7 A-AO84 051 ARMY ELECTRONICS RESEARCH AND DEVELOPMENT COMMAND FO -ETC F/6 9/5

DESIGN OF SILICON DIELECTRIC WAVEGUIDE LINE SCANNING ANTENNAS F--ETCIU)AUG 78 K L KLOHN, R E HORN, H JACOBS

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MICROCOPY RESOLUTION TEST CHART

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RESEARCH AND DEVELOPMENT TECHNICAL REPORT

DELET-TR-78-19

' DESIGN OF SILICON DIELECTRIC WAVEGUIDE LINE SCANNINGANTENNAS FOR MILLIMETER WAVES •

DTI

MAY 3 1980Kenneth L. Klohn URobert E. HornHarold Jacobs

I Elmer Freibergs

ELECTRONICS TECHNOLOGY & DEVICES LABORATORY

August 1978

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4. TITLE (and Subtitle) " /TYPE OF REPORT & PERIOD

. .7 -e c-i-l e .tDesign of Silicon Dielectric Waveguide YechnicaLine Scanning Antennas for-Millimeter Wavess FE .-

S. AUTHOR(s) 7

" " S. CONTRACT OR GRANT NUMBER(s)

KennetWL ln Robert E.Horn

Harol d/acobs Elmer Freibergs N/A

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Dielectric Waveguide Perturbation SpacingMillimeter Waves Radiation AngleFrequency Scanning Antenna Angular ScanGuide Wavelengths

20. ABSTRACT (Continue on reverse side If necessary and Identify by block number)

The design and experimental findings of a novel approach for a relativelysimple, low cost, frequency scanning millimeter wave antenna are described. Theantenna consists of a silicon dielectric rectangular rod with periodic metallicstripe perturbations on one side. The feasibility of electronically scanningthrough a range of angles by varying the frequency fed into the silicon rod isft shown. Calculations were made to determine the allowable physical size of thesilicon rod in order to maintain a single fundamental mode of operation and theeffect which size variations and perturbation spacing have on the angle of--...

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20. radiation and the range of angular scan for a given frequency shift.Efforts covered the frequency range 55 GHz to 100 GHz with specific points ofinterest at 60, 70 and 94 GNz. The results of experiments conducted arecompared with the theoretical calculations.

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i L, TA -

I b o.. - ,. ,.' 't'

UNCLASSIFIEDSGCUMITY CLASSIPICATION OF T114 PA@6fUrMll 0 &WWte

CONTENTS

Page

INTRODUCTION 1

DESIGN CRITERIA 1

LINE SCAN ANGLE 4

EXPERIMENTAL RESULTS 5

SUMMARY AND CONCLUSIONS 8

ACKNOWLEDGMENT 9

REFERENCES 10

APPENDIX A

CALCULATION OF TRANSVERSE PROPAGATION CONSTANTS IN DIELECTRIC 30WAVEGUIDES

FIGURES

1. Minimum and Maximum Waveguide Dimensions, 60 GHz 11

2. Minimum and Maximum Waveguide Dimensions, 70 GHz 12

3. Minimum and Maximum Waveguide Dimensions, 94 GHz i3

4. Variation of Wavelength with Frequency 14

5. Variation in Guide Wavelength with Frequency as a Function 15of Size

6. Radiation Angle versus Frequency (60 GHz Design Frequency) 16

7. Radiation Angle versus Frequency (70 GHz Design Frequency) 17

8. Radiation Angle versus Frequency (94 GHz Design Frequency) 18

9. Effect of Xg on Radiation Angle 19

10. Effect of Perturbation Spacing d on Radiation Angle 20

11. Effect of Guide Size on Angular Scan with d= XI at 60 GHz 21Design Frequency

12. Test Setup for Measurement of Radiation Angle e versus 22Frequency

13. Silicon Waveguide with Perturbations

14. Polar Plot of Beam Angle:a. y-z Plane 24b. r-O Plane 25

15. Experimental Plot of Radiation Angle versus Frequency 26

16. Comparison of X Obtained Experimentally from the Radiation 27Angle with Theopy

17. Comparison of Theory and Experiment for Radiation Angleversus Frequency for Various Guide Sizes and PerturbationSpacings

a. (Silicon Waveguide # 2) ,28b. (Silicon Waveguide # 7) 29

TABLES

I. Minimum and Maximum Waveguide Sizes for Fundamental 3Mode EYl1

II. Comparison of Exact and Approximate Values for Guide 4Wavelength

III. Angular Scan for Various Size Guides (&fo = 8 GHz) 5

IV. Physical Characteristics of Experimental Waveguides 7

ii:

