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RADC-TR-88-32, Vol I (of two) 

Final Technical Report 

March 1988 



AD-A196 844 


aTKUJLE-Coei 


DIELECTRIC MILLIMETER WAVEGUIDES 


University of California 


Cavour Yeh 


APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. 


This effort was funded totally by the Laboratory Director’s fund. 

ROME AIR DEVELOPMENT CENTER 
Air Force Systems Command 
Griffiss Air Force Base, NY 13441-5700 



DT1C 

ELECTEI 

MAY 2 5 19881 



















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o 


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DIELECTRIC MILLIMETER WAVEGUIDES 

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Cavour Yeh 

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16 . Su PPLEMEN^RYjFjc^A ; Ti^jj e j ectric Waveguide - I, UCLA; Dielectric Mill Waveguide - II, Univ of Texas 
This effort was funded totally by the Laboratory Director's funds. 

17. COSATI COOES 18. SUBJECT TERMS (Continue on reverse if necessery and identity by block number) 

FIELD GROUP SUB-GROUP c 

- jj -^-Dielectric Waveguides /• . 

-Millimeter Waves 

19 ABSTRACT (Continue on revene if necessery and identify by block number) 

This report summarizes the result of the research carried out for the Postdoctoral Task E-6-7108 
administered by the University of Dayton under contract F30602-81-C-0206 with RADC. The primary 
objectives of this research program were to learn whether there exists a dielectric waveguide 
configuration which offers lower loss figure than a circular dielectric rod and to establish an 
experimental technique to measure the guiding characteristics of waves on dielectric structures. These 
objectives were met. Future research areas are also described in this report. i 


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Table of Contents 


Acknowledgment 

I. Introduction.1 

II. Summary of Accomplishments.1 

III. Future Research Areas...9 

IV. Personnel....12 

References.13 


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Acknowledgment 










I. Introduction 


This is a final report on a study sponsored by RADC through the Post 
Doctoral Program (Task E-6-7108, Contract F30602-81-C-0206) administered 
through the University of Dayton) from June 24, 1986 through October 30, 
1986. The principal objectives of this research were to learn whether 
there exists a dielectric waveguide configuration which offers lower loss 
figure than a circular dielectric rod and to establish an experimental 
technique to measure the guiding characteristics of waves on dielectric 
structures. This final report gives a summary of our accomplishments dur¬ 
ing this phase of the research program. 


II. Summary of Accomplishments 

At millimeter (mm) or sub-millimeter (sub-mm) wavelengths, the usual metallic 
waveguides become unbearably small and are very difficult to manufacture. Further¬ 
more, insufferably high conduction losses at these frequencies also render these 
guides less than useful. A new mm or sub-mm waveguiding structure must be 
found. A viable/practical mm or sub-mm waveguide should possess the following 
characteristics. »3 

• Low loss 

• Flexible, may be curved or bent (can turn corners) 

• Can be handled easily (this implies reasonable physical size and guided 
energy must not be affected by outside environment) 

• Cost effective (May be manufactured at a reasonable cost) 

• Connectors can be made 

It appears that the most promising candidate for flexible guide is the di¬ 
electric waveguide^*^ while the most promising candidate for integrated milli¬ 
meter circuit is the channel or stripline guide.® It is envisioned that a new 
family of mm/sub-mm wave components, such as mixers, couplers, waveguides, at- 


1 










tenuators, polarizers, etc. can be made with purely dielectric material. There 


are two possible ways of realizing a low-loss millimeter/sub-millimeter (mm/sub-mm) 
waveguide structure: Through the use of low-loss material and/or through the use 
of specially configured structure. We shall first provide a brief discussion of 
available low-loss material suitable for guiding mm/sub-mm waves. Then results 
of a calculation on a specially configured low-loss structure which was the sub¬ 
ject for the short-term innovative research, will be presented. 

Brief summary of low-loss material 

A series of very detailed measurements in the mm/sub-mm wavelength range on 
the dielectric constant and loss tangent of groups of promising low-loss material 
have been performed by the MIT ’Mag-Lab' group in recent years. 7 Results of 
their findings were summarized in a very comprehensive paper by Afsar and Button. 7 
Two types of material appear to possess relatively low-loss characteristic in the 
mm-sub-mm wavelength range: One is a crystalline type material 5 and the other is 
a polymer type material. 7 A sample list of the commercially available low-loss 
material is given in the following: 

Crystalline material 5 





Dielectric constant 

Loss 

tangent 

Alumina 

(at 

10 GHz) 

9.7 

2 

x IO -4 

Sapphire 

(at 

10 GHz) 

9.3-11.7 

1 

x IO * 4 

Quartz 

(at 

10 GHz) 

3.8-4.8 


io- 4 

KRS - 5 

(at 

94.75 GHz) 

30.5 

1.9 

x 10“ 2 

KRS - 6 

(at 

94.75 GHz) 

28.5 

2.3 

x 10* 2 

LiNfc0 3 

(at 

94.75 GHz) 

6.7 

8 

x 10" 3 


Polymer material^ 


Teflon (at 10 GHz) (PTFE) 
Rexolits (at 10 GHz) 

RT/duroid 5880 (at 10 GHz) 
Polyethylene (at 50 GHz) (LDPE) 


Dielectric constant 
2.04 
2.56 
2.2 


Loss tangent 
2 x IO -4 
2.6 x 10“ 3 
9 x 10-4 
io- 4 


2.3 










It can be seen that the polymer material in general has much lower dielectric 
constant than crystalline material. The best lost-tangent is around 10”4. 

