Sikalidis C. (ed.) Advances in Ceramics - Synthesis and Characterization, Processing and Specific Applications

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Advanced Design and Fabrication of Microwave Components

Based on Shape Optimization and 3D Ceramic Stereolithography Process

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Transporting ψ by (4.15) is equivalent to move the boundary of Ω (the zero level-set of ψ)

along the descent gradient direction –J’(Ω).

4.3 Application to the design of dielectric resonator filters

This sub-section presents the application of shape optimization techniques (LS and TG)

coupled with a finite element method for optimizing, in 3D, the shape of microwave

components composed of ceramic objects in order to improve their electrical properties.

More precisely, these components are dielectric resonator filters and, traditionally, their

design consists of optimizing the geometrical dimensions of resonators and coupling

elements in order to achieve the desired function. One can use typical shapes of resonators

and optimize their dimensions as a trade-off between quality factor and isolation

(Fiedziusko & Holme, 2001). The quality factor is related to the achievable insertion losses

while the isolation is related to the stop-band characteristics. In order to relax this

compromise, shape optimization methods (in our case TG and LS methods) can be utilized

in order to improve a reference design obtained with a classical approach, i.e. based on a

dielectric resonator with a regular shape.

4.3.1 Improvement of unloaded quality factor

A single pole filter can be constructed with a dielectric resonator inserted in metallic cavity

and excited with two metallic irises connected to rectangular waveguides as shown in

Figure 4.2. The unloaded quality factor of the dielectric resonator can be estimated by

simulation or measurement of scattering parameters. Consequently, a shape optimization of

the DR can be conducted for improving its unloaded quality factor.

Applying the level-set method, the unloaded Q is increased by more than 50% as shown in

Table 4.1. The optimal shape is depicted in Figure 4.2 (b). The dielectric resonator has been

processed by ceramic stereolithography. The dielectric material is characterized by a relative

permittivity (ε

) equal to 9 and a loss tangent (tanδ) equal to 4.5 10

-5

Simulation Measurement

Reference resonator 2000 900

Optimized resonator 3340 1910

Table 4.1. Simulated and measured unloaded quality factors

4.3.2 Improvement of stop-band performance

A two-pole filter is derived from Figure 4.2(a) by cutting a corner in the dielectric resonator

and rotating the output iris and waveguide as shown in Figure 4.3(a). Stop-band

performance is altered by spurious transmissions due to higher-order modes.

For reducing the impact of spurious transmissions, the shape of the dielectric resonator is

optimized applying the topology gradient technique in order to attenuate S21 parameter

above the passband. The optimized resonator is shown in Figure 4.3(b) and scattering

parameters obtained with reference and optimized resonators are compared in Figure 4.4.

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Fig. 4.2. Improvement of unloaded quality factor: (a) reference resonator, (b) optimized

resonator

(a)

(b)

Fig. 4.3. Improvement of stop-band performance: (a) reference resonator, (b) optimized resonator

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Fig. 4.4. Scattering parameters obtained by simulation of reference and optimized

resonators.

4.3.3 Design of dielectric resonator filters

A four-pole dual-mode filter is constructed using two dual-mode resonators assembled

together with a metallic cross-iris, as shown in Figure 4.5(a). One can optimize the

functionality of the filter by adjusting the dimensions of both, the corners of the dual-mode

resonators and the two arms of the metallic cross-iris.

A first shape-optimized design is conducted for replacing the metallic cross-iris by a ceramic

coupling element in order to obtain a similar behavior in the pass-band and close out-of-

band regions. Optimized resonator is shown in Figure 4.5(b) and scattering parameters are

compared in Figure 4.6.

(a)

Metallic cross-iris

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(b)

Fig. 4.5. Four-pole DR filter: (a) with a metallic cross-iris (reference) and (b) with a dielectric

coupling element

(a)

(b)

Fig. 4.6. S-parameters obtained by simulation (a) and measure (b) of reference and

optimized coupling elements.

Dielectric cou

lin

element

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A second design is performed on the basis of the previous optimization for improving the

out-of-band performance of the filter. The initial and final resonators are shown in Figures

4.7(a) and 4.7(b). The simulation and measure of each resonator are compared in Figures

4.8(a) and 4.8(b).

(a)

(b)

Fig. 4.7. Four-pole DR filter: (a) with reference resonators and (b) with optimized resonators.

