IEEE T R A N S A a I O N S ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. 2, MAY 1992 117

On the Coupling Characteristics of Coplanar Waveguides and Microstrip Lines

to Multilayer Dielectric Media Thomas S. Lind and Magdy F. Iskander, Senior Member, IEEE

Abstract-In medical diagnostics and geophysical well-logging applications of electromagnetic (EM) techniques, it is of critical importance to couple the EM energy to the object under interro- gation efficiently and with minimum external leakage. Coplanar waveguides and microstrip lines have been found experimentally to be very useful in these applications because of the low external leakage. Recently the spectral-domain technique was utilized to analyze the coupling characteristics of the coplanar waveguides and the microstrip lines to highly lossy multilayer dielectric media. It was observed that a superstrate layer may enhance an axial electric-field component and that the coupling to the lossy dielectric media gets stronger with the increase in the dielectric constant of the lossy medium.

In this paper, the spectral-domain technique is utilized to optimize the coupling performance of these structures to lossy dielectric media. It is shown that to enhance the coupling, higher frequencies should be used, the dielectric constant of the substrate should be small ( E = 2.56), and the width of the center conductor and gaps should be as large as possible. The dielectric constant of the superstrate should be low if a leaky-wave type of coupling is desired or large if a strong coupling by the transverse-field components is desired. Furthermore, the possibility of exciting surface waves in the coplanar structure is investigated. It is shown that the quasi-static TEM and T M o modes will be excited if a superstrate is present between a high dielectric lossy medium and the coplanar waveguide.

I. INTRODUCTION N medical diagnostics and geophysical well-logging appli- I cations of electromagnetic (EM) technique, it is of critical

importance to couple the EM energy to the object under inter- rogation efficiently and with minimum external leakage. For example, when methods for measuring changes in lung water content were developed, it was found that higher accuracy could be achieved if the measurements were based on the transmission rather than the reflection coefficient. Radiation type antennas and couplers are consequently not suitable for these applications because of their excessive leakage radiation which will obscure the transmission measurements across the object. Coplanar waveguides and microstrip lines, on the other hand, have proven experimentally to be ideal EM coupling devices for medical and geophysical applications [1]-[3]. However, these devices are guiding rather than ra- diating structures, and efforts should be made to analyze how they effectively couple the energy into high-dielectric-

constant lossy media. These analyses will identify critical parameters that control the coupling efficiency and may lead to their optimization and significantly improve the measurement techniques.

We utilized the spectral-domain technique to analyze the coupling characteristics of the coplanar waveguide to high- dielectric-constant lossy media [4]. Based on extensive anal- ysis of the values and the spatial distribution of various components of electric and magnetic fields, it was observed that the transverse electric-field components are much stronger above the substrate when the coplanar waveguide was placed in direct contact with a high-dielectric-constant lossy medium. These stronger transverse fields thus have an improved pen- etration in the high-dielectric material. It was also found that a lossless superstrate between the high-dielectric lossy medium and the coplanar waveguide sets up an axial electric- field component E, (surface wave type) which exponentially decays as it penetrates the lossy medium. Furthermore, it was found that the fields coupled to the thick dielectric lossy medium could be controlled by varying the height of the superstrate. A comparison between the coplanar waveguide and the microstrip line was also made and it was found that the coplanar waveguide couples the energy more efficiently to high-dielectric-constant lossy media [4].

In this paper the spectral-domain technique is utilized to further optimize the coupling characteristics of coplanar wave- guides to high-dielectric-constant lossy media. The effects that thickness of substrate, width of slots and center conductor, frequency, and dielectric constant of substrate and superstrate have on the coupling characteristics will be investigated. The excitation of the axial electric-field component when a superstrate is present will be explained in terms of surface waves in the superstrate. It is shown that at the frequencies and for the substrates of practical interest, surface waves will not be excited in this region. On the other hand, in the superstrate region a quasi-TFiM mode was found possible in addition to a TM surface wave, which has an axial electric-field component. Therefore, in addition to the dielectric losses encountered in the coupled field, there will be additional losses encountered due to the excitation of the surface waves.

