structure, @)Slot

Aperture (c)Power Flow

On the top of the antenna there is an aperture with slots which form a highly directive array. The radiator element consists of a pair of slots. Different kind of pairs are used depending on the polarization. The radiators are placed along concentric rings. The main goal of this study is the determination of the optimal radii of the rings.

Waveguide mode analysis reveals that, underneath the slot array, where the two dielectric materials coexist, the only possible modes are the TM ones[5]. We assume that only the angle independent modes exist. We also assume that only the inward or outward, depending on antenna type, travelling wave modes are taken into account. Under the above assumptions the eigenvalue equation is of the following form:

(1) ~ - k , i c o ~ h j J k , 2 - k : . d i ) . ~ i n [ ~ ~ . d,)=O

550

500

450

5 400

h

E xu v

350

300

250

0 20 40 60 80 100

d,/d (Yo) Fig. 3 The propagation constant and the wavelength inside the waveguide, versus the percentage thickness of the upper

dielectric to the total one. Solving (1) we can find the unknown k,. Fig. 3

shows kc and h, for one case with = 4.5, c2 = 1, a t 12GHz. I t can be shown that k, and ,Ic depend on the total thickness d(=dl+d2) and ratio dl/d. I t is assumed that only the basic mode exists.

As the wave propagates along the radial direction, a par t of power is radiated from the slots. We assume that, due to radiation, the field decays exponentially [2] . Taking into account the cylindrical geometry of the structure, we can write the excitation coefficients in the following form:

where a(m-1) is the attenuation coefficient. If a two layer antenna is considered the wave propagates inward and a must take positive value, otherwise it must be negative. The amplitude of the excitation coefficients for various values of a as a function of the radial distance are given in Fig. 4. The structure of a unit radiator (pair of slots) is given in Fig. 5. I t is defined as a pair of two perpendicular slots[2], numbered #1 and #2 respectively.

For circular polarization the two slots are excited with a d 2 phase difference and almost the same amplitude. They both are inclined by the same angle from the radial direction, so they couple with the radially inward (or outward) travelling field by the same factor. I n general the orientation of the slots can

\ / \ / be such that only the desired polarization waves are coupled into the cavity.

M. Ando et. a1.[2], have published a series of papers concerning the design of RLSA antennas in the 12GHz band, utilizing the radiator described above. Several such pairs, are positioned in a spiral geometry by using a recursive procedure. The antennas appear to behave as broadside both in theory and experiment. According to our numerical procedure it was found that there are several cases where the antenna

are the thicknesses of the dielectric layers are the relative permitivities of the layers with are the corresponding wave numbers, is the unknown propagation constant in the waveguide.

462

behaves as a Bayliss type. An example of such a pattern taken from 2184 slots placed along a spiral is given in Fig. 6.

0 0.00 0.05 0.10 0.15 0.20 0.25 0.30

Radial Distance r(m) Pic 4 Amnlitiirl~ o f t.hP slot's excitation coefficients versus _ _ I___ -__. - _.._-.______. .. - ~ . . - - m . - ----- the radial distance, r , for different attenuation coefficients

a (m-1).

X

-Y

Fig. 5 Slot pair used as a unit radiator.

In the above case the slot coupling, was ignored. I t is assumed that the slot array is lying on the xy plane with the center at the origin. The angles are measured from the x axis to the center of each slot.

Keeping in mind tha t the relative positions of the slots in each pair are constant, we consider pairs being in polar positions. According to [2] the radial difference between polar pairs is hg/2.

We also can find that the amplitudes of the exci ta t ion coefficients b e t w e e n t h e po la r radiators differ by 0.1-1%, depending on the attenuation coefficient a and their distance from the center. As the positioning procedure produces slots with constant inclination with respect to radius, it can be assumed that two polar radiators are identical elements excited with opposite amplitudes (phase difference equal to n).

The array factor of the two radiators, with reference the slot which is closest to the center, is written

where k , is the free space propagation constant, r is the distance of the nearest to the center

radiator and

= sin@). COS(+)

-5 t c I

(4)

Slots 21 84 Placement along spiral

Reproduction from [Z]

-80 -60 -40 -20 0 20 40 60 80

Angle (")

Fig. 6 Pat te rn of a 2184 slot array with Bayliss performance.

The normalized amplitude of the array factor becomes

lAFl =icos[ko . u[r + + :)l=isin[ko . u[r + $))I (5)

The angles of maxima are at:

while t h e corresponding minima at:

Om,, and 0,,, can be found to be near and almost symmetrical from both sides of 00. Narrow slots

463

'b,

e, 6 0.505

$ 0.500 z n 2 0495 a ' 0.490

smaller than or equal to 112 in length are broadside elements with wide HPBW and their presence in the array cannot alter the previous conclusion.

