Composite corporate traveling-wave power dividers for slot array waveguide antennas

Composite Corporate Traveling-Wave PowerDividers for Slot Array Waveguide Antennas

Dominic Deslandes,1 Francois Boone,2 Ke Wu3

1 Department of Computer Science, Universite du Quebec a Montreal, Montreal, QC, Canada2 Department of Electrical and Computer Engineering, Universite de Sherbrooke,Sherbrooke, QC, Canada3 Department of Electrical Engineering, Ecole Polytechnique de Montreal, Montreal, QC, Canada

Received 24 January 2008; accepted 26 April 2008

ABSTRACT: A composite corporate traveling-wave power divider is presented. The single-

layer structure is composed of three parts: two interdigital traveling-wave subsections com-

bined with a power splitter. An iterative design technique is described in which the divider

is split into a number of basic blocks. Large-scaled networks are then easily designed

because the whole structure does not need to be simulated. A method to take into account

the insertion losses is also proposed and bandwidth enhancement is discussed, which is done

by increasing the number of corporate layers. Experimental results are also shown for a 1:4

subsection. It provides equal output power with 0.5 dB of insertion loss. The phase-shift

between output ports is close to the specifications of 21508 at 30 GHz, with an error of lessthan 28. It is also shown that this topology is well suited for frequency scanning antenna. VVC 2008

Wiley Periodicals, Inc. Int J RF and Microwave CAE 19: 177–186, 2009.

Keywords: antenna feeds; power dividers; rectangular waveguides; slot arrays; traveling-wave

devices

I. INTRODUCTION

Slot array waveguide antennas are widely used in

communication and radar systems. These antennas

are composed of two parts, namely, an array of slots

and a feed network. Many different topologies of

feeders have been proposed over the last years. The

most common technique to distribute the power is to

use the well-known corporate feeder. However, in

high-gain antenna design, a large number of parallel

waveguides must be used and the feeders become

bulky. A more compact feed network can be obtained

with a perpendicular feeder located under the antenna

waveguides. The coupling is then achieved with the

help of alternatively inclined slots to obtain an in-

phase excitation [1]. This structure is very compact

but requires the precision manufacturing and align-

ment of two pieces.

A similar feeder realized on a single-layer was

also proposed [2]. The perpendicular feed waveguide

is then coupled to the waveguide array with irises.

This structure is, however, limited to alternating-

phase fed antennas, thus preventing the design of a

broadside array. This problem can be circumvented

by coupling two waveguides together instead of one,

as shown in [3]. The coupling irises are then spaced

one wavelength apart and all the waveguides of the

array are fed in-phase. But, it is impossible to design

a feeder with different phase shifts between the out-

puts in this configuration. An inclined feeder can pro-

vide certain flexibility in the choice on the output

Correspondence to: D. Deslandes; e-mail: [email protected]

DOI 10.1002/mmce.20338Published online 20 August 2008 in Wiley InterScience (www.

interscience.wiley.com).

VVC 2008 Wiley Periodicals, Inc.

177

phases [4]. Nevertheless, this last structure is bulky

and does not allow designing feeders with an arbi-

trary combination of phase and amplitude.

On the other hand, traveling-wave structure has

been successfully applied to design compact power

divider/combiner for high-power amplifier applica-

tions [5]. For these applications, the relative output

phase shifts of the divider are not important since it is

compensated by the combiner. The outputs can then

be spaced apart which decreases the effect of higher-

order modes. However, for antenna applications, the

antenna waveguides must be placed closely to avoid

grating lobes. The design then becomes much more

complex due to the higher-order mode effects. These

effects may be circumvented by using an interdigital

structure, as applied in the design of dual-polarization

antennas [6].

The topology presented in this article is not

purely traveling-wave but a composite corporate

traveling-wave structure. A topology using this

scheme has been proposed and was briefly dis-

cussed by the authors in [7]. This article is to extend

the work presented at the conference by including

the evaluation of the coupling level, a method to

take into account the insertion losses, a comprehen-

sive description of the design steps, and a discus-

sion on bandwidth enhancement. The topology and

operating mechanism are discussed in Section II.

The iterative design process is detailed in Section

III. Section IV deals with the concept of bandwidth

enhancement and an experimental validation is pre-

sented in Section V.

