A novel 90-degree waveguide twist is presented. The design features compactness by utilizing a central triple-mode quarter-wave transformer region between input and output waveguides of different cross sections. Return-loss values in excess of 30 dB are obtained over an operating bandwidth close to 20 percent. Larger bandwidths are obtained by using additional quarter-wave steps preceding and/or succeeding the central transformer region. Several different design examples at 4, 6, 19 and 26 GHz are presented for this unique 90- degree twist transformer approach. Experimental verification is provided in the 6 and 19 GHz range

Amari, Smain

Bornemann, Jens

Rosenberg, Uwe

English

AMS Acta

A COMPACT AND BROADBAND 90-DEGREE WAVEGUIDE TWIST 
TRANSFORMER FOR INTEGRATED WAVEGUIDE SUBSYSTEMS
Uwe Rosenberg
Marconi Communications GmbH, D-71522 Backnang, Germany
Jens Bornemann
Dept. of Elec. & Comp. Engr, University of Victoria, Victoria, BC, V8W 3P6 Canada
Smain Amari
Dept. of Elec. & Comp. Engr, Royal Military College, Kingston, ON, K7K 7B4 Canada
Abstract: A novel 90-degree waveguide twist is presented. The design features compactness
by utilizing a central triple-mode quarter-wave transformer region between input and output
waveguides of different cross sections. Return-loss values in excess of 30 dB are obtained
over an operating bandwidth close to 20 percent. Larger bandwidths are obtained by using
additional quarter-wave steps preceding and/or succeeding the central transformer region.
Several different design examples at 4, 6, 19 and 26 GHz are presented for this unique 90-
degree twist transformer approach. Experimental verification is provided in the 6 and 19 GHz
range.
I. INTRODUCTION
Among a wide variety of polarization rotating components, 90-degree rectangular waveguide
twists play an important role for interconnections of waveguide systems or subsystems. Ear-
lier, twisted waveguide structures have been experimentally designed, e.g., [1], [2]. With the
advent of modern integrated waveguide technology, several restrictions are placed on the real-
ization of waveguide twist sections. They must be computer-aided designed, fabricated with-
out post-assembly tuning and realizable by CNC milling techniques as part of integrated
waveguide structures. Moreover, they need to cover a reasonable bandwidth and must be as
short as possible. Two attempts to satisfy such requirements have been reported. The continu-
ously varying L-shaped design in [3] can readily be machined but is several wavelengths long
and does not lend itself to fast CAD procedures. The design in [4] is built on a series of rectan-
gular waveguide sections and satisfies most of the above expectations. Its major drawback,
however, is the exceptional low bandwidth due to the utilization of only a single return-loss
zero in the stepped junction between the input and output guides. 
Therefore, this paper introduces a new design which is based on a central triple-mode quarter-
wave transformer region in order to enhance considerably the bandwidth of the twists in [4],
while maintaining a compact structure and the possibility of impedance transformation; i.e.,
input and output waveguides can have different geometries. The principal layout is depicted in
Fig. 1. The central transformer region is based on the propagating TE10, TM11, and TE01 tri-
ple-mode set representing electrically a three-section quarter-wave transformer. Hence, this
design permits the creation of a relatively large operating bandwidth with excellent return-loss