Manuscript received September 1, 1989: revised February 20, 1991. The authors are with the Electrical Engineering Department, University of

Utah, Salt Lake City, UT, 84112. IEEE Log Number 9106275.

11. ANALYSIS PROCEDURE

The spectral-domain technique has become by far the most popular method of analyzing the dispersion characteristics of

001~9375/92$03.00 0 1992 IEEE

118 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. 2, MAY 1992

microwave and millimeter-wave integrated circuits. It provides an elegant way of reducing a partial differential equation to ordinary ones which may then be solved analytically. The spectral-domain technique has been used to analyze the disper- sion and coupling characteristics of a coplanar waveguide to high-dielectric lossy media [4]. A detailed solution procedure has been described elsewhere [4], [5], so only a brief summary will be included here for completeness. Consider the four- layer coplanar waveguide shown in Fig. 1. Layer 2 represents the substrate, while layers 3 and 4 represent the coupling superstrate and the high-dielectric lossy media, respectively. We start by assuming an err propagation, where r = Q + jp , which helps us replace the partial derivative d2/dz2 in the wave equation by r2. Next we perform the Fourier transform of the TE and TM scalar wave function 9 (x, y) in the z-direction so that the resulting scalar functions would be independent of x and hence there will be no need for analytically expressing the x-dependence of the function. After utilizing a suitable expansion of the Fourier transformed scalar function in the remaining spatial coordinate y, we apply the boundary conditions at the interfaces between the various dielectric layers to determine the unknown expansion coefficients. The following set of coupled equations are then obtained:

G d T , r ) G12(T,r) B d 7 ) J d T )

where E, and E, denote the Fourier transform of the x- and z-dir?cted electric field in the slot, respectively, while j, and J, denote the Fourier transform of the x- and z-directed current density components on the metal, respectively. These electric-field quantities are obtained from the TE and TM scalar wave function using well-known equations [6]. The variable 7 was introduced in taking the Fourier transform with respect to the spatial variable x [4]. To solve (1) we use the method of moments. This involves expanding the electric fields in the gaps in terms of a known set of basis functions and applying Galerkin's method for testing [7]. Following this procedure we obtain the following set of equations:

[ G Z l W ) Gzz(T,r)] = [Jz(T, l (l)

M 00

n=l n=1 03

n=l n=l

where 00

where fjm(7) and (,(T) are Fourier transforms of the expan- sion function used to express the E, and E, components of the electric fields in the gaps. Expressions similar to those of Q,, %re obtained for P,,, R,,, and S,, in terms of G,(T) and C n ( 7 ) , and the dyadic Green's function Gzj(T,I'), i = 1,2, and j = 1,2. The propagation constant can then be found by making the determinant of the matrix (2) go to zero.

I x

1

Fig. 1. Four-dielectric-layer coplanar waveguide.

The spatial-domain expressions of the field are then found by taking the inverse Fourier transform with respect to T and recovering the spatial coordinate x in the field expressions [4]. In these calculations, a set of single-term expansion functions of the E, and E, fields was used to expand the fields in the gaps in the coplanar waveguide. We utilized expansions that include the singularity of the E, field at the metallic edges as described elsewhere [4].

111. OPTIMIZATION OF THE COUPLING CHARACTERISTICS

A computer program to solve (2) was written. In addition to calculating the propagation constant of coplanar struc- tures, the spatial distribution of the various field components was also determined by taking the Fourier transform of the spectral-domain expressions. Detailed analysis of these field components showed that a superstrate can be used to set up an axial component of the electric field E, and that the thickness of the superstrate can be used to control the energy coupled to the high-dielectric-constant lossy media [4]. It was also found that the magnitude of the axial-field component increases with the increase in the gap width in the coplanar waveguide. It was suspected that the coupled energy to the high-dielectric media could also be controlled by other parameters such as the width of the center conductor, thickness of substrate, frequency, and E, of the substrate. In this paper we examine the role of these parameters on optimizing the coupling characteristics -of coplanar waveguides to lossy dielectric media.