DESIGN OF SILICON WAVEGUIDE FREQUENCY LINE SCANNING ANTENNASFOR MILLIMETER WAVES

INTRODUCTION

Recent demands for a very high resolution radar in terminal homing formissiles and shells and for radar surveillance in general, have generated aneed for developing new concepts in low-cost millimeter wave antennas. Ameans of providing electronic line scanning rather than mechanical scanningis very advantageous in order to be able to reduce the system complexity andhigh cost. It is especially important to eliminate the use of gimbals tomechanically scan an antenna since they are expensive and slow. This reportdescribes the design and experimental findings of a novel approach for aside-looking electronic line scanner consisting of a dielectric (silicon)rectangular rod with periodic perturbations on one side. Angular scan inthis approach is achieved by varying the frequency. The numerical values ofthe scan angles are a function of operating frequency, waveguide size (heightand width) and perturbation spacing. Work was concentrated in the 55 GHz -100 GHz frequency range.

The effect of varying the physical parameters will be shown in thisreport and comparisons made between theoretical calculations and experimentalfindings.

DESIGN CRITERIA

The key elements in the antenna design are operating frequency (interms of A.),,guide wavelength and perturbation spacing. These values de-termine the angle of radiating energy as seen in the following equation.1 ,2

Twhere 9= beam angle from broadside (normal)

?a= free space wavelength

?~= guide wavelength

d = perturbation spacing

n 3 space harmonic; 0, + 1, + 2,.....

1. A. A. Oliner, Informal Communication, Class Notes from PolytechnicalInstitute of New York.

2. A. Hessel, "General Characteristics of Traveling-Wave Antennas", AntennaTheory Part 2, McGraw-Hill Book Company, New York, N. Y., 1969.

• 1

The operating frequency f- in a system is principally chosen by appli-cation requirements such as resolution, range and size of components. In amore practical sense, fo depends on the availability of millimeter wavepower sources which are small, rugged, reliable and with sufficient poweroutput for the intended application. Gunn and IMPATT diodes have been theprimary solid state sources used to date. Preliminary work has been accom-plished in incorporating these devices directly in dielectric waveguides atmicrowave frequencies where the guides are physically much larger than thosestudied in this report. 3-5 The bulk of the experimental work reported herewas done near 60 GHz since sufficient test equipment and power sources wereavailable. Some work was completed at 70 GHz and future experimental plansare aimed at 94 GHz.

The guide wavelength, for a given material and frequency, is determinedby the physical size of the guide, i.e., width "a" and height "b". Since itis advantageous from a practical point of view to avoid as much multi-signalcomplexity as possible, single mode operation must be maintained in the pro-pagation of energy in the waveguide with only a single beam of energy radia-ing from the antenna. Thus, the designs presented in this report which givethe range (minimum and maximum) of guide sizes, allow only the EYll mode inthe guide and the n = -1 space harmonic in the radiated energy.

Ideally, the waveguide should be kept as large as possible for anygiven frequency of operation as it eases fabrication problems and lessens theeffect of size variations on the guide wavelength and scan angle. Themaximum guide size is defined as that above which multiple mode operation ispossible. The minimum guide size is defined as that below which the electricfield becomes unguided. The maximum and minimum guide sizes were determinedby calculating the propagation constants k1, k and k, (see Appendix A)using the transcendental equations formulated gy Marc~tili6 and exactlysolving them on a programed calculator7 using the relationship

which indicates that there is no propagation down the guide (z - direction)when (k 2 + k 2) exceeds k1

2. Figures 1, 2 and 3 were plotted for the funda-mental I mri de and the next two higher order modes EY21 and EY12 for the

3. M. M. Chrepta and H. Jacobs, "Millimeter-Wave Integrated Circuits",Microwave Journal, Vol 17, Nov 1974.

4. H. J. Kuno and Y. Chang, "Millimeter-Wave Integrated Circuits", U.S. ArmyElectronics Command Final Report No. ECOM-73-0279-F, June 1974.

5. Y. Chang and H. J. Kuno, "Millimeter-Wave Integrated Circuits", U.S. ArmyElectronics Command Final Report No. ECOM-74-0454-F, Oct 1975.

6. E. A. J. Marcatili, "Dielectric Rectangular Waveguide and DirectionalCoupler for Integrated Optics", Bell System Technical Journal, Vol. 48,No. 7, September 1969.

7. K. L. Klohn, J. F. Armata, Jr., and M. M. Chrepta, "Transverse Propa-gation Constants in Dielectric Waveguides", R&D Technical Report ECOM-4242, U.S. Army Electronics Command, Fort Monmouth, N. J., August 1974.