performance that can be further extended and improved by using additional transformer sec-
tions preceding and/or succeeding the central region. Several different computed and mea-
sured results demonstrate the validity of this unique design.
II. THEORY
The theoretical analysis of the compact twist is based on the coupled-integral-equations tech-
nique which combines several advantageous features, particularly for the computation of cas-
caded waveguide sections. (For details the reader is referred, e.g., to [5].) One of the salient
features of the method is the simultaneous inclusion of all edge conditions. Let a1, b1 and a2,
b2 in Fig. 2 be the cross-section dimensions of two connected waveguide sections at an arbi-
trary discontinuity in Fig. 1, then the basis function chosen to represent the electric field in the
common aperture are
where T0hr and T
0
es are the TE- and TM-mode cross-section functions of the common aper-
ture, and cr and cs are the respective coefficients of the basis functions. If one or more walls of
two connected guides are aligned, then the edge conditions of the respective mirror images are
included. 
Fig. 1 Principal layout of compact and broadband Fig. 2 Discontinuity formed by two offset- 
90-degree waveguide twist transformer. connected rectangular waveguides.
The design of this novel twist initially starts with the rough dimensioning of the central trans-
former region having a square cross section and a length of approximately a quarter guided
wavelength at the center frequency of the operating band. The interconnecting waveguides –
aligned at the lower (or upper) edge of the first cross section and at the right (or left) edge of
the second one – are associated with irises or transformer sections for further refinement of the
design. Final optimization of the complete structure as, e.g., in [6] fine tunes the design.
III. RESULTS
The twist design for WR137 waveguides serving the lower 6 GHz band (5.8 to 6.4 GHz)
shows extremely high performance (c.f. Fig. 3), i.e., the return-loss response exhibiting the
characteristic three transformation zeros exceeds 40 dB over more than the 12 percent band-
width. For experimental verification, this twist has been realized in two halves by CNC mill-
ing techniques (see photograph in Fig. 4). Despite the milling radii, the measured return loss
exhibits excellent properties (40 dB) within the desired band and is in good agreement with
the computed data.
Additionally, a 26 GHz twist has been designed for a 20 percent frequency band considering
an impedance transformation from a reduced-height input to a standard output waveguide
(WR34) of aspect ratio 2:1. Over the desired frequency band, a return loss - with the inherent
three zeros - of more than 30 dB (c.f. Fig. 5) is obtained which will suffice for the majority of
applications.
In order to enhance the bandwidth, we use an additional quarter-wave transformer section pre-
ceding the central triple-mode region. The performance of a 4 GHz design example for
WR229 waveguides is shown in Fig. 6. The computed response demonstrates the excellent
wide band performance based on the four return-loss zeros associated with the number of elec-
Xap x y,( )
Thr
0∇ ez×[ ]cr
1 x
e
--– 
  x
g
-- 1– 
  1 y
c
--– 
  y
d
-- 1– 
  1 3⁄
------------------------------------------------------------------------------------
Tes
0∇–[ ]cs
1 x
e
--– 
  x
g
-- 1– 
  1 y
c
--– 
  y
d
-- 1– 
  1 3⁄
------------------------------------------------------------------------------------
s
∑+
r
∑=
0
y
x
c
eg
b2
b1
a1
a2
d
 