First, the effects of changing the dielectric constant and the thickness of the substrate are examined. The results showing the effect of the dielectric constant of the substrate were re- ported in Fig. 11 in [4], and Fig. 2 shows the effect of changing the thickness of the substrate. It may be observed from Fig. 11 in [4] and from Fig. 2 that the fields in the lossy high- dielectric-constant medium are reduced as E, of the substrate is increased. Fig. 2 shows that the thickness of the substrate has little effect on the field distribution when d > 1 mm, which is of practical interest. Fig. 3 shows that the transverse electric- field components increase with the increase in the dielectric constant of the superstrate. At the same time, an increase in the dielectric constant of the superstrate results in a decrease in the axial electric field as shown in Fig. 4. In other words, the increase in E, of the superstrate causes a decrease in the leaky-wave type coupling. It can also be seen from Fig. 4 that the height of the superstrate at which the E, field reaches its maximum value increases with the increase in E, of the

LIND AND ISKANDER: COUPLING CHARACTERISTICS OF COPLANAR WAVEGUIDES

~

119

cm _ _ - - - . I

: \ Y 4:- , , , . _ _ _ _ _ , ' ! " - _ _ - - - . \ . , . , - - - - - , " ' ! " ' . - - - - - . . I

, , - - - - -

. . . . . . . . . . . . ) , , . . . . . . . . . . . . . . . < I . . . . ,3j-, . . . . . . . . . . . , r r . , r r r r r r , ~ . . . . . . . . . . . .

X

X

(b)

Fig. 2. Spatial distribution of the transverse components of the electric field for (a) d = 2.0 cm, (b) d=0.1 cm. In both cases, the substrate has :,.z = 11. w = s = 1.0 cm, a lossy dielectric medium of E A = 60 +J20, and frequency of 1 GHz.

superstrate. Therefore, the choice of the value of E, of the superstrate is related to the choice of either maintaining leaky- wave type coupling (small E,) or relying on strong coupling by the transverse components (high E,). Fig. 5 shows that the fields in the high-dielectric-constant medium are greatly reduced with a reduction in frequency. Frequency is also the parameter that can be most easily changed while measure- ments are being conducted. Hence, variation of the coupling characteristics with frequency provides a simple procedure for controlling the coupling to the lossy medium. Finally, the effects of the width of the gaps w and the width of the center conductor s on the coupling of the field is shown in Fig. 6. The energy coupled to the lossy high-dielectric media is reduced as both the widths of the center conductor and slot are reduced.

Observations in this section indicate that the optimum cou- pling to a lossy high-dielectric medium is achieved at higher frequencies and when the coplanar waveguide is fabricated on a substrate of low E,. The choice of small or high E, for the su- perstrate depends on the type of coupling desired. The widths of the slot and/or the center conductor should be kept large. Howeyer, the sizes of the center conductor and slot are limited in practice by the overall size of the coplanar waveguide and the desirability of maintaining a 50-0 input impedance when the device is coupled to the lossy medium [ 2 ] . This should be taken into account when determining the size of the slot and the center conductor. It is of interest to note that similar

X

X

(c)

Fig. 3. Spatial distribution of the transverse components of the electric field for (a) a superstrate of ~~3 = 1.0, (b) a superstrate of ~ ~ - 3 = 2.56, (c) a superstrate of :,-3 = 11. In all cases, w = s = d = 1.0 cm, a lossy dielectric medium of ~ , .4 = 60 + j20, and frequency of 1 GHz.

observations have been made previously based on experimen- tal measurements on phantoms and animals [ 2 ] . Specifically, it was observed that coplanar waveguides made on a Lucite substrate ( E , = 2.56) have improved coupling as compared to those made on a substrate of E, = 10. When experimental difficulties were encountered with a coupler made on the E, = 10 substrate, new couplers were developed which were directly taped on the object with no substrate required [ 2 ] . In this case, a much wider gap width was utilized in the coplanar design and the coupling efficiency was improved significantly [ 2 ] . The analysis provided in this paper has analytically confirmed these experimental observations. It should be noted that coplanar waveguides of finite length were used in the experimental measurements [ 2 ] . These waveguides, however, were terminated by 50-0 loads (chip resistors) and hence resembles the two-dimension analysis described in this paper.