2

operating frequencies 60, 70 and 94 GHz. These plots show that the EY12mode is the limiting mode for maximum guide size if a unity aspect ratio(a=b) is to be maintained. However, since kx is independent of the guideheight, the guide width could be made somewhat larger than the guide height;the limiting value being the cut-off point (size below which the mode willnot propagate) for the E 21 mode. The figures also indicate that A 1, thewavelength in an infinite dAedium 1 (silicon in this case), can be used as agood first order approximation for the maximum allowed guide size and A, /2as the minimum guide size. The equation for X, is

/ = irvi /N (31

where n1 = index of refraction for medium 1

The figures for maximum and minimum guide size, both exact and approximatevalues, are listed in Table I.

TABLE IMINIMUM AND MAXIMUM WAVEGUIDE SIZES FOR FUNDAMENTAL MODE F-19

GUIDE SIZE (mm)

FREQUENCY (GHz) MIN X1/2 MAX Ai

60 0.775 0.722 1.4 1.443

70 0.67 0.619 1.2 1.237

94 0.50 0.416 0.9 0.921

For any given waveguide size, the gui de wavelength is also a funct on ofoperating frequency. Figure 4 illustrates how the guide wavelength varieswith frequency for a silicon guide, a=b=O.9 mm (maximum guide size forsingle mode operation at 94 GHz.) As the operating frequency falls belowthe design frequency, Xg increases rapidly. The An (approximate) curveshown in the figure was obtained by using the folloging simplifying assump-tions (See Appendix A).

(k/4 13 lr) << avia kyA,14/AT z [<I 4)

and then solving the transcendental equations in closed form. Table IIshows the difference between )g (exact) and (approximate).

3

TABLE II

COMPARISON OF EXACT AND APPROXIMATE VALUES FOR GUIDE WAVELENGTH

FREQUENCY (GHz) EXACT(m) APPROX(m) A% DIFFERENCE

60 3.431 3.900 0.469 13.7

70 2.069 2.125 0.056 2.7

80 1.552 1.568 0.016 1.0

90 1.262 1.269 0.007 0.6

At frequencies above 80 GHz, A Xg becomes relatively insignificant. Thevariation in guide wavelength when "a" and "b" are changed but kept equal toeach other, is shown in Figure 5. The smaller the guide size, the larger Xgwill be; a 10% change in guide dimensions changes ,\ approximately 5%. Itwill be illustrated later in this report how the chinges inAg indicated inFigures 4 and 5, affect the angle of radiation from periodic radiating ele-ments. Once the physical dimensions of the dielectric guide are chosen fora given frequency (In Fig. 1 a=b=l.4 mm is obtained as the maximum guide sizefor 60 GHz) the guide wavelength will be fixed for this frequency.

The only remaining variable to choose in Equation[1)for a given spaceharmonic (n = -l in our case), is the perturbation spacing d. To obtainbroadside radiation at a given frequency, d must be chosen equal to the guidewavelength at that frequency, thereby reducing 1n to zero degrees. Actuallyit is nearly impossible to match d= X exactly, therefore, the frequency atwhich 0 n = 00 will be slightly differgnt than the one designed to be zero.

LINE SCAN ANGLE

Figures 6, 7 and 8 give the angular scan that is theoretically possible(calculated from Equation [1by varying the operating frequency f + 4 GHz fromthe design frequency. A new set of propagation constants was calculated foreach design frequency in order to determine the corresponding guide wavelength.It should be noted that the degrees of angular scan per GHz of frequencychange decreases as the design frequency increases; 4.10/GHz at 60 GHz, 3.50/GHz at 70 GHz, and 2.50/GHz at 94 GHz. In addition, for frequencies abovethe design frequency, higher modes propagating in the guide is a possibility.Calculations indicated that radiation angles are very sensitive to changes orerrors in X . Experiments conducted to measure Xg as a function offrequengy, i~dicated that the measured values always exceeded the calculatedvalues.

8. H. Jacobs, G. Novick, C. M. LoCasio and M. M. Chrepta, "Measurement ofGuide Wavelength in Rectangular Dielectric Waveguide", IEEE TransactionsMicrowave Theory and Techniques, Vol MTT-24, No 11, November 1976.

4

Figure 9 illustrates the effect on the radiation angle if X is either + 10%from the calculated value while the perturbation spacing isgkept approxTmatelyequal to the calculated A value. Over the frequency range examined, thescan angles for X -10% averaged ~ 180 higher and for Xg + 10%,-140 lowerthan the angles cayculated for Xg.