Using a nominal dielectric constant of 2.0, the attenuation constant for plane 
wave in this bulk material is 1.3 dB/m at 100 GHz which is already better than 
the 3 dB/m loss for conventional metallic waveguides at this frequency. The at¬ 
tenuation constant for plane wave is calculated from the following equation: 

a = 8.686 (n /T/X 0 )tan6 * (1) 

Here e is the relative dielectric constant, 1 0 is the free-space wavelength and 
tan6 is the loss tangent. According to Equation (1) , it appears that in addition 
to requiring as small a loss tangent as possible lower dielectric constant is also 
helpful in achieving lower loss. Hence, flexible polymers such as LDPE (Poly¬ 
ethylene) and PTFE (Teflon) are the natural choice for the making of low-loss 
mm/sub-mm waveguides. 

Low-loss configurations 

Other than the material loss factor which we discussed above, the major fac¬ 
tor that may influence the attenuation characteristic of guided wave along a di¬ 
electric structure is the size and shape of the waveguide. The attenuation con¬ 
stant for a dielectric waveguide with arbitrary cross-sectional shape and sur¬ 
rounded by free-space is given by the following expression:®'® 










Here, e and tan6 are, respectively, the relative dielectric constant and 
loss-tangent of the dielectric waveguide, X 0 is the free-space wavelength, e 0 
and y 0 are, respectively, the permittivity and permeability of free-space, e 2 
is the unit vector in the direction of propagation, Ai is the cross-sectional 
area of the dielectric structure, A is the total cross-sectional area of the 
guide, and E and H are the electric and magnetic field vectors of the guided 
mode under consideration. The loss factor R which is sensitive to the guide 
configuration and the frequency of operation could vary from a very small value 
to l//c“ which is the case for a plane wave propagating in a dielectric medium 
with dielectric constant e . Typical behavior of R as a function of k 2 A where 
k is the free-space wave number and A is the cross-sectional area of the di¬ 
electric waveguide, for the dominant mode is shown in Figure 1. It is seen that 
if the propagating mode is somewhat loosely bounded to the guiding structure, 
i.e., if k 2 A is small, the attenuation factor R can be made quite small giving 
rise to a significantly lower attenuation constant a. 

The objective of the short-term innovative research program is to perform 
calculation for the attenuation factor R for a number of flattened low-loss 
structures using the finite-element method. Results of our calculation are 
shown in Fig. 1 in which the attenuation factors R for the dominant e HEn mode 
along a flattened dielectric waveguide as a function of the normalized cross- 
sectional area for various values of (major-axis/minor-axis) ratios, are dis¬ 
played. It can be seen that for the same cross-sectional area the flatter di¬ 
electric structure yields significantly lower loss for the dominant gHE^ mode. 
This evidence points to the advantage of using flattened dielectric structure 
rather than the usual circular dielectric rod, to achieve low loss factor for 
the dominant mode. Since the guided field extends beyond the core region of 
the guide it is important to learn the field extent of the guided mode. We have 
performed such calculation for the flattened guides. Results are shown in Fig. 2. 






(2q ccsh £q/\qK ianh £q 


Fig. 1. Attenuation factor R for the e HE ll wave as a function 
of normalized cross-sectional area of an equivalent ellipse; 
tanh C 0 = b/a» where a is the semi-major axis, b is the semi-minor 
axis and q is the semi-focal distance of the ellipse. 









0.2 

2q cob h 


0.6 0.7 


tftsh t 


ng. 2 


Rorrx.llzed axial electric field extent B/x as a 

o 

function of nora&Hzed crosB-sectional area for the 
^HZ,^ node . B la the distance measured from the 
origin to the point of observation vhere (e /e ) 2 - 0.1 













One notes that the field extent as measured from the center of the guide is 
relatively insensitive to the flatness of the guide. This means no sacrifice in 
having larger field extent is necessary in order to achieve lower loss factor by 
using flatter guides. 

Let us now consider a specific numerical example: Using Teflon 
(with t “ 2.065 and tan6 * 2 x 10”^) as the dielectric waveguide material, the 


dimensions of a typical low-loss guiding structure for a 94 GHz signal can be 

2a “ 2.4 mm 
2b ■ 0.8 mm. 

At 94 GHz, the calculated loss factor R for a 3:1 (Major: Minor axis ratio) 
flattened guide supporting the dominant e H£n mode is 0.06, while R for an 
equivalent circular guide (with the same cross-sectional area) supporting the 
dominant HEn mode is 0.4. So, the ratio of the attenuation constant for these 
two structures is 

cl / o 

flattened guide circular guide “ 0.15. 