The radiation pattern of the antenna can be constructed from the superposition of the pattern of polar slots and it seems that maximum at 00 is not possible.

/- ....... A . . . . . s

.. R

v .-. ,.. - .... *:.. ... ..... ..... ........ .... - ......

- ** . . .................. .. .... ........ .... . E "

* a * .. > - . . . . - -2 a

.. . I ..... . . . . . . . . . . . ... - .. ..........

.-

Fig. 8 The results given by the pair match algorithm applied on the array described in [2]. (a) matched pairs, (b)

unmatched pairs.

In order to confirm the validity of the approximations made before an algorithm was designed for the determination of the position of the non-polar and polar radiators.

At the completion of the algorithm two lists were made. The 1st list contains the non-polar, while the 2nd

one c'ontains the polar radiators. The program execution implementing the algorithm of the slot position as described in [%] gives the results shown in Fig. 8. From this figure we can see that most of the radiators are polar. Only 42 radiators or 3.85% of the overall are unmatched.

Fig, 9 shows the difference of the matched radiators distance from the center. For the majority of the cases the divergence from h$2 is less than ?1.5%.

The same results can be derived from Fig. 10,

183

where the divergence of the matched pairs angles from 1800 is shown. Again for the majority of cases the error is less than k1.5%.

- 2 . . . . .

0'515 E 0.510 1 *:- -12

*. . . . 1 7 6 ' I * ' I * ' I I ' I

0.10 0.15 0.20 0.25 0.30

Radius (m) Fig. 10 Divergence of the matched pairs from 180°, for the

positioning described in [l]. ' I ' I ' I ' I ' I

0 , 0 Numerical Results - , Theoretical Results

0.05 0.10 0.15 0.20 0.25 0.30

Radius (m) Fig. 11 Array factor maxima and minima of the diametrical

slot pairs. The Theoretical Results are calculated from (6) and (7), while the numerical are based on the exact

calculations.

464

From the resultant pairs, maximum and minimum values of the array factor around 0 0 are verified. Fig. 11, for operational parameters given in [Z], shows the theoretical (see Eq. (6) and (7)) and accurate values. It is obvious that the computational results are in agreement and confirm the validity of our first assumptions.

The same behaviour was found from a sequential increase of the number of radiators of the array. Figs. 12 and 13 show the main lobe shape and the corresponding geometry of the array for different number of slots. No assumption about polar pairs has been made. For 10 and 50 slots the spiral is not completed and maximum value appears to be near 00. For 100 and 200 slots the main lobe is shaped as in a Bayliss array.

11. R i n g Slot Array Design In order to have polar slot pairs in equal phase and

amplitude, ensuring the broadside operation, we place the radiators along concentric rings. Each ring contains the maximum even number of slots, without overlapping between pairs. For each slot there is a polar one excited with the same amplitude and phase.

The slot rings can be arbitrary, within a predetermined overall radius of the structure. The slots should be positioned in a way such that the antenna exhibits its optimal characteristics. Their number and radii should be chosen to optimize a selected index of the antenna.

From these requirements an objective (cost) function, which is to be optimized, can be formed Objective Function = Index

(8) + Penalty for ring overlapping + Penalty for diameter larger than the

predefined In (8) the feasibility constraints are taken into account as additive penalty parts. Taking under consideration all the above we have:

"-1

Penalty for ring overlapping = 1 f, ( 9 4 , = i

if R, 5

e . (R, - r , ) if R, > q+,

Penalty for diameter larger than the if R 2 R,, (" s .(Rn - R) if R < Rn

predefined =

where the rings are numbered from i=l to n in ascending radius order r, , R, is the inner and the outer radius of the i-th

R e, s

ring, respectively, is the predefined antenna radius, are sufficiently large, positive constants.

0

-2 5- 9 a, U 3 -4

E <

1 .- - Q

V -6 a,

m

0 -8 z

.- - E

-10 -10 -5 0 5 10

Angle (O) Fig. 12 The evolution of the main lobe for 10, 50, 100, 200

slots i n array.

:: \!-

I -

(c> (4 Fig. 13 Slot positioning for successively increasing number

of slots. (a)10 slots, (b) 50, (c) 100, (d) 200.

In our work SLL must be minimized where a closed form expression for it cannot be derived. Its values are calculated through an algorithm. The objective function (8) is a multiextrem one. In order to obtain the optimum construction its global minimum is seek, with respect to ring radii.