As previously mentioned, if the perturbation spacing is made equal tothe radiation will be normal to the waveguide at the design frequency.

The entire range of angular scan however, can be shifted more positive ornegative by changing the spacing of the perturbations. (See Figure 10.)Closer spacing shifts the angle more negatively and conversely, increasedspacing shifts the angle more positively. The slope, A degrees/Afrequency,remains essentially constant. For each 0.1 mm change in d, the radiationangle changes approximately 80.

The range of scan angle, i.e., slope of the radiation angle curves,may be deliberately altered by changing the waveguide dimensions. As longas the dimensions remain between the minimum and maximum values, the energywill be guided and no higher modes will appear. (See Figure 11.) Smallerguide dimensions increase the slope, thereby increasing the scan range for agiven Afo. In each case, the perturbation spacinq was adjusted to match A gas close as practical. The curve for a=b=l.4 mm, crosses 8=00 at 59 GHzrather than 60 GHz because the perturbation spacing does not match Ag as wellas for a=b=O.9 mm and a=b=l.O mm. The results are tabulated in Table III.

TABLE III

ANGULAR SCAN FOR VARIOUS SIZE GUIDES (A fo = 8 GHz)

GUIDE SIZE PERTURBATION RANGE OF ANGULAR SCANa=b SPACING, d

0.9 mm 3.4 mm 560

1.0 2.6 430

1.4 1.9 330

A variation of guide size and/or perturbation spacing to adjust the scan rangecould be used. Precautions should be taken to avoid multi-moding which wouldadd to the complexity of the system by producing more than one radiatingbeam.

EXPERIMENTAL RESULTS

The objectives of the following experiments were to determine if asilicon waveguide with surface perturbations was an effective radiatingstructure; if the radiated beam was narrow in the y-z plane; and if the beam wassteerable as a function of frequency.

Numerous silicon waveguides were fabricated with various cross-sectionaldimensions and lengths to determine their effect on the radiation angle andrange of angular scan.

5

The silicon waveguides, examined in this report, had dimensions of0.969 mm x 1.071 mm x 10 cm for silicon waveguide #7 and 0.92 mm x 0.91 mmx 7 cm for silicon waveguide #2.

A series of perturbations (grating structures) on the silicon waveguideare required to provide a radiating surface. A grating structure, withgrooves n a dielectric strip, used in a leaky wave antenna have been reportedby Itoh.' The radiating structures covered in the following discussion usesmetal perturbations on the top of a rectangular silicon rod. The perturba-tions consisted of 16 to 22 rectangular copper foil stripes with dimensionsof 0.3 mm x 1 mm. The stripes were cemented to the top of the silicon toprovide the perturbation structure. The distance from leading-edge-to-leading-edge of each metal stripe was set to an experimentally measured sili-con waveguide wavelength X as measured on an unperturbed silicon waveguideand checked with calculatiofs using the Marcatili equations. The guide wave-length was measured using a test setup (see Figure 12) without perturbingstripes on the silicon waveguide and without the radiation angle test fixture.A flanged metal waveguide horn (terminated in a diode detector) was placed ata distance of less than 1 mm above the upper silicon surface in the near fieldof the propagated wave. The standing wave pattern on the silicon, producedby reflections due to an imperfect load, was then detected. The positions ofthe maxima points were determined using a calibrated micrometer (moveable inthe z direction.) To obtain the average distance between maxima points, alarge number of Vmax measurements were made along the surface down the lengthof the guide.

The perturbation copper stripe spacing d was set equal to the measuredsia" The perturbations covered a length of 4 cm using 16 stripes on the

silicon waveguide. The silicon waveguide was then coupled to two adjoiningmetal waveguide sections using thin copper-foil end plates with I mm x I mmcenter openings (see Figure 13). The copper end plates provided the supportfor coupling the metal waveguide to the silicon waveguide by positioning thesilicon in the center of the metal. The pointed silicon waveguide extendedabout 1 cm into each of the two matching metal waveguide sections. Inaddition, the copper end plates provided a shield to prevent radiation fromthe metal waveouide into the air surrounding the silicon guide.

With the silicon waveguide mounted in the test holder, (see Figure 13)the test setup (Figure 12) was subsequently assembled and the radiationpattern from the silicon waveguide was measured. The test setup was used tomonitor forward power (Pf), reflected power (Pr), transmitted power (Pt), fre-quency (f9), relative radiated power (Prad) and radiation angle (G). Theflanged pickup horn (terminated in a dio e detector and sensitive amplifier),was positioned at a distance of 20 cm from the exact center of the pertur-bation stripes. The flanged horn could then be positioned at any angle 8from -850 to + 850 in the y-z plane on a calibrated test fixture. Endabsorbers (carbon compound material) were positioned directly over each end

9. T. Itoh, "Leaky-Wave Antenna and Band Reject Filter for Millimeter-WaveIntegrated Circuits", 1977 IEEE MTT-S International Microwave SymposiumDigest, Jun 21-23, 1977, pp 538-541.