IV. SURFACE WAVES

Multilayer dielectric structures are capable of guiding

120 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. 2, MAY 1992

0.0 0.2 0.4 0.6 0.8 1.0

h (cm)

Superstrate of E, = 1.0 - Superstrate of E, =2.56 - Superstrate of E, = 11 .O - Superstrate of E, = 60.0

Fig. 4. Variation of the magnitude of the axial electric-field component IE;1 with the relative height of the superstrate layer in a coplanar waveguide. Results are shown for three different values of the dielectric constant of the superstrate. In all cases, w= s = d = 1.0 cm, a lossy dielectric medium of cr.4 = 60 + j 2 0 , and frequency of 1 GHz.

X

( b)

Fig. 5. Spatial distribution of the transverse components of the electric field for (a) a frequency of 0.5 GHz, (b) a frequency of 1.0 GHz. In both cases, the substrate has E,Z = 11, w= s = 1.0 cm, and a lossy dielectric medium of ~~4 = GO + j 2 0 .

surface waves. Two well-known structures which can support surface waves are the dielectric-slab waveguide and the dielectric-coated conductor. When a surface wave is excited on a transmission line such as the coplanar waveguide and

X

. . . . . . . . . . i . . . . . . . . . .

/////A t, d

em C 4.p - _ _ - -

- - . - _ - - I

_ _ _ - . , . _ - - - - - . . . . . . . . . . . . . . . . . .

3 + , , , . . . , . . , . , ( , . . . . . . . . . . . . . . l l , , ~ c , , \ ~ l I , - ~ . . , . . . . , . . , , . . . . , . , i , . . . . . . . . . . .

I I a I I / / / /

X

Fig. 6. Spatial distribution of the transverse components of the electric field for (a) w= 1.0 cm and s = 0.5 cm, (b) w= 0.5 cm and s = 1.0 cm, (c) w= s = 1.0 cm. In all cases, the substrate has c , . ~ = 11, d = 1.0 cm, a lossy dielectric medium of c',.4 = GO + ~ 2 0 , and frequency of 1 GHz.

microstrip line, it will introduce additional losses due to power leakage. Rutledge et al. [8] discussed the possibilities of exciting surface waves in coplanar transmission lines surrounded by air and the additional losses that would be encountered. Both the dielectric-slab waveguide and the dielectric-coated conductor geometries have been thoroughly investigated and their analyses have been widely discussed [8]. They showed that to excite surface waves in a dielectric-coated conductor, the propagation constant of the surface waves must exceed the propagation constant of the structure.

Analyses of surface waves in coplanar waveguides and microstrip lines coupled to a lossy dielectric medium through a superstrate layer may be based on those of dielectric-coated conductors as described in [8]. Specifically, the coplanar waveguide shown in Fig. 1 can be divided into two cases, A and B, as shown in Fig. 7. Case A is the common dielectric-

.-

LIND AND ISKANDER: COUPLING CHARACTERISTICS OF COPLANAR WAVEGUIDES 121

CASE A I CASEA Air

Fig. 7. A four-dielectric-layered coplanar structure divided into two cases where surface waves can occur.

/ I Conductor X

t ' Conductor

( b) Fig. 8. Structures supporting surfaces waves. (a) An air gap with a perfect conductor on one side and a high dielectric on the other. (b) Dielectric-coated conductor.

coated conductor with a dielectric layer placed on an infinite conductive plane with air on the other side as shown in Fig. 8(b). Case B is the opposite of Case A. It includes an air gap or low dielectric placed between the perfectly conducting plane and a lossy high-dielectric medium as shown in Fig. 8(a). By calculating the propagation constant of the entire coplanar structure and comparing it with the propagation constants of the surface waves in the super- and sub-strate regions, cases A and B, it is possible to examine the excitation of the surface waves in these regions. In addition, it can be seen from Fig. 8(a) that when the dielectric constant and losses of the top layer are high, the behavior of this structure will be similar to that of a parallel-plate guide, which can support the quasi-TEM mode and other possible higher order modes.

