The theoretical and experimental results for a pair of mode-selective directional couplers designed to detect the TE sub 11 and TE sub 12 modes in a multimode circular wavelength are described. A brief description of the design of the couplers is presented, followed by a comparison of their measured and calculated parameters. The couplers were used to measure the characteristics of a circular waveguide mode converter. The results of these measurements are described

Hoppe, D.

English

NASA Technical Reports Server

TDA Progress Report 42-88
N87-17945
October- December 1986
Directional Couplers for Detecting the TEll and TEl2
Circular Waveguide Modes
D. Hoppe
RadioFrequency and MicrowaveSubsystemsSection
This article describes the theoretical and experimental results for a pair of mode-
selective directional couplers designed to detect the TEl] and TEl2 modes in a multi-
mode circular waveguide. A brief description of the design of the couplers is presented,
followed by a comparison of their measured and calculated parameters. The couplers
were used to measure the characteristics of a circular waveguide mode converter. The
results of these measurements are described.
I. Introduction
This article is the last in a series describing the transmission-
line components required for a proposed high-power (400-kW)
millimeter-wave (34.5-GHz) transmitter. The high-power and
high-frequency requirements pose many problems that are
unique to this transmitter (Ref. 1). In order to transmit power
from the amplifier to the antenna focus without breakdown,
an oversized multimode circular waveguide must be used.
Directional couplers that are sensitive to individual modes are
required for monitoring transmitter output power, and for
testing the waveguide components and the proposed gyrokly-
stron amplifier. This article describes theoretical and experi-
mental results for two such couplers, one for detecting the
TEll circular waveguide mode, and the other for detecting
the TEl2 mode.
II. Mode-Selective Coupler Design
The theory used to design the mode-selective directional
couplers is basically the loose coupling theory described by
Miller (Ref. 2). The main circular waveguide is coupled to a
rectangular waveguide through a series of coupling holes as
depicted in Fig. 1. For TE couplers, the coupling is designed
to be through the longitudinal magnetic field (Hz) in the
circular and rectangular waveguides; therefore, the rectangular
guide is attached to the circular guide through its small (b)
dimension as shown in Fig. 1. This configuration eliminates
any coupling of TM power from the main waveguide.
Coupling to a particular TE mode in the circular guide is
maximized by adjusting the rectangular waveguide's wide (a)
dimension so that the phase velocity of its dominant mode
matches that of the circular waveguide mode of interest. The
coupling waveguide is then tapered down to a standard size
for connection of a detector. High directivity is assured by
spacing the holes at one quarter of a guide wavelength. Since
the coupler is mode-selective, it must by definition reject
power present in other circular waveguide modes traveling
in the forward and reverse directions. This rejection is usually
specified in dB and is called the selectivity. Selectivity for
specified modes can be optimized by using a large number of
11
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coupling holes and tapering the coupling profile with distance
(i.e., changing hole size). These effects can be simulated quite
easily with a simple computer program that adds up the
contributions from each hole in the coupling array to obtain
the total coupling for each circular waveguide mode at each
frequency of interest. Finite wall thickness and the effects
of various coupling profiles can be included in the model with
little complication.
III. Final Design Parameters
TEll and TEl2 couplers were designed for a circular
waveguide with a diameter of 1.75 in. operating at a center
frequency of 34.5 GHz. Design goals included a directivity of
at least 40 dB and a selectivity of at least 30 dB for each of the
forward and reverse traveling spurious TEln modes over a
1% bandwidth.
The TE 11 coupler requires a highly oversized coupling guide
with a wide dimension of 1.493 in. in order to match the
phase velocities of the TEll circular mode and the TEIo
rectangular mode. Since for the frequencies of interest and
these dimensions the TE3o mode is allowed to propagate in
the coupling guide (and it is strongly coupled to the TEl2
mode in the circular guide), great care must be taken in
tapering the coupling guide down to standard WR28 size. A
highly nonlinear taper was used to avoid coupling large
amounts of this TE3o power into the TElo mode during the
transition. A first prototype of the coupler used a linear taper
and showed poor selectivity for the TEl2 mode due to these
effects. In both couplers, the small dimension of the coupling
guide was chosen to be the standard WR28 dimension of
0.14 in. The number of holes required to meet the selectivity
requirements was determined to be 154 through computer