I t is known that the global optimization problems are very hard. In general, they belong t o a problem class named NP (Non Polynomial time) hard[l4] where the computational time required to solve the problem increases a t least exponentially with the number of independent variables (they have a t least exponential complexity).

Moreover, due to the fact that SLL cannot be written in closed form, no special properties (e.g.

465

Diameter 65cm

smoothness and differentiability) of the objective function can be used to simplify the process. The most well known classes of methods with weak requirements from the objective function are Genetic Algorithms[15] and Simulated Annealing[l6]. They are both stochastic procedures and are based in random search.

Even though there are :known domains in which one class outperforms the other, the choice among them is not so easy. In this work a variant of Simulated Annealing, named Cauchy machine[20], is used, because both the algorithm and problem presentation, in programmiing level, are simpler.

Global optimization procedures are slowly convergent. For evaluation of the construction capabilities and the optimization model fitness, the use of more robust algorithms, such as local optimization[l7] methods is desirable. They belong to the algorithm class P (Polynomial time)[l4]. Eventhough they do not give the optimal solution, they show a suitable performance for engineering purposes .

For initial evaluation of the construction a Modified Newton method has been used. This method runs several times with random initial values and from the results the best one is chosen. Despite the lack of theoretical support of such an approach, the results are comparable to that given by the slower Simulated Annealing.

Using the above mentioned assumptions with the optimization procedure a double layer antenna has been designed. In this antenna it is assumed that the first dielectric material is air. The structural parameters are given in Table 1.

The r:mg radii, as calculated from the optimization process are given in Table 2. The resultant slot array is shown in Fig. 1b.

Using the above geometry we can calculate the radiation pattern of the antenna. This pattern refers to f=12GrHz and a=5m-1. The pattern is almost the same for both main planes. That is because the antenna exhibits almost perfect circular polarization. The slight difference between the patterns is not visible in the graph. The half power beamwidth is about 2.4-0 while the side lobe level is -22dB.

The main consideration of the design is to keep the SLL as ltow as possible. For the majority of the cases SLL is under -16dB. Better behaviour is achieved for frequenctes closer to 12GHz.

The antenna gain, as a function of the attenuation factor a and frequency f, is given in Fig. 15. I t can be shown that for a 4 m - 1 and f=12GHz the gain is about 31.2dB. Higher value of gain (31.5dB) exists for f=11.9GHz and a = 3 and 4m-1.

The second antenna thait has been designed is a single layer one. In this antenna, the first dielectric is a n epoxic material with relaitive dielectric constant, at

Slot Width 1mm

12GH2, ~ ~ = 6 . 2 and thickness d1=1.5mm. The other is PP (Polypropylene) with ~ ~ ~ 2 . 4 and d2=4mm. The radiation pair characteristics is the same, as in the case of the double layer antenna. I t was found that we need 14 rings with radii given in Table 3. The resultant slot array is shown in Fig. 2b.

4 5

11.32 9 22.29 -

13.38 10 24.94 -

~~1 No. Of Rings

Slot Length 1.15cm 6 0.5"

Table 2 The radius of each ring, as given from the optimization

procedure. Ring Radius Ring Radius Ring Radius No. (cm) No. (cm) No. (cm)

11 26.45 12 29.71

f=IPGHz

E -10 8

-80 -60 -40 -20 0 20 40 60 80

Angle (') Fig. 14 Radiation pattern of double layer antenna for both

main planes, at f=12GHz and attenuation coefficient a =5m-1. The HPBW is 2.4O and the SLL is -22dB.

The radiation pattern (see Fig. 16) refers to f=12GHz and a = -5 m-1 and it is valid for both main planes. The HPBW is 3.10 while the SLL is -32dB.

For all frequencies and all attenuation factors, SLL is less than -20dB. The antenna gain, as a function of the attenuation factor a for several frequencies is given in Fig. 17. For a = -5 m-1 and f=12GHz (design

466

conditions) gain is about 34dBi. Maximum value exists for f=12.1GHz and a = -1 m-1 (35.2dBi).

l l ~ l ~ ~ ' l ~ ~ - ~ ' ~ l 31.5 -

31.0 -

30.5 - 30.0 -

29.5 - e

E .: 29.0 -

28.5 : 28.0 -

27.5 1

- a=2 - a=3 - a=4 - a=5 - a=6 -a=? - a=8 - a=9

11 7 11 8 11 9 12 0 12 1 12 2 12 3

f (GHz) Fig. 15 Gain of Double Layer an tenna as a function of

frequency f and attenuation factor a (m-l).

