RADC-TR-88-32, Vol I (of two)
Final Technical Report
DIELECTRIC MILLIMETER WAVEGUIDES
University of California
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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.
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- jj -^-Dielectric Waveguides /• .
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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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JAMES C. SETHARES
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Table of Contents
II. Summary of Accomplishments.1
III. Future Research Areas...9
Avail ability Codes
Aval 1 ! and/or
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
• 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-
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
x IO -4
x IO * 4
KRS - 5
x 10“ 2
KRS - 6
x 10* 2
x 10" 3
Teflon (at 10 GHz) (PTFE)
Rexolits (at 10 GHz)
RT/duroid 5880 (at 10 GHz)
Polyethylene (at 50 GHz) (LDPE)
2 x IO -4
2.6 x 10“ 3
9 x 10-4
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
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.
2q cob h
Rorrx.llzed axial electric field extent B/x as a
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.
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
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.
. Itie Proposed Shielded Low-Loss MM Wave
Other Research Personnel
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-
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
6. R. Rudokas and T. Itoh, "Passive millimeter-wave IC components made of
inverted strip dielectric waveguides", IEEE Trans, on MTT, MTT-29, pp.
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).