trical transformer sections. 
Fig. 3 Measured (light line) and computed (dark line) Fig. 4 Photograph of 6 GHz prototype twist
performance of 6 GHz prototype twist transformer. transformer.
Fig. 5 Computed performance of triple-mode twist Fig. 6 Computed performance of quadruple- 
transformer in 26 GHz band. section twist transformer for the 4 GHz band.
In modern integrated waveguide systems, milling radii need to be accounted for in order to
avoid experimental fine adjustments [7]. Therefore, a regularly designed 19 GHz twist includ-
ing transformation from reduced-height to full-height waveguide (WR42) was redesigned for
reasonable milling radii of 1.05 mm; the length of the center section (incl. radii) is 4.5 mm. A
commercial software package providing the representation of the corner radii by boundary con-
tour mode-matching (BCMM) library elements was used for this purpose [8]. Fig. 7 shows the
comparison between measured and computed results. Between 17.5 and 20.6 GHz, the return
loss is better than 35 dB. The photograph in Fig. 8 depicts the prototype of this design with mill-
ing radii. Notice the different waveguide cross sections at the input (reduced height, upper port)
and output (full height, lower port).
IV. CONCLUSION
A compact 90-degree twist transformer providing high performance over broad operating fre-
quency bands has been established. The design is favorably suited for integrated waveguide
-80
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5.0 5.5 6.0 6.5 7.0
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R
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Lo
ss
,   
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-60
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0
20 22 24 26 30
Frequency,  GHz
R
et
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ss
,  
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-60
-20
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3.0 3.5 4.0 4.5 5.0
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-40
subsystems. It is based on a central triple-mode quarterwave transformer region that simulta-
neously permits impedance matching of different interface waveguide cross sections.  Deter-
mination of the geometry with exact performance prediction is obtained by the application of
effective EM CAD tools. Validation of the design strategy is provided by several different
designs for microwave and millimeter-wave frequency bands. Comparisons between com-
puted and measured results involving same and different input/output cross sections at 6 GHz
and 19 GHz demonstrate the effectiveness of the components. Moreover, the incorporation of
milling radii is accomplished.
Fig. 7 Measured (light line) and computed (dark line) Fig. 8 Photograph of the 19 GHz prototype twist 
performance of 19 GHz prototype twist transformer transformer with milling radii. Note the transfor- 
including milling radii of 1.05mm. mation from reduced-height to full-height wave-
guide 
REFERENCES
[1] H.A. Wheeler and H. Schwiebert, "Step-twist waveguide components", IRE Trans. Mi-
crowave Theory Tech., vol. MTT-3, pp. 44-52, Oct. 1955.
[2] B.C. DeLoach, "Step-twist-junction waveguide filters", IRE Trans. Microwave Theory
Tech., vol. MTT-9, pp. 130-135, Mar 1961.
[3] H.F. Lenzing and M.J. Gans, "Machined waveguide twist", IEEE Trans. Microwave The-
ory Tech., vol. 38, pp. 942-944, July 1990.
[4] J. Bornemann, "Design of integrated waveguide twist components", IEE Proc.-Microw.
Antennas Propag., Vol. 142, pp. 345-349, Aug. 1995.
[5] J. Bornemann, S. Amari and R. Vahldieck, "Analysis of waveguide discontinuities by the
coupled-integral-equations technique", Recent Res. Devel. Microwave Therory & Tech.,
Vol. 1, pp. 25-35, Dec. 1999.
[6] K. Madsen, H. Schaer-Jacobsen and J. Voldby, “Automated minimax design of net-
works,” IEEE Trans. Circuits Systems, Vol. CAS-22, pp. 791-796, Oct. 1975.
[7] R. Beyer, J. Bornemann, U. Rosenberg and J. Uher, "CAD of waveguide components for
antenna feed systems: State-of-the-art", in Proc. 8th Int. Symp. Microwave Optical Tech-
nology, pp. 413-420, Montreal, Canada, June 2001.
[8] Mician, µWave Wizard 4.0, User’s Manual, 2001 (www.mician.com).
 