simulation, and a linearly tapered coupling profile was also
found to be necessary in order to meet the specifications.
Hole spacing was 0.087 in. and wall thickness was 0.020 in.
The actual coupling value can be set by scaling the hole
diameters, and a coupling value of about 70 dB was obtained
using a maximum hole diameter of 0.060 in. A photograph
of the fabricated TE 11 coupler is shown in Fig. 2.
The design of the TEl2 coupler is similar, requiring a
coupling guide width dimension of 0.516 in. and 144 coupling
holes with a spacing of 0.092 in. Once again, a linearly profiled
coupling profile was used. A maximum hole diameter of
0.050 in. gave a coupling value near 55 dB at the design fre-
quency of 34.5 GHz. The predicted coupling and selectivities
for the forward traveling spurious modes are displayed for
this coupler versus frequency in Fig. 3. Selectivities for the
reverse traveling modes are predicted to be greater than 60 dB
and are not plotted.
IV. Coupler Results
Measurements were performed to determine the coupling,
directivity, and selectivity values for the two couplers using
an HP8510 automatic network analyzer and additional
components required to extend the instrument to the 26.5-
to 40-GHz range. The measurement of the TEI I coupling is
compared to the theoretical results in Fig. 4. A WR28-to-
circular waveguide transition and taper up to the 1.75-in.
circular waveguide size were used to launch a pure TE 11 mode
into the 1.75-in. circular waveguide in order to make the
measurement. The loss through these components was calcu-
lated and removed from the measured data. The difference
between the theory and measurement is within the error
specification for the HP 8510 network analyzer for these large
values of attenuation. A measurement of the reverse coupling
was also attempted, but no reverse coupling was detectable
down to the noise floor of the HP8510, which is about
-100 dB. From this, we conclude that the directivity is
greater than 30 dB.
A similar measurement was made for the TEl2 coupler. In
this case, a TEll to TEl2 mode converter was included in the
experimental setup. This device, which was described in a
previous report (Ref. 3), is capable of generating a highly
pure TEl2 mode over a limited bandwidth around 34.5 GHz.
The measured coupling value of 53.49 dB at 34.5 GHz for the
TEl2 coupler may be compared to the calculated value of
55.50 dB. The agreement here is seen to be somewhat worse
than that for the TE 11 coupler, but still satisfactory consider-
ing the possible measurement errors and approximations made
in the theoretical calculations.
The measured reverse coupling at 34.5 GHz once again
approached the limits of the HP 8510, reaching 99.4 dB. This
translates to a directivity near 46 dB at the center frequency.
Further measurements involving the mode converter and the
two couplers are described later in this article.
An effort was also made to determine the selectivities for
the couplers. Since with the available mode converter and
tapers it was possible to produce only relatively pure TE 11 and
TEl2 modes, the TEll coupler's rejection of the TEl2 mode
and the TEl2 coupler's rejection of the TEl1 mode were
measured. A known composition of TEl1 and TEl2 modes
was injected into each of the couplers. The phase between
the two modes entering the couplers was then changed by
adding straight sections of guide before the couplers. As the
length is changed by at least one beat wavelength, all rela-
tive phases between the two modes can be observed. The
interference caused by the unwanted mode can then be seen
as a ripple in the coupled power. The technique is very similar
to the sliding short method of determining coupler direc-
tivity. By placing a limit on the observed ripple, and by know-
12
ing the mode composition in the waveguide, one can calcu-
late the desired selectivity. Measurements at the center fre-
quency of 34.5 GHz revealed that the selectivity of the TE 11
coupler for the TEl2 mode was slightly better than 20 dB,
while the TEl2 coupler rejected the TEll mode by more than
30 dB, and thus met the selectivity goal. Although the selec-
tivity of the TE 11 coupler with respect to the TEl2 mode was
lower than expected, this should not pose a serious problem
in the expected applications of the coupler. This is the case
because the coupler will be used to detect the TEll mode,
where only small amounts of spurious power are expectea
to be present, whereas the TEl2 coupler will be used to
detect small amounts of TEl2 power in the presence of large
TEl I signal levels.
V. Mode Converter Measurements
This section of experimental results discusses measurements
of the frequency response and mode content versus distance
for the TEll to TEl2 mode converter. These measurements
were also made using the far-field pattern measurement
method described previously (Ref. 3). Once mode-selective
couplers have been built and characterized, the above mea-
surements can be made more easily and directly. The direc-
tional coupler method is also better suited to high-power
measurement than the far-field pattern method.
The frequency response of the TEll to TEl2 mode con-