Table 3

IV. Alternative Ring Slot Array Design

An alternative design can be made by using different techniques. These have been applied first by Goebels and Kelly[7].

The structure of the antenna is similar to that of the single layer for circular polarization. Its difference is based on the feeder as well as the slot pair design and the r i n g positioning.

Instead of feeding through a metallic post a circular aperture a t the center of the rear face is used. The aperture is excited from a circular horn and creates the fields inside the radial cavity.

The absence of the metallic post creates a field which depends on the Bessel function of the first kind, instead of the Hankel one.

In the following discussion a cylindrical coordinate system (p, (p, z) is used. I t is assumed that the only mode inside the cavity is the TMiio. The field expression is of the form

HP cc-. ( k cos($) (1la> P

-80 -60 -40 -20 0 20 40 60 80

Angle (") Fig 16 Radiation Pa t te rn of the Single Layer, circularly

polarized antenna. 36 I I I

11.7 GHZ

-122GHz

.10 -8 -6 -4 -2

a(m-' ) Fig. 17 Gain of the Single Layer, circular polarization antenna, for all operating frequencies and attenuation

coefficient

where HP , H, are the magnetic field components in p and

kc

J , , J , '

We consider the radii where !HD I = (H, 1 . In this case

it is found[7] that, the current flows always on the cavity walls in the same direction (see Fig. 18). The total current is:

$ direction, respectively, is the propagation constant inside the cavity, are the Bessel function of first kind and order and its derivative.

I,o,o, = gP . I , . sin(+ + y) + g+ . I , . cos(@ + y) (12)

where iP and ib are the unit vectors of p and (p

y is mode's inclination with respect x axis and

(13) J ( k .PI I , a k ; J , ' ( k ; p ) = ~

P

These radii are discrete and it is found that they

467

4 5

correspond to the roots of J, (kc .p)

i' 90'

10.79 11 9 17.64 I 14 27.23 12.16 11 10 19.01 I 15 28.60

lSO' i I / I /

3-

270' Fig. 18 The current on an annular slot, at the points where

Assuming that in these radii a thin annular slot exists, we have the presence of a magnetic current density. The electric field on the slot, Esiot can be written as

IHp I := IH, I

E., = e p W P ) W + + " Y ) + 2 . , ' E S ( P ) . C O S ( + + Y ) (14)

To radiate a n arbitrary polarization field, two TMuo modes, with the appropriate difference both in amplitude and phase are required.

Two rings positioned a t the successive roots of J,(kc .p> are excited with opposite phases. For this reason, only those which correspond to either odd or even order roots are used.

Instead of using annular rings, field sampling can be performed by means of narrow slots. The unit radiator consists of normally crossed slots either + or X with respect to the radial direction. In our design X form radiators are used. That is because they need less ring thickness. Our design is based on slot rings with predetermined radii. However it is not necessary to use all of them. For optimization purposes the rings should be chosen to give the best antenna performance.

There are two possible cases for each ring. Either to participate in the array or to be absent. These two cases can be represented by a bit. Whenever it is 1, the corresponding ring is present in the antenna. If a maximum number of N rings can be used, the actual configuration could be described by a N bit binary number. I t becomes obvious that 2 N discrete configurations exist.

An algorithm can be made tha t executes a loop from i=l to 2N-1. Each i is transformed to a binary number. By considering the bits that have value 1 the rings that actually participate in the design are

that results in the optimum value of the chosen index. Following the above procedure and using the same

materials and slot dimensions as in the case of the Single Layer Circularly polarized antenna, we determine the optimum slot array geometry given in Fig. 19.

determined. I t is then easy to select the configuration _ _

Fig. 19 The optimum slot array configuration for 60cm diameter antenna

Table 4

The slot array consists of 3248 slots arranged in 15 concentric rings. The ring radii are presented in Table 4.

The radiation pattern in Fig. 20 refers to frequency f=12GHz and attenuation factor a =-5m-1.

It can be shown that SLL is less than -26dB, while the HPBW is approximately 3.60. The radiation pattern difference between the two main planes is negligible. From the above figures it can be seen that the antenna gives almost the same radiation patterns in both planes for all operating conditions. Symmetry in pattern characteristics, a t both sides of the design frequencies can also be concluded.

The lowest SLL level is almost -28dB and is achieved for f=12GHz and a =-8m-1.

The antenna gain for several frequencies and attenuation factors is given in Fig. 21. Maximum gain is approximately 32dBi, a t f=12GHz and a >-3m-1.