-60
-20
0
17 18 19 20 21
Frequency,  GHz
R
et
ur
n 
Lo
ss
,  
 d
B
-40
 


A compact and broadband 90-degree waveguide twist transformer for integrated waveguide subsystems

Crossref

A Compact and Broadband 90-Degree Waveguide Twist Transformer for Integrated Waveguide Subsystems

A COMPACT AND BROADBAND 90-DEGREE WAVEGUIDE TWIST TRANSFORMER FOR INTEGRATED WAVEGUIDE SUBSYSTEMSUwe RosenbergMarconi Communications GmbH, D-71522 Backnang, GermanyJens BornemannDept. of Elec. & Comp. Engr, University of Victoria, Victoria, BC, V8W 3P6 CanadaSmain AmariDept. of Elec. & Comp. Engr, Royal Military College, Kingston, ON, K7K 7B4 CanadaAbstract: A novel 90-degree waveguide twist is presented. The design features compactnessby utilizing a central triple-mode quarter-wave transformer region between input and outputwaveguides of different cross sections. Return-loss values in excess of 30 dB are obtainedover an operating bandwidth close to 20 percent. Larger bandwidths are obtained by usingadditional quarter-wave steps preceding and/or succeeding the central transformer region.Several different design examples at 4, 6, 19 and 26 GHz are presented for this unique 90-degree twist transformer approach. Experimental verification is provided in the 6 and 19 GHzrange.I. INTRODUCTIONAmong a wide variety of polarization rotating components, 90-degree rectangular waveguidetwists play an important role for interconnections of waveguide systems or subsystems. Ear-lier, twisted waveguide structures have been experimentally designed, e.g., [1], [2]. With theadvent of modern integrated waveguide technology, several restrictions are placed on the real-ization of waveguide twist sections. They must be computer-aided designed, fabricated with-out post-assembly tuning and realizable by CNC milling techniques as part of integratedwaveguide structures. Moreover, they need to cover a reasonable bandwidth and must be asshort as possible. Two attempts to satisfy such requirements have been reported. The continu-ously varying L-shaped design in [3] can readily be machined but is several wavelengths longand does not lend itself to fast CAD procedures. The design in [4] is built on a series of rectan-gular waveguide sections and satisfies most of the above expectations. Its major drawback,however, is the exceptional low bandwidth due to the utilization of only a single return-losszero in the stepped junction between the input and output guides. Therefore, this paper introduces a new design which is based on a central triple-mode quarter-wave transformer region in order to enhance considerably the bandwidth of the twists in [4],while maintaining a compact structure and the possibility of impedance transformation; i.e.,input and output waveguides can have different geometries. The principal layout is depicted inFig. 1. The central transformer region is based on the propagating TE10, TM11, and TE01 tri-ple-mode set representing electrically a three-section quarter-wave transformer. Hence, thisdesign permits the creation of a relatively large operating bandwidth with excellent return-lossperformance that can be further extended and improved by using additional transformer sec-tions preceding and/or succeeding the central region. Several different computed and mea-sured results demonstrate the validity of this unique design.II. THEORYThe theoretical analysis of the compact twist is based on the coupled-integral-equations tech-nique which combines several advantageous features, particularly for the computation of cas-caded waveguide sections. (For details the reader is referred, e.g., to [5].) One of the salientfeatures of the method is the simultaneous inclusion of all edge conditions. Let a1, b1 and a2,b2 in Fig. 2 be the cross-section dimensions of two connected waveguide sections at an arbi-trary discontinuity in Fig. 1, then the basis function chosen to represent the electric field in thecommon aperture arewhere T0hr and T0es are the TE- and TM-mode cross-section functions of the common aper-ture, and cr and cs are the respective coefficients of the basis functions. If one or more walls oftwo connected guides are aligned, then the edge conditions of the respective mirror images areincluded. Fig. 1 Principal layout of compact and broadband Fig. 2 Discontinuity formed by two offset- 90-degree waveguide twist transformer. connected rectangular waveguides.The design of this novel twist initially starts with the rough dimensioning of the central trans-former region having a square cross section and a length of approximately a quarter guidedwavelength at the center frequency of the operating band. The interconnecting waveguides –aligned at the lower (or upper) edge of the first cross section and at the right (or left) edge ofthe second one – are associated with irises or transformer sections for further refinement of thedesign. Final optimization of the complete structure as, e.g., in [6] fine tunes the design.III. RESULTSThe twist design for WR137 waveguides serving the lower 6 GHz band (5.8 to 6.4 GHz)shows extremely high performance (c.f. Fig. 3), i.e., the return-loss response exhibiting thecharacteristic three transformation zeros exceeds 40 dB over