6

at the dielectric-to-metal-waveguide transitions (Figure 13) to preventradiation leakage. The test setup used an IMPATT diode oscillator variablein frequency from 55 to 63 GHz and a PIN diode modulator with a positivesquare wave modulation of about 1 kHz applied from the source. The PIN diodeprovided an amplitude modulated output down the waveguide which subsequentlyradiated out of the silicon surface.

Two experimental waveguides were prepared as indicated in Table IV.

TABLE IV

PHYSICAL CHARACTERISTICS OF EXPERIMENTAL WAVEGUIDES

Silicon a 1 n 11Waveguide width height length Number of Length of Spacing

(Ave) (Ave) (overall) Stripes Exposed betweenSilicon pertur-

m mm mm mm bation mm

# 2 0.91 0.92 7 16 5.4 0.25

# 7 0.969 1.071 10 22 -8 0.18

The radiation pattern of silicon waveguide #7, at a test frequency of 58.49GHz is shown in Figure 14a. The polar plot of relative detected powershows a negative angle B = 540 at the peak radiation point. The half-powerpoints occur at 50 units (power plot) indicating a beamwidth of about 40.The plot was obtained by arbitrarily setting the maximum value of radiatedpower at 100 units on the ac amplifier meter and moving the pickup hornthrough an angle - 8 on either side of the peak to obtain the detectedpower plot.

Figure 14b shows a typical cross-sectional radiation pattern in aplane r-O which is perpendicular to the plane shown in Figure 14a. Thus,the three dimensional radiation pattern is narrow in the y-z plane andwide (fan shaped) in the r-# plane. Point-by-point frequency tests onsilicon waveguide #7 yielded the relationship between radiation angle G andfrequency. (See Figure 15.) For frequencies between 57 GHz and 65 GHz, thecenter of the radiated beam (emax) varied from -680 to -70, a change of 7.50/GHz. The above measurements were based on operation in the fundamental wave-guide EY mode. The I mm by 1 mm guide dimensions do not allow higher modesto propagate.

Using Equation (1], X can be estimated by measuring 9, the angle ofradiation and d the pertubation spacing. The wavelength in air >o can becalculated from the measurement of frequency.

In Figure 16, a plot was made of the guide wavelength X for silicon

waveguide #2 which had dimensions 0.92 mm by 0.91 mm with d 2.5 mm. Theexperimental X is plotted from 61 to 66 GHz and is greater than the theo-retical values texact and approximate) obtained from the Marcatili equations.

7

The radiation angle B (experimental and theoretical) vs frequency forsilicon waveguide #2, is plotted in Figure 17a. A comparison of the experi-mental and theoretical angles (see Figure 17a) indicates that the experimentalvalues are more negative than the theory. A comparison was also made inFigure 17b between the experimental measurements and theoretical calcu-lations for silicon waveguide #7 with d = 1.8 mm. It is again noted that theexperimental points (circled points) occur at a more negative angle 8 thanthe theoretical curve, indicating that experimental X is, in both cases,greater than the theoretical A This agrees with privious direct measure-ments of A using probe techniques.

SUMMARY AND CONCLUSIONS

Line scanning antennas were designed at millimeter wave frequencies(55 GHz to 100 GHz) with confirming experiments using rectangular siliconwaveguides with metal stripe perturbations. Experiments indicated that anarrow beam of radiated power can be deliberately scanned through a range ofangles by altering the input frequency. Using Marcatili's basic equations,the maximum and minimum waveguide sizes were determined allowing only thefundamental Ey mode for 60, 70 and 94 GHz. The key parameters of Equation[1], guide wav9length )n and perturbation spacing d, 'were theoretically andexperimentally varied to determine their effect and criticality to the angleof radiation and range of angular scan. The theoretical results indicatethat the radiation angle is very sensitive to changes in X ; a 10% changecausing an angular shift of approximately 15 to 200. The Ouide wavelength,in turn, for a given material and frequency, is determined by the physicaldimensions of the guide; width a and height b.

Small changes in the spacing of the perturbations can also cause signi-ficant angular changes; 80 shifts for each 0.1 mm change in d. These resultsgave an indication as to how an antenna could be designed to cover a desiredrange of angular scan by altering the physical dimensions of the guide and/orchanging the perturbation spacing.