II. POWER DIVIDER TOPOLOGYAND MECHANISMS

An exploded view of the composite corporate travel-

ing-wave power divider topology, including the slot

array waveguides, is shown in Figure 1. The power

divider topology can be divided in three parts: two

interdigital subsections joined by a power splitter, all

identified in Figure 1 by numbers 1–3, respectively.

The two interdigital subsections are composed by

a cascade of T-junctions interconnected by wave-

guide sections. In Ref. [2], the length between two T-

junctions was around half a wavelength. The interac-

tion of higher-order modes is then non-negligible and

the structure must be optimized in a single bloc, sig-

nificantly increasing the simulation time. The struc-

ture of Figure 1 has solved this problem by using an

interdigital topology. The spacing between two con-

secutive T-junctions of a subsection is then approxi-

mately a wavelength. The higher-order modes are

sufficiently attenuated to be neglected and the feeder

can be decomposed in N separated T-junctions joined

by N 2 2 straight waveguides, where N is the number

of antenna waveguides in the array. The problem

then resumes to the design of N T-junctions which,

when cascaded, will provide the right output ampli-

tudes and phases.

In Ref. [7] it has been proved that the proposed to-

pology is universal, which means the structure can be

used to design feeders with any arbitrary combina-

tions of amplitudes and phases. This property is

obtained by using two different mechanisms. First,

the T-junctions are set to provide the right amplitude

level and secondly, widths of waveguide sections

interconnecting T-junctions are adjusted to fix the

phase shift. Thus, each block of the two interdigital

sub-sections is designed to adjust only one parameter

(amplitude or phase). This leads to the use of an itera-

tive design technique to fix the coupling levels and

connecting waveguide widths, which will be pre-

sented in Section III.

Figure 1. Exploded view of the composite corporate

traveling-wave power divider including the slot array

waveguide antenna: (1) first interdigital sub-section; (2)

second interdigital sub-section; (3) power splitter.

178 Deslandes, Boone, and Wu

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

The last part of the divider is the power splitter

subsection. This is realized with a power splitter and

two bends. There are many different ways to achieve

these functions. First of all, the power splitter can be

realized with a full-height post [8], a partial-height

post [9], a stub [10], or different matching structures

used to obtain the right output levels. The corner is

realized with a curved bend [11], a mitered bend

[12], or with posts [13]. Different combinations are

shown in Figure 2.

It is important to realize that this feeding subsec-

tion must not always provide an in-phase division. In

fact, the required phase is related to the number of

slots in each waveguide. Figure 3 shows two consec-

utive antenna waveguides in the array. The arrows

over the slots represent the polarization of the electric

field in the slots. The phase of the electric field

required to adequately excite the slots is shown

beside each slot, in the center of the antenna wave-

guides. This phase is either 08 or 1808. When the

number of slots is odd, all antenna waveguides must

be excited in-phase as described in Figure 3a. The

power splitter must then provide an in-phase division.

However, if the number of slots is even, the two

interdigital subsections must be excited out of phase,

as indicated in Figure 3b. This is easily realized by

offsetting the power-splitter by a quarter wavelength,

as shown in Figure 4.

III. ITERATIVE DESIGN TECHNIQUE

Different techniques have been used to synthesize

slot array waveguide antenna feeders. Coupling-slot

feeders have been analyzed with the method of

moments and a pattern synthesis technique was used

Figure 2. Three different topologies of power splitter:

(a) mitered bends with stepped power-splitter; (b) rounded

bends and splitter; (c) bends and splitter realized with

posts.

Figure 3. Required phase at the input of antenna waveguides: a) if the number of slots is odd,

waveguides are fed in-phase; b) if the number of slots is even, the waveguides are fed out of phase.

Corporate Traveling-Wave Power Dividers 179


to obtain a shaped beam broadside antenna [1]. Pla-

nar waveguide feeders have been analyzed with nu-

merical technique including method of moment [2, 3]

and finite element method [4]. The synthesis is

achieved by successively designing and cascading

each junction [2–4]. An iterative procedure can then

be applied to improve the results [2]. This last tech-

nique is suitable for traveling-wave structures

because each junction parameter is dependant of all

the others junctions.