more than the 12 percent band-width. For experimental verification, this twist has been realized in two halves by CNC mill-ing techniques (see photograph in Fig. 4). Despite the milling radii, the measured return lossexhibits excellent properties (40 dB) within the desired band and is in good agreement withthe computed data.Additionally, a 26 GHz twist has been designed for a 20 percent frequency band consideringan impedance transformation from a reduced-height input to a standard output waveguide(WR34) of aspect ratio 2:1. Over the desired frequency band, a return loss - with the inherentthree zeros - of more than 30 dB (c.f. Fig. 5) is obtained which will suffice for the majority ofapplications.In order to enhance the bandwidth, we use an additional quarter-wave transformer section pre-ceding the central triple-mode region. The performance of a 4 GHz design example forWR229 waveguides is shown in Fig. 6. The computed response demonstrates the excellentwide band performance based on the four return-loss zeros associated with the number of elec-Xap x y,( )Thr0Ñ ez´[ ]cr1 xe--–è øæ ö xg-- 1–è øæ ö 1 yc--–è øæ ö yd-- 1–è øæ ö 1 3¤------------------------------------------------------------------------------------Tes0Ñ–[ ]cs1 xe--–è øæ ö xg-- 1–è øæ ö 1 yc--–è øæ ö yd-- 1–è øæ ö 1 3¤------------------------------------------------------------------------------------så+rå=0yxcegb2b1a1a2d trical transformer sections. Fig. 3 Measured (light line) and computed (dark line) Fig. 4 Photograph of 6 GHz prototype twistperformance of 6 GHz prototype twist transformer. transformer.Fig. 5 Computed performance of triple-mode twist Fig. 6 Computed performance of quadruple- transformer in 26 GHz band. section twist transformer for the 4 GHz band.In modern integrated waveguide systems, milling radii need to be accounted for in order toavoid experimental fine adjustments [7]. Therefore, a regularly designed 19 GHz twist includ-ing transformation from reduced-height to full-height waveguide (WR42) was redesigned forreasonable milling radii of 1.05 mm; the length of the center section (incl. radii) is 4.5 mm. Acommercial software package providing the representation of the corner radii by boundary con-tour mode-matching (BCMM) library elements was used for this purpose [8]. Fig. 7 shows thecomparison between measured and computed results. Between 17.5 and 20.6 GHz, the returnloss is better than 35 dB. The photograph in Fig. 8 depicts the prototype of this design with mill-ing radii. Notice the different waveguide cross sections at the input (reduced height, upper port)and output (full height, lower port).IV. CONCLUSIONA compact 90-degree twist transformer providing high performance over broad operating fre-quency bands has been established. The design is favorably suited for integrated waveguide-80-60-40-2005.0 5.5 6.0 6.5 7.0Frequency,  GHzReturn Loss,   dB-60-20020 22 24 26 30Frequency,  GHzReturn Loss,   dB-4028 -60-2003.0 3.5 4.0 4.5 5.0Frequency,  GHzReturn Loss,   dB-40subsystems. It is based on a central triple-mode quarterwave transformer region that simulta-neously permits impedance matching of different interface waveguide cross sections.  Deter-mination of the geometry with exact performance prediction is obtained by the application ofeffective EM CAD tools. Validation of the design strategy is provided by several differentdesigns for microwave and millimeter-wave frequency bands. Comparisons between com-puted and measured results involving same and different input/output cross sections at 6 GHzand 19 GHz demonstrate the effectiveness of the components. Moreover, the incorporation ofmilling radii is accomplished.Fig. 7 Measured (light line) and computed (dark line) Fig. 8 Photograph of the 19 GHz prototype twist performance of 19 GHz prototype twist transformer transformer with milling radii. Note the transfor- including milling radii of 1.05mm. mation from reduced-height to full-height wave-guide REFERENCES[1] H.A. Wheeler and H. Schwiebert, "Step-twist waveguide components", IRE Trans. Mi-crowave Theory Tech., vol. MTT-3, pp. 44-52, Oct. 1955.[2] B.C. DeLoach, "Step-twist-junction waveguide filters", IRE Trans. Microwave TheoryTech., vol. MTT-9, pp. 130-135, Mar 1961.[3] H.F. Lenzing and M.J. Gans, "Machined waveguide twist", IEEE Trans. Microwave The-ory Tech., vol. 38, pp. 942-944, July 1990.[4] J. Bornemann, "Design of integrated waveguide twist components", IEE Proc.-Microw.Antennas Propag., Vol. 142, pp. 345-349, Aug. 1995.[5] J. Bornemann, S. Amari and R. Vahldieck, "Analysis of waveguide discontinuities by thecoupled-integral-equations technique", Recent Res. Devel. Microwave Therory & Tech.,Vol. 1, pp. 25-35, Dec. 1999.[6] K. Madsen, H. Schaer-Jacobsen and J. Voldby, “Automated minimax design of net-works,” IEEE Trans. Circuits Systems, Vol. CAS-22, pp. 791-796, Oct. 1975.[7] R. Beyer, J. Bornemann, U. Rosenberg and J. Uher, "CAD of waveguide components forantenna feed systems: State-of-the-art", in Proc. 8th Int. Symp. Microwave Optical Tech-nology, pp. 413-420, Montreal, Canada, June 2001.[8] Mician, µWave Wizard 4.0, User’s Manual, 2001 (www.mician.com). -60-20017 18 19 20 21Frequency,  GHzReturn Loss,   dB-40 