Experiments were carried out to verify the calculated values of ) bydetecting the standing wave pattern and measuring the distance betweenmaxima, X /2. In addition, X was determined from Equation [1] using ex-perimentafly measured angles o? radiation. The experimental X values areplotted in Figure 16 and compared to the theoretical calculatiogs. Both ofthe experimental techniques for determining X indicate la rer numericalvalues for any given frequency than theory wou~d predict8 , Ts. Both tech-niques, however, show that the difference between experiment and theorydecreases as the frequency increases. The experimentally measured radiationangles for silicon waveguides #2 (w = 0.91 mm, F = 0.92 mm, 9 = 2.5 mm) and#7 (w = 0.97 n, V = 1.07 mm, -d = 1.8 mm) are plotted in Figures 17a and 17b,respectively. These angles are compared with theoretically calculated anglesfor guide sizes a-d perturbation spacings closely matching the average values.

10. H. Jacobs, G. Novick, C. M. LoCasio, "Probe Measurements of Guide Wave-length in Rectangular Silicon Dielectric Waveguide", 1977 IEEE MTT-SInternational Microwave Symposium Digest, Jun 21-23, 1977, pp 118-120.

8

The values for a, b and d used in the theoretical calculations, bracketthe actual variation in parameters for the experimental waveguide antennas.The results show that the observed radiation angles fall within the theoreti-cal limits and agreement is good, especially since, the angle On is verysensitive to changes in ),g (and therefore a and b) and d.

The feasibility has been shown of electronically scanning through arange of angles by varying the frequency fed into a relatively simpleantenna structure consisting of a rectangular silicon rod with copperstripes (perturbations) attached to the upper surface and how the range ofscan can be altered by changing the physical dimensions of the guide andthe spacing between perturbations.

ACKNOWLEDGMENT

This work was supported by the Ballistic Missile Defense AdvancedTechnology Center, Huntsville, Alabama, and by the U. S. Army In-HouseLaboratory Independent Research Program, Fort Monmouth, New Jersey. Theauthors would like to thank Fan King of the Ballistic Missile Defense AdvancedTechnology Center for his helpful discussions and encouragement.

9

REFERENCES

(1) A. A. Oliner, Informal Communication, Class Notes from PolytechnicalInstitute of New York

(2) A. Hessel, "General Characteristics of Traveling-Wave Antennas",Antenna Theory Part 2, McGraw-Hill Book Company, New York, N.Y., 1969

(3) A. M. Chrepta and H. Jacobs, "Millimeter-Wave Integrated Circuits",Microwave Journal, Vol 17, Nov 1974

(4) H. J. Kuno and Y. Chang, "Millimeter-Wave Integrated Circuits", U.S.Army Electronics Command Final Report No. ECOM-73-0279-F, June 1974

(5) Y. Chang and H. J. Kuno, "Millimeter-Wave Integrated Circuits", U.S.Army Electronics Command Final Retrt No. ECOM-74-0454-F, Oct 1975

(6) E. A. J. Marcatili, "Dielectric Rectangular Waveguide and DirectionalCoupler for Integrated Optics", Bell System' Technical Journal, Vol 48,No. 7, September 1969

(7) K. L. Klohn, J. F. Armata, Jr., and M. M. Chrepta, "Transverse Propa-gation Constants in Dielectric Waveguides", R&D Technical ReportECOM-4242, U. S. Army Electronics Command, Fort Monmouth, N.J.,August 1974

(8) H. Jacobs, G. Novick, C. M. LoCasio and M. M. Chrepta, "Measurementof Guide Wavelength in Rectangular Dielectrir Waveguide", IEEE Trans-actions Microwave Theory and Techniques, Vol MTT-24, No 11, November 1976

(9) T. Itoh, "Leaky-Wave Antenna and Band Reject Filter for Millimeter-WaveIntegrated Circuits", 1977 IEEE MTT-S International Microwave SymposiumDigest, Jun 21-23, 1977, pp 538-541

(10) H. Jacobs, G. Novick, C. M. LoCasio, "Probe Measurements of Guide Wave-length in Rectangular Silicon Dielectric Waveguide", 1977 IEEE MTT-SInternational Microwave Symposium Digest, Jun 21-23, 1977, pp 118-120