In the proposed divider, each interdigital subsec-

tion is decomposed into basic building blocks, as

shown in Figure 5a. Since the length of the inter-

connecting waveguides is about a wavelength, a

single mode representation is sufficient and the

analysis of the whole structure can be done by cas-

cading 2 3 2 S-matrix, as illustrated in Figure 5b.

However, all building blocks are not independent

and an iterative technique must be applied to take

into account mutual coupling effects. It is important

to note that the numbering of T-junctions begins at

the short-circuit side and not at the input port side

as shown in Figure 5a.

A. Evaluation of the Coupling Level

The T-junction shown in Figure 6 can couple any

power level between 0 dB and 21 dB. In the spe-

cific case of 0 dB, the Port 2 is short-circuited and,

with a proper design, all the power is transferred to

Port 3. This is always the case for junction number 1.

When the coupling level tends to be 21, the iris

width and inset length tend to be zero, which gives a

straight waveguide section. In all other cases, the iris

width is used to adjust the coupling level and the

inset length and offset are used to match the junction.

The first step in the design process is to evaluate

the required coupling level in every T-junction. This

level is fixed by the power distribution required to

obtain the desired radiation pattern. This distribution

can be uniform, binomial, Chebychev, etc. In all T-

junctions, the incident power at Port 1 is completely

transferred to Ports 2 and 3, if the losses are neglected.

Since all the junctions are perfectly matched at Port 1,

there is no reflected power at Port 1 and, consequently,

no incident power at Port 2. This comes from the fact

that all the junctions are cascaded and Port 2 of junc-

tion number n þ 1 is connected to Port 1 of junction

number n. Also, there is no incident power at Port 3 at

the central frequency since it is connected to a

matched antenna. In all T-junctions, the transmission

coefficient between Ports 1 and 3, S3l, n, can be written

in the form of a power ratio:

S3l;n�� 2¼ P3;n

Pl;n; ð1Þ

where Pl,n is the incident power at Port 1 and P3,n is thetransmitted power at Port 3, both for the nth junction. Fur-thermore, the input power of the nth junction is equal to

the sum of the output power of the preceding junctions:

Figure 4. Phase adjustment for the power splitter: (a) in-

phase outputs for an odd number of slots; (b) out-of-phase

outputs for an even number of slots.

Figure 5. Decomposition of the power divider into basic blocs: (a) physical representation; (b)

electrical representation.



Pl;n ¼Xnk¼1

P3;k� ð2Þ

Combining (1) and (2), we obtain:

S3l;n�� 2¼ P3;nPn

k¼1P3;k

: ð3Þ

However, the amplitude distribution of feeder net-

works is more often given in terms of voltage other

than power. In this case (3), becomes equal to:

S3l;n�� 2¼ V2

nPnk¼1

V2k

; ð4Þ

where Vk is the desired voltage for the array

shaping.

B. Insertion Losses

When there are a large number of outputs in the

power divider, the insertion loss can yield influence

on the amplitude ratio. The traveling wave will be

more and more attenuated as it propagates through

the divider. It is, however, possible to take it into

account in the design process. Equation (1) can be

rewritten in the following form:

P3;n ¼ Pl;n S3l;n�� 2: ð5Þ

Also, the output power of the first T-junction can be

expressed as a function of the input power of the nth

junction:

P3;l ¼ Pl;n S3l;l�� 2Yn

k¼2S2l;k�� 2 S2l;ðk;k�1Þ�� 2: ð6Þ

In the last equation, S3l,l is the transmission coeffi-

cient between Ports 1 and 3 for the first T-junction,

S2l,k is the transmission coefficient between Ports 1

and 2 for the kth T-junction and S2l,(k,k2l) is the trans-

mission coefficient of the connecting waveguide

between the kth and k21th T-junctions. Dividing (6)

by (5) and rearranging it, we obtain:

S3l;n�� 2¼ P3;n

P3;lS3l;l�� 2Yn

k¼2S2l;k�� 2 S2l;ðk;k�1Þ�� 2: ð7Þ

If a voltage distribution is used in place of the power

distribution, we obtain:

S3l;n�� 2¼ V2

n

V2l

S3l;l�� 2:Yn

k¼2S2l;k�� 2 S2l;ðk;k�lÞ�� 2: ð8Þ

C. Iterative Design Technique

The relative phase shift between two consecutive T-

junctions in an interdigital subsection, by neglecting

the internal phase shift of the T-junction, is given by:

