novel dispersive modal approach

8/10/2019 Novel Dispersive Modal Approach ..

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A NEW FULL-WAVE MODAL TECHNIQUE FOR FAST MODELING OF

ISOTROPIC/ANISOTROPIC ASYMMETRIC CPW

A. Khodja*, M.C.E. Yagoub**, R. Touhami* and H. Baudrand***

*Instrumentation Laboratory, Faculty of Electronics and Informatics, U.S.T.H.B, Algiers, Algeria

**EECS, University of Ottawa, 800 King Edward, Ottawa, Ontario, K1N 6N5, Canada

***ENSEEIHT, 2 rue Charles Camichel 31071, Toulouse Cedex 7, France

ABSTRACT

In this paper, an original dispersive numerical modal

approach combining accuracy and speediness is presented as

promising tool for fast analysis of asymmetric coplanar

waveguide on isotropic/anisotropic substrates. For this

purpose, a quasi-symmetric model was introduced using C

and mode trial functions along with the formalism ofoperators to efficiently study the dispersion effect of

coplanar structures. Comparisons with published and

asymmetric model data are presented to further confirm the

adequate choice of trial functions used in this quasi-

symmetric approach.

Index TermsAdmittance operator, dispersion, quasi-

symmetric approach, trial functions

1. INTRODUCTION

Due to their higher performance over conventional

microstrip structures requiring shunt and series connections,coplanar waveguides (CPWs) on isotropic/anisotropic

substrates have been widely investigated to design and

manufacture millimeter-wave integrated circuits [1].Coplanar-type structures do not require any via to ground

[2]. An asymmetric version of the coplanar waveguide

(ACPW) has been introduced mainly because of the

additional flexibility offered by the asymmetric

configuration in the design process. Several theoretical

analyses of CPW have been reported based on quasi-static

and full-wave techniques. To efficiently analyze asym-

metric coplanar structures, a full-wave modal integral

technique combined with the electromagnetism operator

formalism has been proposed in this work. It consists toadequately formulate the boundary conditions by

considering the fictitious propagation in the transverse

direction of the CPW. Then, by properly selecting the trial

functions to be used in the asymmetric case, an original

quasi-symmetric approach was developed leading, via the

Galerkin's technique, to a smaller-size dispersion matrix and

thus, significantly reducing the computational effort

required to fully characterizing ACPW on isotropic or

anisotropic substrates. However, for the general case of

ACPW, the propagation constants and coupling

characteristics were determined by C- and -modes whichare the most convenient way to describe the behavior of

asymmetrical structures [3]. The method formulation

depends on the expression of the uniaxial diagonal relative

permittivity tensor, where the diagonal tensor can be noted

as r = [r2-r2-r3] with rx = rz = r2 and ry = r3. Acomparative study of the propagation characteristics, withrespect to electrical and physical parameters, demonstrated

the advantages of the proposed quasi-symmetric model

within a certain range of shielding and slot width

dimensions.

2. METHOD OF ANALYSIS

The key issue in the proposed approach is the evaluation of

the admittance operator to which the Galerkin's techniquewas applied. A homogeneous system of algebraic equations

can be obtained from which the propagation constant or

the effective permittivity eff can be determined. In thiswork, the analyzed asymmetric coplanar structure is arectangular waveguide containing homogeneous anisotropic

and lossless dielectric substrate. The upper face of this

substrate is partially metallized by three parallel uniform

and perfectly conducting strips along the oz-direction of

propagation, separated by two slots where the thickness of

the conducting strips is negligible as shown in Fig. 1. To

reach the Galerkin's procedure, an equivalent circuit

representation was used from which the admittance

operators can be determined. Thus, let us assume a

propagation in the oy-transverse direction instead of the real

oz-longitudinal direction. The transverse section of the

structure is considered as a set of cascaded transmission

lines terminated by short-circuited loads, noted "sc" (Fig. 2).

To reach the Galerkin's procedure, an equivalent circuit

representation was used from which the admittance

operators can be determined. Thus, let us assume a

propagation in the oy-transverse direction instead of the real

oz-longitudinal direction. The transverse section of the

structure is considered as a set of cascaded transmission

lines terminated by short-circuited loads, noted "sc" (Fig. 2).

2013 26th IEEE Canadian Conference Of Electrical And Computer Engineering (CCECE)

978-1-4799-0033-6/13/$31.00 2013 IEEE


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transmission line. This choice must respect several

convergence criteria such asboundary and proportionalityconditions, as well as metallic edge effect conditions.