10

60G~z, X0 - 5.0mm

Si X I -1.443 MM

212I'~ Yk

+ CUTOFF

10-

0.5 1.0 1.5 2.0

ab DIMENSION (mm

Flaure 1 Minimum and Maximum Wavecide Dimensions. 60 GHz

70 GHz, X0 - 4.286mm7, X -1.23T mm

XSib -- m

II ~ ~II- -k2130- E -

122

252

25

20

CUTOFF

+

5

I I II0.5 1.0 1.5 2.0

a-b DIMENSION (mm)

Fiqure 2 Minimum and Maximum Waveouide Dimensions, 70 GHz

12

45 \ ,k

40-

35-

30 lk CUT OFF30 \

25-

20- 4zX0-.11MX, =O.921mm

15- I/ q1a] 21-

I 12

0.5 1.0 .5

a-b DIMENSION (Mm)

Flqure 3 Minimum and Maximum Wavegulde Dimensions, 94 GHz

13

L . ... '.,.. J ...

7.0- E y MODE

a b -0.9 mm6.0-

~5.0-

E

C-04.0-

LU X (APROX.)'~3.0-

2.0-

1.0-

60 70 80 90 100FREQUENCY (GHz)

Figure 4 Variation of Wavelength WItn Frequency

14

E'1 MODE

1.4

E1.3-

C-

__ 1.2 -

o.b (mm)- LI 0.815

0.9

1.0IO-

85 90 95 100FREQUENCY (GHz)

Figure 5 Variation in Guide Wavelength with Frequency as a Function of Size

15.1 '

607 Xg (6GHZ) -1. 853 mm

b b -1.4 mm

Cn 40- d: 1.mm

0

-0

-20-~ 4. 10 /GHZ

-60-

L--4f-

'56 58 60 62 64FREQUENCY (GHz)

Figure 6 Radiation Angle versus Frequency (60 GHz Deslqn Frequency)

L 16

60- Xg (70GHZ) 1.588 mm

S a b-1.2 mm40 d - .6 mm

n*-

S 20-

C=,

-20-' 3.5 0/GHz

~-40-

-60-

66 88 TO 72 14FREQUENCY (GHz)

Figure 7 -Radiationi Angle versus Frequenicy (70 GHZ Uesign Frequency)

17

60- X(94 GHz) 1. 178mm

Si b ab0-.9mm

Cm 40- d - 1. 2mmI n a-~

S 20-

C=

-D

-20 2. 5 0 GHz

~-40o

-60-

7 go 92 94 96 98 100FREQUENCY (GHz)

(Figure 8 Radiation Anale versus Frequency (94 GHz Desiqn Frequency)

18

7 1b-.4mm60- b Xg (60OGHz) - 1. 853 mm

d -1.9mma n*

'n 40-

20-

L-

S-20-

-40-

-60-

L-4$I

56 58 60 62 64FREQUENCY (GHz)

Figure 9 Effect of, on Radiation Anglet 19

60- X 7 Xg(6OGHZ)-I.853mm

40-

S 20-

C>

2..9~~2.0

-F 1.8

~~-40

-60-

'~56 58 60 62 64

FREQUENCY (GHz)

( Flqure 10 Effect of Perturbation spacing d on Radiation Angle

20

I I I I I

-Io-30- S b

a *b(mm)

a-- /0.9" 20 1.4=" 1.0

a -b Xg(6OGHz)

1 4 mm 1. 853 mm

1.0 2.6180.9 3.431

0 0

-.J

-10 d (mm)

I-1.9

c= -20-

2.6

-30/

3.4I I I I

56 58 60 62 64FREQUENCY (GHz)

Figure 11 Effect of Guide Size on Angular Scan with d ZXg at 60 GHz

Design Frequency

21"7.

U..,

I-

ap .Ccc,CLL

..-.

CN,,cm 7 ss

COC

WC

.

4,Ilk, 0

"Mr, %- t CC c_j CL- Lij L0

S LLAin I.

LLLczn

LLL

4-0

IAJ-

0- C.>

-C

LJLLJJ

x L

LCU

uJ.j

.um-

<-) C%*

4-)

C= LAJ .0LAJLI CL.

LAL

233

e. +8

fl 22SRIEdw1C

2024

134

4.0.9Mso8.6 ~

Figue 14 Polr Plt ofBeamAngl

25Plaee

CIOD

0~ _0 4

C%j I- 03'OfCQ C2 c

---"C-

U.' 0-A

t Lai c.

= CIOp--

LU -J

* - --12CD p.

')I 0__C=

C)C> LUJi 4-J

al

4-)

0

LC-

al

ocn, Co OCRI.

(8) 31NV NOIVIO,

26.