D/� 2mp ¼ �bal0; ð9Þ

where ba is the propagation constant of the feeder

waveguide, l0 is the spacing between two adjacent T-

junctions of a subsection and m is a constant that has

Figure 6. T-junction basic building block: (a) ports and

reference plane; (b) dimensions.



been defined in [7]. The propagation constant is equal

to:

ba ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik20 �

pa

� �2:

rð10Þ

The distance between two T-junctions can be found

as:

l0 ¼ 2bþ 2g; ð11Þ

where b is the antenna waveguide width and g is the

thickness of walls between these waveguides.

The phase shift between Ports 1 and 2 as well as

Ports 1 and 3 (ffS2l and ffS3l), referring to Figure 6a,

varies with the coupling value of the T-junction.

They must then be taken into account with an itera-

tive technique. First of all, variables cn, dn, and en areoptimized for every T-junction under the following

conditions:

1Þ Minimize S1l;n��

2Þ S3l;n ¼ 10 logV2nPn

k¼1V2k

0BB@

1CCA:

ð12Þ

If the insertion losses are not negligible, the follow-

ing equation must then be used in place of (12):

1Þ Minimize S1l;n��

2Þ S3l;n ¼ 10 logVnVl

S3l;l�� 2:Yn

k¼2S2l;k�� S2l;ðk;k�lÞ�� !

:

ð13Þ

The values of ffS2l,n and ffS3l,n calculated in this first

iteration, with the reference plane as defined in Fig-

ure 6a, are then applied to resize the width of wave-

guide sections ain,nþ1, as follows. The length of the

waveguide section between T-junction numbers nand n þ 1, at the iteration step i, is given by:

lin ¼ l0 þ ein � einþ1; ð14Þ

where l0 is defined in (11) and ein is the offset length

of inset number n at iteration number i. When the in-

ternal phase shifts of T-junctions are taken into

account, (9) becomes:

D/n;nþ1 � 2mp ¼ ffSi2l;nþ1 þ ffSi3l;n � ffSi3l;nþ1 � binlin:ð15Þ

Solving (15) for bin and combining with (10), the

width of interconnecting waveguide section number nfor the next iteration can be found by

aiþ1n;nþ1 ¼pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

k20 � bin� �2q : ð16Þ

The widths of ports 1 and 2 in every T-junction are

then set to be their new values for the next iteration.

D. Design Steps

The design steps required to obtain the power divider

with specifications are:

1. Estimate the initial dimensions: At the first

step, variables a, b, and g must be selected in

order to respect (9) combined with (10) and

(11). In other words, the waveguide dimen-

sions and spacing must be selected to obtain

the specified phase shift when the T-junction

internal phase shifts are neglected. There are

indeed multiple solutions and the designer

must take into account other parameters in

his/her choice, as mechanical feasibility, gra-

ting lobes, single mode propagation, physical

interconnection, etc.

2. Initialize all variables: Then, the initial

dimensions, referring to Figure 6, are set to be

cn 5 an, n þ 1/2, dn 5 an, n þ 1/2, and en 5 0.

3. Evaluate the required coupling level values:The coupling levels are evaluated by using (4)

or (8) if insertion losses are not negligible.

For the later, the values of S2l,k are not

known, so they are preliminarily set to be

zero. However, it is possible to initially evalu-

ate the losses in the waveguide sections inter-

connecting the T-junction, S2l,(k, k þ 1). Wave-

guide width an and length l0 have been esti-

mated in step 1 and the insertion losses is

readily evaluated [14].

4. Optimize all T-junctions: All the T-junctions

are optimized by following the criteria defined

in (12) or (13) if the insertion losses are not

negligible. Only parameters cn, dn, and en are

optimized. For the first T-junction, however,

the length of the short-circuited stub placed at

Port 2 must also be optimized.

5. Compute the width of the waveguide sections:The width of the waveguide section is reeval-

uated, taking into account the internal phase

shift through (15).