AMS Acta - Alm@DL - Università di Bologna

A COMPACT AND BROADBAND 90-DEGREE WAVEGUIDE TWIST 
TRANSFORMER FOR INTEGRATED WAVEGUIDE SUBSYSTEMS
Uwe Rosenberg
Marconi Communications GmbH, D-71522 Backnang, Germany
Jens Bornemann
Dept. of Elec. & Comp. Engr, University of Victoria, Victoria, BC, V8W 3P6 Canada
Smain Amari
Dept. of Elec. & Comp. Engr, Royal Military College, Kingston, ON, K7K 7B4 Canada
Abstract: A novel 90-degree waveguide twist is presented. The design features compactness
by utilizing a central triple-mode quarter-wave transformer region between input and output
waveguides of different cross sections. Return-loss values in excess of 30 dB are obtained
over an operating bandwidth close to 20 percent. Larger bandwidths are obtained by using
additional quarter-wave steps preceding and/or succeeding the central transformer region.
Several different design examples at 4, 6, 19 and 26 GHz are presented for this unique 90-
degree twist transformer approach. Experimental verification is provided in the 6 and 19 GHz
range.
I. INTRODUCTION
Among a wide variety of polarization rotating components, 90-degree rectangular waveguide
twists play an important role for interconnections of waveguide systems or subsystems. Ear-
lier, twisted waveguide structures have been experimentally designed, e.g., [1], [2]. With the
advent of modern integrated waveguide technology, several restrictions are placed on the real-
ization of waveguide twist sections. They must be computer-aided designed, fabricated with-
out post-assembly tuning and realizable by CNC milling techniques as part of integrated
waveguide structures. Moreover, they need to cover a reasonable bandwidth and must be as
short as possible. Two attempts to satisfy such requirements have been reported. The continu-
ously varying L-shaped design in [3] can readily be machined but is several wavelengths long
and does not lend itself to fast CAD procedures. The design in [4] is built on a series of rectan-
gular waveguide sections and satisfies most of the above expectations. Its major drawback,
however, is the exceptional low bandwidth due to the utilization of only a single return-loss
zero in the stepped junction between the input and output guides. 
Therefore, this paper introduces a new design which is based on a central triple-mode quarter-
wave transformer region in order to enhance considerably the bandwidth of the twists in [4],
while maintaining a compact structure and the possibility of impedance transformation; i.e.,
input and output waveguides can have different geometries. The principal layout is depicted in
Fig. 1. The central transformer region is based on the propagating TE10, TM11, and TE01 tri-
ple-mode set representing electrically a three-section quarter-wave transformer. Hence, this
design permits the creation of a relatively large operating bandwidth with excellent return-loss
performance that can be further extended and improved by using additional transformer sec-
tions preceding and/or succeeding the central region. Several different computed and mea-
sured results demonstrate the validity of this unique design.
II. THEORY
The theoretical analysis of the compact twist is based on the coupled-integral-equations tech-
nique which combines several advantageous features, particularly for the computation of cas-
caded waveguide sections. (For details the reader is referred, e.g., to [5].) One of the salient
features of the method is the simultaneous inclusion of all edge conditions. Let a1, b1 and a2,
b2 in Fig. 2 be the cross-section dimensions of two connected waveguide sections at an arbi-
trary discontinuity in Fig. 1, then the basis function chosen to represent the electric field in the
common aperture are
where T0hr and T
0
es are the TE- and TM-mode cross-section functions of the common aper-
ture, and cr and cs are the respective coefficients of the basis functions. If one or more walls of
two connected guides are aligned, then the edge conditions of the respective mirror images are
included. 
Fig. 1 Principal layout of compact and broadband Fig. 2 Discontinuity formed by two offset- 
90-degree waveguide twist transformer. connected rectangular waveguides.
The design of this novel twist initially starts with the rough dimensioning of the central trans-
former region having a square cross section and a length of approximately a quarter guided
wavelength at the center frequency of the operating band. The interconnecting waveguides –
aligned at the lower (or upper) edge of the first cross section and at the right (or left) edge of
the second one – are associated with irises or transformer sections for further refinement of the
design. Final optimization of the complete structure as, e.g., in [6] fine tunes the design.
III. RESULTS
The twist design for WR137 waveguides serving the lower 6 GHz band (5.8 to 6.4 GHz)
shows extremely high performance (c.f. Fig. 3), i.e., the return-loss response exhibiting the
characteristic three transformation zeros exceeds 40 dB over more than the 12 percent band-
width. For experimental verification, this twist has been realized in two halves by CNC mill-
ing techniques (see photograph in Fig. 4). Despite the milling radii, the measured return loss
exhibits excellent properties (40 dB) within the desired band and is in good agreement with
the computed data.
Additionally, a 26 GHz twist has been designed for a 20 percent frequency band considering
an impedance transformation from a reduced-height input to a standard output waveguide
(WR34) of aspect ratio 2:1. Over the desired frequency band, a return loss - with the inherent
three zeros - of more than 30 dB (c.f. Fig. 5) is obtained which will suffice for the majority of
applications.
In order to enhance the bandwidth, we use an additional quarter-wave transformer section pre-
ceding the central triple-mode region. The performance of a 4 GHz design example for
WR229 waveguides is shown in Fig. 6. The computed response demonstrates the excellent
wide band performance based on the four return-loss zeros associated with the number of elec-
Xap x y,( )
Thr
0Ñ ez´[ ]cr
1 x
e
--–è ø
æ ö x
g
-- 1–è ø
æ ö 1 y
c
--–è ø
æ ö y
d
-- 1–è ø
æ ö 1 3¤
------------------------------------------------------------------------------------
Tes
0Ñ–[ ]cs
1 x
e
--–è ø
æ ö x
g
-- 1–è ø
æ ö 1 y
c
--–è ø
æ ö y
d
-- 1–è ø
æ ö 1 3¤
------------------------------------------------------------------------------------
s
å+
r
å=
0
y
x
c
eg
b2
b1
a1
a2
d
 