468

0

5

ig -10 v

-40 -80 -60 4 0 -20 0 20 40 60 80

Angle (“)

Fig. 20 The far field radiation pattern for the antenna of Table 4, for f=12GHz and a =-5m-1

-S-f=ll 7GHz - f = l l 8GHz

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

a(m”) Fig. 21 Gain of the 60cm diameter antenna for several

operating hequencies and excitation coefficients.

IV. Discussion In order to evaluate the efficiency of our

methodology, we compare our antennas with similar given in the literature.

In [3] a 60cm diameter, double layer RLSA with SLL more than -14dB is presented. Our corresponding antenna gives SLL less than -22dB in the design conditions, while only for the worst cases exceeds

The single layer, circular polarization antenna presented in [4] exhibits SLL of -17dB, which is 15dB more than our prediction (-32dB). Moreover SLL less than -20dB can be achieved in our worst case.

The arbitrary polarization antenna, which in our design yields SLL less than -26dB, can be compared with the linear polarization ones presented in [6] and [9]. The first shows SLL more than -15dB while the other about -18dB.

These comparisons show that optimization techniques make the improvement of the characteristics of the antennas possible.

-15dB.

V. Conclusion An optimization design of RLSA antennas has been

presented. Three antennas of 60cm diameter, through simulated annealing and complete enumeration for minimum SLL have been designed. The whole procedure was made by using the suitable objective functions. Numerical results have been given for all parameters and operating frequencies of the three antennas. The antennas have depicted performances better than those of similar designs, referred in the literature. The suitability of these antennas for DBS TV reception is obvious.

[31

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Konstantinos Kechagias was born in Thessaloniki, Greece in 1966. He received the B.SC. degree in Physics in 1989 and the Diploma of Postgraduate Studies in Electronics in 1994, both from Aristotle University of Thessaloniki, Greece. Since then he has been a research assistant in the RadioCommunications Laboratory a t the Department of Physics, Aristotle University of Thessaloniki, Greece and an Assistant

Professor at the Department of Electronics, Technological Educational Institute of Thessaloniki, Greece. He is currently pursuing his Ph.D. in antenna design. His research interests include antenna design, computational and CAD techniques for electromagnetics, microwave engineering and RF measurements.

Elias E. Vafiadis was born in Thessaloniki, Greece, in 1952. He received the B.Sc. degree in Physics in 1975 and the Diploma of Postgraduate Studies in Electronics in 1979, both from Aristotle University of Thessaloniki, Greece. On February 1981, he joined the Democritus University of Thrace,

a Research Associate at the Electrical Engineering Department, Xanthi, Greece. He received his Ph.D. degree in Electrical

Engineering from the Democritus University of Thrace, in 1985. From 1986 to 1993 he served as a Lecturer and as an Assistant Professor a t Microwaves Laboratory, Xanthi, Greece. Since 1993 he has been an Assistant Professor a t the School of Science, Aristotle

University of Thessaloniki, Greece. His research interest include the electromagnetic theory of waveguiding and radiating structures and CAD techniques for microwave circuits design. Dr. Vafiadis is a member of the Hellenic Physical Society. He is married, he has three children and lives in Thessaloniki.

John N. Sahalos (M’75-SM’84) was born in Philipiada Greece, in November 1943. He received the B. Sc. degree in physics and the Diploma in civil engineering from the University of Thessaloniki, Greece, in 1967 and 1975, respectively, as well as the Ph.D. in electromagnetics and the Diploma of Post- Graduate Studies in 1974 and 1975, respectively, from the same university.

From 1971 to 1974, he was a Teaching Assistant of physics a t the University of Thessaloniki, as well as an Instructor from 1974 to 1976 During 1976, he worked at the ElectroScience Laboratory, Ohio State University, Columbus, as a Post-Doctoral Fellow. From 1977 to 1985, he was a Professor in the Electrical Engineering Department, University of Thrace, Greece and Director of the Microwaves Laboratory. During 1982, he was a Visiting Professor at the department of Electrical and Computer Engineering, University of Colorado, Boulder. Since 1985, he has been a Professor a t the School of Science, University of Thessaioniki, Greece, where he is the leader of the RadioCommunications group. During 1989, he was a Visiting Professor a t the Universidat Politechnica de Madrid, Madrid, Spain. He is the author of three books and more than 190 articles published in the scientific literature. His research interests are in the area of applied electromagnetics, antennas, high-frequency methods, communications, microwaves and biomedical engineering.

Dr. Sahalos is a Professional Engineer and a Consultant to Industry. He has been honored with the Investigation Fellowship of the Ministerio de Education Y Ciencia (Spain). Since 1985, he has been a member of the URSI Commissions A and E He is also a member of five IEEE Societies, the New York Academy of Science and the Technical Chamber of Greece.