(a)

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(b)

Fig. 4.8. S-parameters obtained by simulation and measure of reference (a) and optimized

(b) resonators

5. Conclusion

This chapter is focused on advanced design and fabrication techniques for ceramic-based

microwave and millimeter-wave components. Complementary theoretical and fabrication

approaches have been coupled in order to design innovative RF components successfully.

As shown, the theoretical approaches are based on 3D electromagnetic and shape

optimization methods whereas the rapid prototyping is based on 3D ceramic

stereolithography process.

Moreover, the high electrical performances of these components and their geometrical and

physical properties demonstrate that ceramic materials are suitable for such microwave

applications with high constraints (geometrical, mechanical, thermal and electrical).

At last, this work proves that the 3D ceramic stereolithography process will be in the next

future an interesting alternative technological process for the fabrication of 3-D monolithic

all-dielectric devices at millimeter wavelengths.

6. References

Akel, H. & Webb, J.P. (2000). Design sensitivities for scattering-matrix calculation with

tetrahedral edge elements. IEEE Transactions on Magnetics, Vol. 36, No. 4, pp. 1043-

1046, 2000.

Allaire, G. & Jouve, F. (2002). Optimal design of micro-mechanisms by the homogenization

method. European Journal of Finite Elements, Vol. 11, pp.405-416, 2002

Allaire, G.; De Gournay, F.; Jouve, F. & Toader, A.M. (2003). Structural optimization using

topological and shape sensitivity via a level set method. International Series of

Numerical Mathematics, Vol. 147, pp.1-15, Birkhauser, Basel 2003.

Assadi-Haghi, A.; Bila, S.; Durousseau, C.; Baillargeat, D.; Aubourg, M.; Verdeyme, S.;

Rochette, M.; Puech, J. & Lapierre, L. (2006). Design of microwave components

using topology gradient optimization. Proceedings of the 36th European Microwave

Conference, pp. 462-465, 2006.

Advanced Design and Fabrication of Microwave Components

Based on Shape Optimization and 3D Ceramic Stereolithography Process

275

Bertsch, A.; Jiguet, S., Renaud, P. (2003). Microfabrication of ceramic components by

microstereolithography, J. Micromech., Vol. 14, pp. 197-203, 2003

Brakora, K. F.; Halloran, J.; Sarabandi, K. (2007). Design of 3-D monolithic MMW antennas

using ceramic stereolithography. IEEE Trans. Antennas Propagat.,Vol. 55, No. 3, pp.

790–797, March 2007

Byun, J.K; Park, I.H.; Nah, W.; Lee, J.H. & Kang, J. (2004). Comparison of shape and

topology optimization methods for HTS solenoid design. IEEE Transactions on

Applied Superconductivity, Vol. 14, No. 2, pp. 1842-1845, 2004

Chartier, T.; Chaput, C., Doreau, F., Loiseau, M. (2002). Stereolithography of structural

complex ceramic parts, J. Mat. Sci., Vol. 37, pp. 3141-3147, 2002

Delhote, N.; Baillargeat, D.; Verdeyme, S.; Thevenot, M.; Delage, C. & Chaput, C. (2007a).

Large experimental bandpass waveguide in 3D EBG woodpile manufactured by

layer-by-layer ceramic stereolithography. IEEE/MTT-S International Microwave

Symposium, Honolulu, Hawaï, USA, pp 1431-1434, 2007

Delhote, N.; Baillargeat, D.; Verdeyme, S.; Delage, C.; Chaput, C.; Duterte, C.; Abouliatim, Y.

& Chartier, T. (2007b). Electromagnetic band gap millimeter and submillimeter 3D

resonators manufactured by ceramic Stereolithography. Asia-Pacific Microwave

Conference, Bangkok, Thaïlande, pp 1-4, 2007

Delhote ,N.; Baillargeat, D.; Verdeyme, S.; Delage, C. & Chaput, C. (2007c). Ceramic layer-by-

layer stereolithography for the manufacturing of 3D millimeter wave filters. IEEE

Transactions on Microwave Theory and Techniques, Vol. 55, No. 3, pp. 548-554, 2007.

Delhote, N.; Baillargeat, D.; Verdeyme, S.; Delage, C. & Chaput, C. (2007d). Innovative

Shielded High Q Dielectric Resonator Made of Alumina By Layer-By-Layer

Stereolithography. IEEE Microwave and Wireless Component Letters, volume 17, issue

6, pp 433-435, 2007.

Doreau, F.; Chaput, C.; Chartier, T. (2000). Stereolithography for manufacturing ceramic

parts, Adv. Eng. Mater., Vol. 2, pp. 493-496, 2000

Fiedziuszko, J.S. & Holme, S. (2001). Dielectric resonators raise your high-Q. IEEE

Microwave Magazine, Vol. 2, No. 3, pp. 50-60, 2001.