6. Verify the convergence: The error functions

for the kth section, evaluated between two con-

secutive iterations, are given by:

Ek ¼ aiþ1k � aik�� : ð17Þ

To obtain the convergence, the error for all wave-

guide sections must be smaller than a defined toler-

ance which should also be smaller than the manufac-

turing tolerance. The flowchart of the design process

is depicted in Figure 7.

IV. BANDWIDTH ENHANCEMENT

The design process shown in Figure 7 is achieved

only at the central frequency. Therefore it cannot

assess accurately the bandwidth of the structure. This

bandwidth is limited by the frequency variation of

the matching and coupling levels of T-junctions.

Interestingly, it has been found that the T-junction to-

pology shown in Figure 6 almost provides a constant

coupling level over the entire waveguide bandwidth.

Figure 8 shows the frequency response of a T-

junction optimized to provide a 3 dB coupling at

30 GHz. We can see that the bandwidth is not limited

by the variation of the coupling level but by the

matching level. This one is below 220 dB from 27.4

GHz to 32.8 GHz. Similar behaviors have been

observed for other coupling values.

The topologies shown in Figure 5a can be used to

design antenna feeders with any number of outputs.

However, since this is a composite corporate travel-

ing-wave feeder, the output phase will vary according

to frequency. This phase shift will tilt the main beam

angle. When a large number of outputs are required

or a wide bandwidth is necessary, the composite cor-

porate traveling-wave feeder bandwidth can be

improved by increasing the number of layers of the

corporate part. This concept is illustrated in Figure 9

with a 1:8 power divider.

In Figure 9a the corporate part has one layer and

there are two interdigital sub-sections. In Figure 9b

the corporate part has two layers and there are four

interdigital sub-sections. In Figure 9c the feeder is

completely corporate. In the later case, the bandwidth

is no longer limited by the output phases as they are

all fed in-phase over the entire frequency span. In

this way, it is easier to obtain the best compromise

between size and bandwidth.

Figure 8. Frequency response of a T-junction optimized

to provide 3 dB coupling at 30 GHz.

Figure 7. Flow-chart of the iterative design process.



V. EXPERIMENTAL VALIDATION

The proposed technique has been validated on a 1:8

power divider working at 30 GHz with a uniform am-

plitude distribution and a phase shift of 2758between adjacent antenna waveguides. The feeder is

split in three blocks: two identical interdigital 1:4

subsections linked together with a 1:2 power splitter.

The problem is then simplified to the design of a 1:4

power divider with a uniform amplitude distribution

and a phase shift between adjacent outputs of 21508,that is to say D/n,nþ1 5 22.62 rad for all n. Bycombining (9) and (10) with a 5 7.112 mm (WR28),

f 5 30 GHz, and D/ 5 22.62 2 2p 5 28.9 rad, one

gets l0 5 19.894 mm. A possible combination to

solve (11) is b 5 7.112 mm and g 5 2.835 mm. For

a uniform distribution, Vn 5 1, the coupling level is

found by using (4) which gives these couplings: 0

dB, 23 dB, 24.77 dB, and 26 dB. The design proc-

ess is then applied and the dimensions for all itera-

tions have been reported in [7]. Five iterations are

required to reach the convergence for a variation

lower than 0.1% for all dimensions. Even though the

convergence is not guaranteed, we did not observe

any divergence problems in the different designs we

tested. We also observed that the required number of

iterations is proportional to the number of outputs.

An interdigital subsection has been fabricated and

measured to validate the proposed structure as wellas the design technique. The prototyped structure isshown in Figure 10 without the cover. The measure-ment of this 5 port network is performed with three

waveguide loads and two coaxial transitions. Theposition of the transitions and loads are then per-muted to measure all the reflection and transmissioncoefficients. The main disadvantage of this technique

is that results are highly dependant of the return lossof loads. The measured coefficients of reflection forthe three loads in the bandwidth of interest are shown

Figure 10. Picture of the fabricated traveling-wave sub-section.

Figure 9. Bandwidth enhancement by increasing the

number of corporate layers: (a) one corporate layer; (b)

two corporate layers; (c) completely corporate.



in Figure 11. The return loss is very good but there

are strong ripples in the entire measured bandwidth.

These ripples will slightly affect the measured results,

as shown in the next two figures.