SILICON DIELECTRIC WAVEGUIDE6 0. 92 mm

3.6- b - 0. 91 mm

3.4-0 EXPERIMENTAL X

* E DETERMINED BYe

-03.2 . ANGLE OF RADIATIONd *2.5 mm

~3.O-LUJ

-LJ

2.8-LU

2.6' MARCATILI EQUATIONSEXACT SOLUTION

2.-APPROXI MAT ION

60 62 64 66FREQUENCY (GHz)

Figure 16 Comparison of A Obtained Experimentally from the RadiationAngle with Theopy

27

EXPERIMENTAL POINTS60- / 0 2 MM

0.92 mm

40I 2. 5 mm

20- d (mm)

: 2.6

~0.815

-60 00--

I I Ii

- 86062 64 66

FREQUENCY (0Hz)

Figure 17a Comparison of Theory and Experiment for Radiation Angle _"[Sctngersus Frequency for Various Guide Sizes and Perturbation

Spacings (Slicon Waveguide # 2)

28.

J !| "--

EXPERIMENTAL POINTS6o~~~~ -. -0.97mmi o b - 1.07 mm

40 - - 1.8 mm

-J

S 20-

C>d Wrm

1.8

-20o 1.6

-6000

I I I

58 60 62 64 66FREQUENCY (GHz)

Figure l7b Comparison of Theory and Experiment for Radiation Angleversus Frequency for Various Guide Sizes and Perturbationspacings (Silicon Waveguide # 7)

29i 2

APPENDIX A

Calculation of Transverse Propagation Constants in Dielectric Waveguides

The mathematical equations which contain the transmission properties of arectangular dielectric waveguide relate to the situation shown in Figure Al.The index of refraction ni for medium 1, (silicon) is larger than that of thesurrounding media (air) n2 , ni, n4, and ng. If n2=n3=n4=n,, the field dis-tributions, will be symmetrical about the x and y planes as illustrated.Marcatili 'developed the following basic equations: A

[Al]

and

-*.[A2]

where kl= propagation constant in medium 1, k = axial propagation constant,kx, k A transverse propagation constants in i,y direction, pu1=r U

=̂ perme-ability of medium 1, (,r=l for Si), E1

= o = permittivity of medium I((r=12 for Si). The transverse propagation constants kx and ky are solutionsof the transcendental equations,

k~b: c'n".. 6Ly [A4]

where a equals the x dimension (width) and b equals the y dimension (height)of the silicon waveguide and

,- [A5]

i [A6]

where , A

xo [A7]

I. E.A.J. Marcatili, "Dielectric Rectangular Waveguide and Directional Couplerfor Integrated Optics", Bell System Technical Journal, Vol 48, No. 7,September 1969.

30

4

r!

The number of extrema contained within the guide in the x and y directionsare indicated by p and q,respectively. For the fundamental EYll mode, bothp and q equal one. Figure Al illustrates that t 3 5 and 11 , are thedistances the fields penetrate the respective surrtunding mid ums. A2,34,indicate the maximum physical dimensions of the waveguide which willsupport only the fundamental mode provided the guide is surrounded by auniform medium of equal refractive index. Enations [A33 and [A4] weresolved exactly using a programmed calculator . by plotting the right andleft hand sides of each equation for a range of k and kV values, re-spectively. The exact numerical values for kx an k atythe point ofintersection (right hand side of the equation equal o left hand side)was determined by employing the "coarse grid approach"3 to search forthe minimum difference between the two curves for each equation.

Approximations

If the approximations of Equation [4] are used, based on the fact that forwell-guided modes most of the power will travel within medium. 1, and thefact that the arctan and the argument of a small angle are approximatelyequal, Equations [A3] and [A4] can be simplified to,

ki -61TV + CAg]/-,

These equations can then be readily solved for k and k and the guidewavelength calculated using Equation [A2] and x y

The agreement between ?. (exact) and g (approximate) improves as thewavelength becomes smaler with respect to the cross-sectional dimensionsof the guide. This also means that more of the electric field stays withinthe wavegulde boundaries.

2. K.L. Klohn, J.F. Amata, Jr., and M.M. Chrepta, "Transverse PropagationConstants in Dielectric Waveguides", R&D Technical Report ECOI-4242,US Army Electronics Command, Fort Monmouth, N.J., August 1974.

3. G. L. Neuhauser, Introduction to Dynamic Programing, John Wiley andSons, Inc., New York, N.Y., 1967, pp 104-111.

31

Y/7n. C-ONSTANT eY?

/Z 17 CoskY y +R)

I; *y/14

CONSTANT+Y/7

I CONSTANTe 5

Figure Al Silicon Waveguide n1, Imiersed in Air, n2=nYnynl

HISA-FMr-1390-7832