However, for the general case, sinusoidal type trialfunctions can be deduced from the asymmetric model

[ ]

[ ]

+

=

+

=

=

2dC2,2C x

)2

2d2Cx()

2

2d(

2d

)2Cx()1m(cos

)x(

1dC1,C1 x

)2

1d1Cx()

2

1d(

1d

)1Cx()1m(cos

)x(

)x(

22mx2

22mx1

mx

[ ]

[ ]

+

=

+

=

=

2d2C,2C x2d

)2Cx(msin)x(

1dC1,C1 x1d

)1Cx(msin)x(

)x(

mz2

mz1

mz

We can note that when the two slots have the same width

(d2=d1), and when the central metallic strip is in the middle

of the metallic box of the CPW, trial functions proposedfrom quasi-symmetric approach for C- and -modes, havethe same equations as symmetric structure [5].

5. NUMERICAL RESULTS

To demonstrate the efficiency of our full-wave quasi-symmetric approach while applied to ACPW on isotropicand anisotropicsapphire substrates, we studied the evolutionof fundamental mode dispersion parameters for C- and

modes with respect to physical and electrical parametersby using sinusoidal trial functions. By taking into accountthe metallic edge effects, the convergence was achieved

without exceeding six trial functions per component (K6)

and 2000 modes (N2000) according to the widths ofcentral metallic strip (w) and slots (d1, d2).

Then, the C- and -modes results obtained from bothasymmetric and proposed quasi-symmetric models have

been compared with published data.

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

C (mm)

1

2

3

4

5

6

Effectivepermittivity

(b =b =3.4935mm)

C mode

mode

Symmetric case

Asymmetric case

Quasi-symmetric case

1

1 3=11.6r=[9.4-9.4-11.6]r=9.4r

d =d2 1

0.0 0.5 1.0 1.5 2.0 2.5 3.0

C (mm)

1

2

3

4

5

6


(b =b =3.4935mm)

C mode

mode

Asymmetric case


1

1 3

=11.6r=[9.4-9.4-11.6]r=9.4r

d =2d2 1

(a=3.556mm, b2=0.125mm, d1=0,1mm, w=0.2mm, F=33GHz)

(a)

0.0 0.5 1.0 1.5 2.0

Width of the central conductor strip w (mm)

1.2

1.6

2.0

2.4

2.8

/

C mode

mode

(b =b =3.4935mm)

Asymmetric case


d =d2 1

1 3

=11.6r=[9.4-9.4-11.6]r=9.4r

0.0 0.5 1.0 1.5 2.0

Width of the central conductor strip w (mm)

1.2

1.6

2.0

2.4

2.8

/

C mode

mode

(b =b =3.4935mm)

Asymmetric case


d =2d2 1

1 3

=11.6r=[9.4-9.4-11.6]r

=9.4r

(a=3.556mm, b2=0.125mm, C1=0.5mm, d1=0.1mm, F=33GHz)

(b)

0.5 1.0 1.5 2.0 2.5 3.0

d /d

1.0

1.5

2.0

2.5

3.0

/

(b =b =3.4935mm)

Asymmetric case


mode

C mode

2 1

1 3

r=11.6

r=[9.4-9.4-11.6]r=9.4

(c)

Fig. 3 - Dispersion parameters versus physical parameters

The selected structure was inserted into a WR28rectangular waveguide with a = 3.556 mm and b = b1+b2+b3

= 7.112 mm.

First, we varied different physical design parameters like

the width of lateral metallic strip (C1) or the central metallicstrip (w). As shown in Figure 3, the effective permittivity

(eff) or normalized phase constant (/0) of mode is moresensitive with regard to C1compared to C mode. In addition,

for identical widths of slot (d1=d2), the asymmetric coplanar

structure behaves as a quasi-symmetric one. According to

the same figure, we note that for C mode and for any width

ratio (d2/d1), the asymmetric structure has the samepropagation properties as the quasi-symmetric one. On the

other side, for a d2/d1 ratio up to 2.5 (for most applications

[6], [7], this ratio does not exceed 2), the maximum relative

error of /0 between asymmetric and quasi-symmetricmodels does not exceed 0.25% and 2.2% for C- and -modes, respectively, demonstrating the efficiency of our

quasi-symmetric approach especially for C mode, since the

-mode is more affected by shielding sides or slots.Figure 4 displays the variation of the normalized wave

length (/0) and effective permittivity (eff) with regard tothe electrical parameters on isotropic or anisotropic

substrate for symmetric and asymmetric CPW by varying ror frequency. We note here that our quasi-symmetric

approach is indeed valid for r30, knowing that for thelimit case of d2=2d1, the average error of/0is of 0.3% forC-mode while slightly exceeding 2% for -mode.