The measured results are shown in Figure 12. The

return loss is better than220 dB from 26.9 GHz to 31.2

GHz. All transmission coefficients fluctuate around

26.5 dB, which represents 0.5 dB insertion loss. The

phase shifts between adjacent outputs are shown in Fig-

ure 13. The structure provides a phase shift around

21508 at 30 GHz, with a maximal error of 28.A characteristic behavior of this topology is the fre-

quency dependence of the phase shift between the out-

puts. As described in Section IV, this aspect can reduce

significantly the bandwidth. However, it can also be

used to design frequency scanning antennas. In this

case, the frequency dependence is desired and should be

linear. Figure 13 shows that the subsection provides a

3608 shift from 26 GHz to 36 GHz with good linearity.

VI. CONCLUSION

A novel composite corporate traveling-wave power di-

vider has been proposed and presented in this article.

The modular structure can be designed to provide any

combination of phases and amplitudes. With the itera-

tive design technique proposed in this work, the feeder

is divided into several blocks. Each block is then ana-

lyzed and optimized separately at only one frequency.

In this way, the complete structure would never have

to be simulated, which speeds up the design process.

Furthermore, a technique to overcome the loss

effects on the output amplitudes has been developed.

It opens the way to the design of large-scaled but

compact antenna feeders, without distortion due to

conductor losses in the traveling-wave section.

Experimental results have validated the proposed

structure topology as well as the developed design

process. With the increasing popularity of millimeter-

wave imaging, this structure provides a compact solu-

tion for the design of frequency scanning antennas.

ACKNOWLEDGMENTS

The authors wish to acknowledge the financial support of

the Natural Sciences and Engineering Research Council of

Canada.

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Figure 11. Return losses of the three loads used in the

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BIOGRAPHIES

Dominic Deslandes received the B.Sc.

degree in electrical engineering from the

University of Sherbrooke, Canada, in

1998, and the M.Sc. and Ph.D. degrees

from the Ecole Polytechnique de Mon-

treal, Canada, in 2001 and 2005, all in

electrical engineering. From 2006 to

2007, he was a Post-Doctoral Researcher

at the University of Sherbrooke, Canada.

In December 2007, he joined the Department of Computer Sci-

ence at the University of Quebec in Montreal, Canada, where he

is now assistant professor. His research interests include the anal-

ysis, synthesis, and integration of passive and active components

for microwave and millimeter-wave systems. Dr. Deslandes was

awarded the Natural Sciences and Engineering Research Council

Doctoral Prize (Best Engineering Thesis in Canada) in 2007 and

the Best Student Paper Award at APMC in 2005.

Francois Boone received the Eng. Dipl.

in Electrical Engineering from Ecole

Nationale Superieure d’Electronique,

d’Electrotechnique, d’Informatique et

d’Hydraulique de Toulouse (ENSEEIHT),

France, in June 1992 and the DEA in

microwave engineering from the Institut

National Polytechnique de Toulouse

(INPT) in 1993. In 1997 and 2000,

respectively, he received M.Sc. and Ph.D degrees in microwave en-

gineering, both from Ecole Polytechnique de Montreal, Canada in

October 1999, he joined the Department of Electrical and Computer

Engineering of Faculty of Engineering at the University of Sher-

brooke, Canada, where he is now an associate professor. His research

interests concern analysis, modeling and design of passive and active

microwave, and millimeter-wave components and circuits.

Ke Wu is Canada Research Chair Profes-

sor in RF and millimeter-wave engineer-

ing at Ecole Polytechnique (University of

Montreal). He has been Director of the

Poly-Grames Research Center. He has

authored or coauthored more than 600

referred papers, and a number of books/

book chapters and patents. He has held

key positions in and has served on various

panels and international committees including the chair of many

committees and international conferences/symposia. He has

served on the editorial/review boards of many journals, transac-

tions, and letters including associate editor, editor, and guest edi-

tor. He is an elected IEEE MTT-S AdCom member for 2006–

2009 and serves as chair of the IEEE MTT-S Transnational Com-

mittee. Dr. Wu was the recipient of many awards and prizes. He

is a Fellow of the IEEE, a Fellow of the Canadian Academy of

Engineering and a Fellow of the Royal Society of Canada (The

Canadian Academy of the Sciences and Humanities).



Composite corporate traveling-wave power dividers for slot array waveguide antennas

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