trical transformer sections. 
Fig. 3 Measured (light line) and computed (dark line) Fig. 4 Photograph of 6 GHz prototype twist
performance of 6 GHz prototype twist transformer. transformer.
Fig. 5 Computed performance of triple-mode twist Fig. 6 Computed performance of quadruple- 
transformer in 26 GHz band. section twist transformer for the 4 GHz band.
In modern integrated waveguide systems, milling radii need to be accounted for in order to
avoid experimental fine adjustments [7]. Therefore, a regularly designed 19 GHz twist includ-
ing transformation from reduced-height to full-height waveguide (WR42) was redesigned for
reasonable milling radii of 1.05 mm; the length of the center section (incl. radii) is 4.5 mm. A
commercial software package providing the representation of the corner radii by boundary con-
tour mode-matching (BCMM) library elements was used for this purpose [8]. Fig. 7 shows the
comparison between measured and computed results. Between 17.5 and 20.6 GHz, the return
loss is better than 35 dB. The photograph in Fig. 8 depicts the prototype of this design with mill-
ing radii. Notice the different waveguide cross sections at the input (reduced height, upper port)
and output (full height, lower port).
IV. CONCLUSION
A compact 90-degree twist transformer providing high performance over broad operating fre-
quency bands has been established. The design is favorably suited for integrated waveguide
-80
-60
-40
-20
0
5.0 5.5 6.0 6.5 7.0
Frequency,  GHz
R
et
ur
n 
Lo
ss
,   
dB
-60
-20
0
20 22 24 26 30
Frequency,  GHz
R
et
ur
n 
Lo
ss
,  
 d
B
-40
28
 
-60
-20
0
3.0 3.5 4.0 4.5 5.0
Frequency,  GHz
R
et
ur
n 
Lo
ss
,   
dB
-40
subsystems. It is based on a central triple-mode quarterwave transformer region that simulta-
neously permits impedance matching of different interface waveguide cross sections.  Deter-
mination of the geometry with exact performance prediction is obtained by the application of
effective EM CAD tools. Validation of the design strategy is provided by several different
designs for microwave and millimeter-wave frequency bands. Comparisons between com-
puted and measured results involving same and different input/output cross sections at 6 GHz
and 19 GHz demonstrate the effectiveness of the components. Moreover, the incorporation of
milling radii is accomplished.
Fig. 7 Measured (light line) and computed (dark line) Fig. 8 Photograph of the 19 GHz prototype twist 
performance of 19 GHz prototype twist transformer transformer with milling radii. Note the transfor- 
including milling radii of 1.05mm. mation from reduced-height to full-height wave-
guide 
REFERENCES
[1] H.A. Wheeler and H. Schwiebert, "Step-twist waveguide components", IRE Trans. Mi-
crowave Theory Tech., vol. MTT-3, pp. 44-52, Oct. 1955.
[2] B.C. DeLoach, "Step-twist-junction waveguide filters", IRE Trans. Microwave Theory
Tech., vol. MTT-9, pp. 130-135, Mar 1961.
[3] H.F. Lenzing and M.J. Gans, "Machined waveguide twist", IEEE Trans. Microwave The-
ory Tech., vol. 38, pp. 942-944, July 1990.
[4] J. Bornemann, "Design of integrated waveguide twist components", IEE Proc.-Microw.
Antennas Propag., Vol. 142, pp. 345-349, Aug. 1995.
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A compact and broadband 90-degree waveguide twist transformer for integrated waveguide subsystems

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