This numerical example clearly demonstrates the importance in the choice of 
guiding configuration to obtain low-loss guidance. 

The Pose Doctoral program provided us with the opportunity to perform 
analysis to confirm this initial observation. 

Experimental Setup 

This basic experimental arrangement is shown in Fig. 3. This setup will 
yield detailed information on the guided wave along a dielectric structure, such 
as the field decay characteristics, propagation constants, mode configurations, 
etc. The output of a signal source modulated with 1 KHz square wave is connected 
to an isolator followed by an attenuator, a frequency meter, a coupling section, 
the dielectric waveguide, and an appropriate termination. Two ways of terminating 
the dielectric waveguide may be considered: one consisting of a flat reflecting 
place which reflects all of the guided power and sets up a strong standing wave 











Figure 3(a). Schematic Diagram for the Experimental Setup 
















3(b). Picture of the Experimental Setup. 














on the dielectric guide, while the other consisting of a low-reflection coupling 
section terminated into a matched load with a Schottky detector. The standing 
wave set up by the reflecting plate can be measured to yield information on 
guide wavelength and attenuation factor. A picture of the setup is shown in 
Fig. 3(b). 

As a demonstration, this experimental setup was used to measure the guide 
wavelength of the dominant HE^ mode on a circular Teflon guide. Measured date 
are shown in Fig.4. Also plotted in the figure are the calculated results. 
Excellent agreement was achieved. One may also measure the attenuation factor R 
for a dielectric waveguide using this setup. Verification with the calculated 
results for the circular dielectric guide can provide us with the confidence 
to perform measurements on non-circular low loss dielectric guiding structures. 
Performance merits in terms of attenuation, bending loss, propagation constant, 
field extent, mode stability, polarization preserving characteristics and ease of 
handling, can now be studied and compared with our theoretical results. 

III. Future Research Areas 

Having shown that there exists a configuration which may yield lower loss 

factor than a circular dielectric rod and having established a mm wave experimental 

setup, we are now in a position to propose additional research tasks as follows: 

Verify experimentally the findings of the Post Doctoral research program. 

Study the effects of shielding the low-loss structure by a layer of 
dielectric sheath as shown in Fig. 5- 

Study the effects of curvature and explore ways to minimize bending losses. 

Explore and study compatible waveguide components such as dielectric wave¬ 
guide couplers, filters, branches, phase shifters, polarizers, horns, at- ... 
tenuators, mode converters, etc. 

Study ways to improve the loss-tangent of guiding materials. 


Investigate ways to manufacture these non-circular dielectric waveguides. 



















ili Electric field lines of 
« »i the doninant »ode. 


Figure 



. Itie Proposed Shielded Low-Loss MM Wave 
Dielectric Waveguide. 



IV. Personnel 


Principal Investigator: 

Cavour Yeh 

Other Research Personnel 
V. Casey 
J. Brown 
E. MacDonald 


(Senior Engineer) 

(Engineer) 

(Engineer) 

(Laboratory Technician) 








References 


1. T. Yoneyama and S. Nishida, "Nonradiative dielectric waveguide for millimeter- 
wave integrated circuits," IEEE Trans, on Microwave Theory and Tech., MTT-29 , 
pp. 1182-1192 (1981). 

2. J. F. Miao and T. Itoh, "Hollow Image Guides and Overlayed Image Guides 
Coupler", IEEE Trans, on Microwave Theory and Tech MTT-30 . pp. 1826- 
1931 (1982). 

3. S. T. Peng and A. A. Oliner, "Guidance and leakage properties of a class of 
open dielectric waveguides: Part I-Mathematical formulations," IEEE Trans, 
on Microwave Theory and Tech, MTT-29 , pp. 834-854 (1981). 

4. K. Yamamoto, "A novel low loss dielectric waveguide for millimeter and sub¬ 
millimeter wavelength," IEEE Trans, on MTT, MTT-28 , pp. 580-584 (1980). 

5. William B. Bridges, "Low loss flexible dielectric waveguide for millimeter 
wave transmission and its application to devices," California Institute of 
Technology, Report #SRO-005-1 and #SR0-005-2 (1979-1982); William B. Bridges, 
Marvin B. Kline and Edgard Schweig, IEEE Trans, on MTT, MTT-30, pp. 286-292 
(1982). 

6. R. Rudokas and T. Itoh, "Passive millimeter-wave IC components made of 
inverted strip dielectric waveguides", IEEE Trans, on MTT, MTT-29, pp. 

978-981 (1976). 

7. M. N. Afsar and K. J. Button, "Millimeter-Wave dielectric Measurement of 
Materials", Proc. IEEE-73, pp. 131-153 (1985); R. Birch, J. D. Dromey and 
J. Llsurf, "The optical constants of some common low-loss polymers between 
4 and 40 cm -1 ". Infrared Physics Vol. 21, pp. 225-228 (1981). 

8. C. Yeh, "Attenuation in a dielectric elliptical cylinder", IEEE Trans, on 
Antennas and Propagation, Vol. AP-11 , pp. 177-184 (1963). 

9. C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys. Vol. 33 , 
pp. 3235-3243 (1962).