The spectral-domain analysis of Section I1 may be used to calculate the propagation constants of the entire coplanar structure such as rl, r 2 of Figs. 9 to 11. The characteristic equation for surface waves in both cases shown in Figs. 7 and 8, however, need to be found by solving the Helmholtz equation [9]. For simplicity we assumed the problem to be two- dimensional, hence allowing no variation in the y direction. By assuming an er.' propagation, where rS = a, + j p s , and then satisfying the boundary conditions at y = 0 and y = h or d,

0 1 2 3 4

d (cm) Fig. 9. Surface waves in a dielectric-coated conductor with E~ = 11. Propagation constant for a coplanar waveguide where w = s = 1 cm and E,.Z = 11 as a function of the thickness d. rl is the propagation constant for the coplanar waveguide when ~ , . q = 1, rz is the propagation constant for the coplanar waveguide when ~ , . q = 11, and r3 is the propagation constant for the coplanar waveguide when c^,.4 = 30 + j20 . All calculations were made at a frequency of 2.0 GHz.

the following set of equations can be obtained [9]:

2 = - tanh ( n t ) TE modes ( 3 4 7 2

= - tanh ( n t ) TM modes (3b) E 2 7 1

where

The only unknown in (3) is the propagation constant I?,, which can be determined for TE and TM modes. It can be shown from (3) that the lowest TM mode has no cutoff frequency and, consequently, is the mode that can first be excited. It can also be shown that more modes can be excited as the frequency or thickness of the dielectric substrate is increased.

Let us consider Case A in greater detail. In Fig. 9 we plotted the propagation constants for the surface waves in a dielectric with E, = 11 versus the thickness of the dielectric while the frequency was held constant. On the same plot of Fig. 9 we also showed the propagation constants for the coplanar waveguide having a substrate with a dielectric constant of ~ , 2 = 11 and for three different ~ , 4 . It is observed that when ~ , 4 = 1 (air), the propagation constant for the TMo mode exceeds the propagation constant for the coplanar waveguide and consequently can be excited at a thickness of about 1.8 cm. Because the propagation constant of the coplanar waveguide increases as ~~4 is increased, the possibility of exciting any surface waves becomes unlikely when the coplanar waveguide is coupled to media of high values of ~ , 4 .

The situation is different for Case B. The surface waves are expected to be excited at values of h (thickness of superstrate) at which propagation constant of the surface wave intercepts that of the coplanar structure. In Fig. 10, the propagation constant for the TMo mode is plotted as a function of the

122 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 34, NO. 2, MAY 1992

8.0 - U" \

c c ~ 6.0-

4.0 -

2 0 -

e- 8

kd

Fig, 10. Surface waves for an air gap with a perfect conductor on one side and a high dielectric of E,. = GO + j 3 0 on the other. Propagation constant for a coplanar waveguide where w= .s = 1 cm and E,.Z = 11 as a function of the thickness h . rl is the propagation constant for the coplanar waveguide when E ? . ~ = GO + j30, r2 is the propagation constant for the coplanar waveguide when z?., = GO + jG0. All calculations were made at a frequency of 2.0 GHz. A.,! is calculated for e,. = GO.