Hinczewski, C. (1998). Ph. D., Institut National Polytechnique de Lorraine, France, 1998

Hull, C.; (1986). Apparatus for production of three dimensional objects by stereolithography,

U.S. Pat. No. 4575 330, 1986

Khalil, A.H.; Delhote, N.; Pacchini S.; Claus, J.; Mardivirin, D.; Baillargeat, D.; Verdeyme, S.;

Leblond, H. (2011). 3-D pyramidal and collective Ku band pass filters made in

Alumina by ceramic stereolithography. IEEE/MTT-S International Microwave

Symposium, Baltimore, USA, 2011

Khalil, H; Delhote, N.; Bila, S.; Aubourg, M.; Verdeyme, S.; Puech, J.; Lapierre, L.; Delage, C.

& Chartier, T. (2008). Topology optimization applied to the design of a dual-mode

filter including a dielectric resonator. IEEE MTT-S International Microwave

Symposium Digest, pp. 1381-1384, 2008.

Khalil, H.; Bila, S.; Aubourg, M.; Baillargeat, D.; Verdeyme, S.; Puech, J.; Lapierre, L.; Delage,

C. & Chartier, T. (2009). Topology optimization of microwave filters including

dielectric resonators. Proceedings of the 39th European Microwave Conference, pp. 687-

690, 2009

Khalil, H.; Bila, S.; Aubourg, M.; Baillargeat, D.; Verdeyme, S.; Jouve, F.; Delage, C. &

Chartier, T. (2010). Shape optimized design of microwave dielectric resonators by

Advances in Ceramics - Synthesis and Characterization, Processing and Specific Applications

276

level-set and topology gradient methods. International Journal of RF and Microwave

Computer-Aided Engineering, Vol. 20, No. 1, pp 33-41, 2010

Khalil, H.; Bila, S.; Aubourg, M.; Baillargeat, D.; Verdeyme, S.; Jouve, F. & Chartier, T. (2011).

Shape optimization of dielectric resonators for improving their unloaded quality

factor. International Journal of RF and Microwave Computer Aided Engineering, Vol. 21,

No. 1, pp 102-126, 2011

Kim, Y.S.; Byun, J.K & Park, I.H. (2009). A level set method for shape optimization of

electromagnetic systems. IEEE Transaction on Magnetics, Vol. 45, No. 3, pp. 1466-

1469, 2009.

Kozak, A. & Gwarek, W. (1998). Unrestricted arbitrary shape optimization based on 3D

electromagnetic simulation. IEEE MTT-S International Microwave Symposium Digest

1, pp. 17-20, 1998

Li, B.; Xu, Y. & Choi, J. (1996). Applying Machine Learning Techniques, Proceedings of ASME

2010 4th International Conference on Energy Sustainability, pp. 14-17, ISBN 842-6508-

23-3, Phoenix, Arizona, USA, May 17-22, 2010

Lima, P.; Bonarini, A. & Mataric, M. (2004). Application of Machine Learning, InTech, ISBN

978-953-7619-34-3, Vienna, Austria

Liu, B.; Gong, X.; Chappell, W.J. (2004). Applications of layer-by-layer polymer

stereolithography for three-dimensional high-frequency components. IEEE Trans.

Microwave Theory Tech., Vol. 52, No. 11, pp. 2567–2575, November 2004

Mader, P.; Masmoudi, M. & Mangenot, C. (2001). Topological asymptotic for waveguide

optimization. IEEE Antennas and Propagation Society, AP-S International Symposium

(Digest 1), pp 616-619, 2001.

Monneret, S. (2005). La microstereolithographie et ses applications,” Méc. & Ind., Vol. 6, pp.

457-462, 2005

Nguyen, N.T.; Sauleau, R.; Delhote, N.; Baillargeat, D. & Le Coq, L. (2010). Design and

Characterization of 60-GHz Integrated Lens AntennasFabricated Through Ceramic

Stereolithography. IEEE Transactions on Antennas and Propagation, Vol. 58 No. 8 , pp

2757 – 2762, 2010.

Osher, J.S. & Sethian, J.A. (1988). Fronts propagating with curvature dependent speed:

algorithms based on Hamilton-Jacobi Formulations. Journal of Computational Physics,

Vol. 79, No. 1, pp. 12-49, 1988.