verter is depicted in Fig. 5. For these measurements, a pure
TEll mode enters the mode converter, and the relative power
in the TEll and TEl2 modes exiting the device is measured
using the mode-selective couplers. Theoretical and measured
results are given for both modes. Near the center frequency
of the converter, nearly all of the input power is converted
into the TEl2 mode. Therefore, the power coupled out by the
TEl2 coupler peaks, while the TEll-coupled power dips. Good
agreement is found for all frequencies for the TEl2 power.
Good agreement is also found for the TEll power at all
frequencies except for those near maximum TEl2 output and
minimum TEll output. Here, only a 20-dB drop in TEll
power is seen, even though a much larger drop is predicted.
This is to be expected due to the finite selectivity of the
TEll coupler with respect to the TEl2 mode. The TEll
coupler only rejects the TEl2 mode by 20 dB, so when the
TEl2 power exceeds the TEll power by more than 20 dB,
the TEll coupler's output power is primarily due to TEl2
leakage. These results are then consistent with the previous
measurements, which showed 20-dB selectivity for the TEll
coupler.
Next, the mode content as a function of distance along
the mode converter at a frequency of 34.5 GHz was measured
using the couplers. This is possible since the mode converter,
which is a ripple-walled circular waveguide, was manufactured
in several sections. The complete device contained 7 ripples,
and was made up of two sections with 2 ripples each, and one
section with 3 ripples. By using different combinations of
these sections, the mode content after O, 2, 3, 4, 5, and 7
ripples may be determined. The theoretical mode content
may be calculated for any position in the device, however,
and is plotted in Fig. 6. The mode content after 0, 2, 3, 4, 5
and 7 ripples as measured by the couplers is aiso plotted for
comparison. For reference purposes, each ripple is 1.364-in.
long. Once again, excellent agreement is found for almost all
of the data points. There is some disagreement for the 0-
and 7-ripple cases due to the finite selectivities of the couplers.
For the 0-ripple case, essentially no TEl2 power is present,
but the TEl2 coupler does produce some output power due
to its finite selectivity for the TEll mode. Note that the
measured power is over 30 dB below the TEll power. This
is consistent with a selectivity value of greater than 30 dB
for the TEl2 coupler with respect to the TE ll mode, as
was quoted earlier. For the 7-ripple case, the finite selectivity
of the TE ll coupler comes into play, and gives an artificially
high value for the measured TE 11 power.
VI. Conclusions
A brief description of the method used to design mode-
selective couplers has been presented, along with parameters
for a TEll and a TEl2 coupler that have been fabricated and
tested. Good agreement between predicted and actual per-
formance has been obtained. These couplers were then used
to determine the characteristics of other multimode devices,
once again with good agreement between theory and experi-
ment. These latter experiments also demonstrated the limita-
tions that these couplers have due to the finite rejection of
other modes. Couplers may be designed to detect other TE
modes by a change in coupling guide and hole dimensions,
while couplers for the TM modes would require coupling
through the broad wall of the rectangular waveguide instead
of the narrow wall.
13
Acknowledgments
The author would like to acknowledge the excellent work of Max Rodarte, who
fabricated the two directional couplers.
References
1. Bhanji, A., Hoppe, D., Hartop, R., Stone, E.W., Imbriale, W.A., Stone, D., and
Caplan, M., "High Power Ka-Band Transmitter for Planetary Radar and Spacecraft
Uplink," TDA Progress Report 42-78, pp. 24-48, Jet Propulsion Laboratory, Pasa-
dena, Calif., April-June 1984.
2. Miller, S.E., "Coupled Wave Theory and Waveguide Applications," Bell System
Technical Journal, 33, pp. 661-719, 1954.
3. Hoppe, D., "An Experimental TF,12-TEll Circular Waveguide Mode Converter,"
TDA Progress Report 42-82, pp. 43-56, Jet Propulsion Laboratory, Pasadena, Calif.,
April-June 1985.
14
"k 
Fig. 1. Mode-selective coupler configuration 
Fig. 2. Fabricated TE,, coupler 
80 
70 
60 
% 50 
40 
30 
20 
-TE12 COUPLING '. 
----FORWARD T E l l  SELECTIVITY .-- ~ 
---FORWARD TE13SELECTIVITY 
FORWARD TE14 SELECTIVITY 
FORWARD TE15 SELECTIVITY 
-. - -- 
32 33 34 35 36 
FREQUENCY, GHz 
Fig. 3. Predicted coupling and selectivities for TE,, coupler 
15 
-69
-7O
I 1 I I
_ EXPERIMENT
THEORY *,..,,..,.,...,,... ,...
-71 I I I I
32 33 34 35 36 37
FREQUENCY. GHz
Fig. 4. The TEll coupling measurement vs theoretical results
0
-5
-10
-15
-20
-25
-30
-35
-40
/x.y
Y-TE, 
//
13 x TEl2
I I I I
32 33 34 35 36 37
FREQUENCY, GHz
Fig. 5. The TEll to TEl2 mode converter frequency response
10 I I I I
2
01 3 --x
_......_._ _x --
x_ 4 5
-10
-30
-40 ] _,,,,,,._TE12 THEORY
-5o I I I I
0 2 4 6 8
Z, in.
Fig. 6. Mode converter mode content vs distance
-20
10
16


Directional couplers for detecting the TE sub 11 and TE sub 12 circular waveguide modes

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