thickness of the air gap while the frequency is kept constant. First, whenever there is an air gap, a TEM mode propagation is expected and the propagation constant will be close to ko. It can also be observed from Fig. 10 that the TMo surface waves can be excited at a thickness h of about 0.22 mm. Consequently, whenever a superstrate is used, the TEM and TMo will become excited and this should increase the coupling to the lossy medium. The additional losses contributed by these surface waves can be determined following a procedure similar to that discussed by Rutledge et al. [8]. In our previous paper it was observed that the E,-field component became excited when the superstrate had a thickness larger than 0.25 mm [4]. It was also discovered that the thickness of the superstrate needed to excite the E, field does not change much as the dimension of the coplanar structure is changed. We observe from Fig. 10 that the propagation of the TMo surface wave crosses the propagation constant of the coplanar waveguide at about the same thickness of the superstrate. In Fig. l l (a) we plotted the excitation of the E, field in the coplanar waveguide. In Fig. l l ( b ) the surface wave in the superstrate was plotted as function of the height of the superstrate. Both plots were made at a frequency of 700 MHz, and the correlation between the surface waves and the excitation of the &-field component may again be observed at a superstrate thickness of approximately 0.45 mm. Based on the comparison of Fig. 8 in [4] and Figs. 10 and 11 of this paper, it is clear that the increase in the E,-field component reported in [4] for a superstrate thickness of h > 0.25 mm at 2 GHz and h > 0.45 mm at 700 MHz resulted from the excitation of the TMo surface wave mode. It should be noted, however, that the integrations over r involved in the quantities P,, , Qmn. R,, . and S,, of ( 2 ) will not be properly evaluated in some cases unless the integration path is deformed. For cases involving strong surface wave leakage and low material loss, there will be a pole in the complex r plane which crosses the real T axis and must be carefully considered as discussed elsewhere [lo].

8.0j :kd I 0

2 t

2 3 4 5 6 7 8

h ("1 ( b)

Fig. 11. Comparison of surface waves in a superstrate and excitation of the E , -field component in the coplanar waveguide at a frequency of 700 MHz. All other dimensions are the same as in Fig. 10. (a) Propagation constant for the coplanar waveguide and the TMo surface wave in the superstrate. (b) E, -field component in the coplanar waveguide.

V. CONCLUSION

The spectral-domain method is used to further optimize the coupling of coplanar waveguides to a lossy dielectric medium and to analyze some previous analytical [4] and experimental (21 observations made regarding the obtained spatial distribution of the various electric-field components. The effect of the thickness of the substrate, the widths of the center conductor and slot, the frequency, and the of the substrate on the coupled electric field has been discussed. From the results presented in this paper and others presented in an earlier contribution [4], it was found that to increase the coupling to the lossy dielectric media it is necessary to operate at higher frequencies, construct the coplanar waveguide on a substrate of small dielectric constant, and select a design where the width of the slots and/or the center conductor are as large as possible. When a superstrate is used, it should have a low dielectric constant to maintain a leaky-wave-type coupling. Al- ternatively, it should have a high dielectric constant if relying on the coupling by strong transverse field components. These observations regarding optimizing the coupling characteristics agree well with experimental observations reported earlier on an improved performance of these coupling structures [2].

We have also investigated the possibility of exciting surface waves in the coplanar waveguide to help analyze the char-

LIND AND ISKANDER: COUPLING CHARACTERISTICS OF COPLANAR WAVEGUIDES 123

acteristics of the various coupled E-field components. It was found that when a high-dielectric lossy medium is placed on top of the coplanar waveguide, the propagation constant of the coplanar waveguide becomes large, and, consequently, surface waves cannot be excited in the substrate. However, excitation of the TMo surface waves is possible whenever a superstrate is introduced, thus explaining the E, -field component when a superstrate is present. The cutoff frequency of the TMo surface wave mode agreed with the observation reported earlier regarding the variation of the different components of the electric field versus the width of the superstrate layer [4].

REFERENCES

[ 11 M. F. Iskander and C. H. Dumey, “Electromagnetic energy coupler/ receiver: Apparatus and method,” U.S. Patent no. 4,240,445.

[2] M.F. Iskander and C.H. Dumey, “Microwave methods of measuring changes in lung water,”J. MicrowavePower, vol. 18, pp. 265-275,1983.

[3] M. F. Iskander and C. H. Dumey, “Electromagnetic techniques for medi- cal diagnostics: A review,” Proc. IEEE, vol. 68, pp. 126-132, 1980.