(8)

(9)

(11)

(10)

(a=3.556mm,

b2=0.125mm,

C1=1.2mm,

d1=0,1mm,

w=0.2mm,

F=33GHz)


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5 10 15 20 25 30

r

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

/

=[ ]

9.4 9.4

C mode

Asymmetric case (d = 2d )

Symmetric case (d =d )

2 1

2 1

r r r r

=[ ]r r r 11.6

=[ ]r r

Quasi-symmetric case (d = 2d )2 1

5 10 15 20 25 30

r

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

/

=[ ]

9.4 9.4

mode



2 1

2 1

r r r r

=[ ]r r r 11.6

=[ ]r r


(a=3.556mm, b2=0.125mm, d1=0.1mm, C1=1.578mm, w=0.2mm,

F=33GHz)

(a)

1 10 100

Frequency [GHz]

0

1

2

3

4

5

6

7

Effectiv

epermittivity

C mode

mode



=11.6

=[9.4-9.4-11.6]


2 1

2 1

r

r

(b)

Fig. 4 - Dispersion parameters versus electrical parameters

The same figure also shows the dispersion curves ofsymmetric and asymmetric coplanar CPW for both C- and

-modes up to 100GHz. Such curves are characterized by aslight increase of eff for the C-mode and more significantfor the -mode, involving a more dispersive behaviour.Furthermore, when d2=d1, the results from both asymmetricand quasi-symmetric approaches are identical to those of the

symmetric case for both C- and -modes. Also, whend2=2d1, the asymmetric and quasi-symmetric models for the

C-mode give almost same results with a relative error on effless than 0.2%, while for the -mode, this maximal relativeerror approaches 2.3% at 100 GHz. Consequently,

frequency has a slight influence on the accuracy of our

quasi-symmetric approach for C-mode when d2/d12. Inconclusion, within commonly practical ranges (d2/d12 andr30), the validity of the proposed quasi-symmetricapproach is conditional to slots being sufficiently far away

from the horizontal and vertical shielding walls while using

the WR-28 metallic box.

To further demonstrate our approach, Figure 5 shows a

good agreement between our results and those published in[6], [7] especially when using the asymmetric model,

knowing that the average error in all cases does not exceed

1.5%.

0 5 10 15 20 25 30

Frequency [Ghz]

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0


Coplanar line without shielding

C mode

mode


Asymmetric case[ 6 ]

d =d2 1

22 1d = d

0.0 0.4 0.8 1.2 1.6

C (mm)

1.0

1.2

1.4

1.6


Shielded suspendue coplanar line

C mode

mode

1


Asymmetric case

[ 7 ]

Fig. 5 - eff

Comparison between our results and those published

6. CONCLUSION

In this paper, we investigated the limits of the originalquasi-symmetric approach validity with regard to the

physical and electrical parameters in ACPW. It can

significantly reduce the CPU-time required for ACPWcharacterization, leading to faster modeling tools without

sacrificing to the overall design accuracy. Because of the

adequate choice of trial functions used in this fast modalapproach, the obtained results fit well with published data.

7. REFERENCES

[1] S. J. Fang and B. S. Wang, "Analysis of Asymmetric Coplanar

Waveguide with Conductor Backing", IEEE Trans. MicrowaveTheory Tech.,vol. 47, pp 238-240, 1999.

[2] P. Majumdar and A. K. Verma, "Closed Form Expression forConductor Loss of Conductor Backed Asymmetric CoplanarWaveguides", Applied Electromagnetics Conf., New Delhi, India,

pp. 1-3, 2009.

[3]A. Khodja, C. Boularak, M.C.E. Yagoub, R. Touhami, and H.

Baudrand, "Appropriate Choice of Trial Functions for EfficientModeling of Asymmetric Coplanar Structures", Applied Comput.

Electromagnetics Soc. Conf.,Monterey, CA,pp. 144-149, 2009.

[4] A. Khodja, H. Baudrand, R. Touhami, and M.C.E. Yagoub,"Dispersion Characteristics in Unilateral AsymmetricCoplanar Structure on Isotropic/Anisotropic Substrate",

Colloque Int. Optique Hertzienne et Dilectriques, Valence,France,2007.

[5] A. Khodja, M. L. Tounsi, Y. Lamhene, and K. Idinarene,

"Modeling of Suspended Coplanar Structure in Hybrid Mode by

Integral Method", IEEE Int. Conf. on Electronics, Circuits andSystems, Sharjah, UAE, pp. 711-714, 2003.

[6] T. Kitazawa and T. Itoh,"Asymmetrical Coplanar Waveguidewith Finite Metallization Thickness Containing AnisotropicMedia",IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1426-

1433, 1991.

[7] L. P. Schmidt, T. Itoh, and H. Hofmann, "Characteristics of

Unilateral Fin-Line Structures with Arbitrarily Located Slots",IEEE Trans. Microwave Theory Tech., vol. 29, pp. 352-355, 1981.

a

b

b

b

Cd W d

o

o

ro

1

2

3

1 21

h

d1 d2

h=1 mm, w=0.5 mm, d1=1 mm,

r= [9.4- 9.4- 11.6]a=3.556 mm, b1= b3=3. 4935

mm, b2=0.125 mm, w=0.2 mm,

d1=d2=0.1mm, r=2.2, F=33GHz

(a=3.556mm,

b2=0.125mm,

d1=0.1mm,

C1=1.578mm,

w=0.2mm)

novel dispersive modal approach

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