[4] M. F. Iskander and T. S. Lind, “Electromagnetic coupling of coplanar waveguides and microstrip lines to highly lossy dielectric media,” IEEE Trans. Microwave Theory and Tech., vol. 37, pp. 1910-1917, 1989.

[5 ] R. H. Jansen, “The spectral-domain approach for microwave integrated circuits,” IEEE Trans. Microwave Theory and Tech., vol. MlT-33, pp. 847-881, Oct. 1985.

[6] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961.

[7] R. F. Harrington, Field Computation by Moment Methods. Montpelier, F L Krieger, 1982.

(81 D. B. Rutledge, D. P. Neikirk, and D. P. Kasilingam, “Integrated-circuit antennas,” Infrared and Millimeter Waves, vol. 10; Millimeter Compo- nents and Techniques, part 11, 1983, pp. 1-90,

New York: McGraw-Hill, 1961, pp. 163-171.

[lo] A.A. Oliner, “Leakage from higher modes on microstrip line with application to antennas,” Radio Science, vol. 22, pp. 907-912, 1987.

[9] R. F. Harrington, Time-Harmonic Electromagnetic Fields.

Thomas S. Lind was born in Oslo, Norway, on March 1, 1962. He received the B.S. and M.S. degrees in electrical engineering from the University of Utah, Salt Lake City, in 1987 and 1989, respectively. From 1987 to 1989, he was a research assistant in the Electrical Engineering Department at the University of Utah. In 1983, he received a degree in liberal arts from the University of Oslo, Norway.

He worked in the Royal Norwegian Army as an officer and instructor in 1981 and 1982. His fields of interest include microwave circuit design with emphasis on numerical techniques.

Magdy F. Iskander (S’72-M’76-SM’84) has been with the Department of Electrical Engineering at the University of Utah, Salt Lake City, since 1977, where he is currently a Professor of Electrical Engineering and a Research Professor of Materials Science and Engineering. In 1981, he received the University of Utah President David P. Gardner Faculty Fellow Award and was a Visiting Associate Professor at the Polytechnic University of New York. He spent the 1985 and 1986 summers at Chevron Oil Field Research Company as a Visiting

Scientist. From September 1986 to May 1987 he spent a sabbatical leave at UCLA and at the Harvey Mudd College. He spent the last four months of the sabbatical leave with Ecole Superieure d’Electricite, Gif-Sur-Yvette, France. His present fields of interest include numerical techniques in electromagnetics and the use of microwave methods for materials characterization and pro- cessing.

Dr. Iskander edited two special issues of the Journal ofMicrowave Power, one on “Electromagnetics and Energy Applications,” March 1983, and the other on “Electromagnetic Techniques in Medical Diagnosis and Imaging,” September 1983. He authored one book on Electromagnetic Fields and Waves, published by Prentice Hall, 1992; he edited the. first CAEME software book, 1991; and coedited a third book on Microwave Processing of Materials, published by the Materials Research Society in 1991. The holder of seven patents, he has contributed ten chapters to seven research books, published more than 90 papers in technical journals, and made numerous presentations in technical conferences. In 1983, he received the College of Engineering Outstanding Teaching Award and the College Patent Award. In 1984, he was selected by the Utah Section of the IEEE as the Engineer of the Year. In 1984 he received the Outstanding Paper Award from the International Microwave Power Institute, and in 1985 he received the Curtis W. McGraw ASEE National Research Award for outstanding early achievements by a’university faculty member. In 1991 he received the George Westinghouse National Award for innovation in Engineering Education. In 1986 he established the Engineering Clinic Program in the College of Engineering at the University of Utah. Since then the program has attracted more than 35 research projects from 16 different companies throughout the United States. He is also the director of the NSFDEEE Center for Computer Applications in Electromagnetics Education (CAEME). He coorganized symposia on “Microwave Processing of Materials,” held in conjunction with Materials Research Society meetings, spring of 1990 and 1992, in San Francisco. He also organized several workshops and special sessions in conjunction with IEEE symposia.