Osher, J.S. & Santosa, F. (2001). Level set method for optimization problems involving

geometry and constraints I. Frequencies of a two-density inhomogeneous drum.

Journal of Computational Physics, Vol. 171, pp. 272-288, 2001.

Sethian J.A. & Wiegmann, A. (2000). Structural boundary design via level set and immersed

interface methods. Journal of Computational Physics, Vol. 163, No. 2, pp. 489-528, 2000.

Sokolowski, J.S. & Zochowski, A. (1999). On the topological derivative in shape

optimization. SIAM Journal on Control and Optimization, Vol. 37, No. 4, pp. 1251-

1272, 1999.

Suri, J.S.; Liu, K.; Singh, S.; Laxminarayan, S.N.; Zeng, X. & Reden, L. (2002). Shape recovery

algorithms using level sets in 2-D/3-D medical imagery - A state-of-the-art review.

IEEE Transactions on Information Technology in Biomedicine, Vol. 6, No. 1, pp. 8-28,

2002.

Sinterability and Dielectric Properties of

ZnNb

– Glass Ceramic Composites

Manoj Raama Varma, C. P. Reshmi and P. Neenu Lekshmi

Materials and Minerals Division,

National Institute for Interdisciplinary Science and Technology

[NIIST],Thiruvananthapuram,

India

1. Introduction

In the new era of communication technology there are revolutionary developments in

satellite communication, global positioning systems and mobile communication systems,

which has helped the developments in multilayer technologies like low temperature cofired

ceramics (LTCC). The microwave electronic devices have achieved significant

miniaturisation, light weight and became very cost effective using LTCC. The characteristic

properties required for dielectric materials which are used in multilayers are (a) high

dielectric permittivity(

), (b) high quality factor (Q×f) and (c) low temperature coefficient

of resonant frequency (τ

). The size of the resonator is inversely related to the

Dielectric materials should posses near zero temperature coefficient of resonant frequency

(τ

) for thermally stable electronic devices [1-7].

Generally most of the dielectric ceramic materials are known to posses the above said

properties but will sinter at temperatures above 1000

C. Zinc niobates, ZnNb

(ZN) is a

low loss dielectric material with columbite structure having excellent dielectric permittivity,

high quality factor and low temperature coefficient of resonant frequency. Sintering

temperature of ZN is comparatively lower (~1200

C) [8]. Hence it is widely used as

dielectric resonators in microwave communication devices. In multilayer ceramic structures,

the low melting electrodes such as Ag (melting point ~961

C), Cu (melting point ~1083

and Au (melting point ~1064

C) are co-fired with these ceramic materials [9,10]. In the case

of Ag electrodes, processing temperature of the material must be below 950

There are several approaches to reduce the sintering temperature of the ceramics viz. (i)

usage of ultra-fine particles/powders as synthesized by wet chemical methods as starting

materials (ii) addition of low melting glasses to obtain a low temperature sintering

composite [11-14]. Glass addition is known to be the most popular and least expensive

method and hence ZN is widely used in ceramic technology.

Even though the ZN ceramics prepared by conventional ceramic route [1-6] shows excellent

properties, high sintering temperature preclude its application potential in the LTCC. Usage

of nano sized ZN powders (instead of micron size powders) in multi layer technology can

bring down the sintering temperature to a lower value. Hence the procedure for preparing

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ZN ceramic powder as both micron size powders and nanosized powders and the

sinterability of pure materials as well as the glass added ceramics are described in this

chapter. The structural characterisation of the materials can be done using XRD and the

microwave dielectric properties (in the frequency range 2-6 GHz) can be studied and

compared to highlight the effect of particle size on sinterability and microwave dielectric

properties of these materials.

2. Materials and methodologies

ZN ceramic powders can be synthesized using two different well established preparation

techniques such as solid state ceramic method and polymer complex techniques [15-17].

2.1 Synthesis of ZnNb

using solid state synthesis technique

Single phase ZN can be prepared using oxides of Zn (ZnO 99.9+%) and pentoxide of

Niobium (Nb

99.9+%) as raw materials. These oxides can be weighed in stoichiometric

proportion and mixed for 24h in a ball mill, using zirconia balls and distilled water as the

milling medium. The slurry can be dried at 80

C and the dried powder can be calcined at

850

C/4h, to get the phase pure ZN ceramics.

2.2 Preparation of ZnNb

using polymer complex method

Zinc acetate [Zn(CH

COO)

99.99%,] and niobium ethoxide [Nb(OC

)

, 99.95% metal

basis] can be used as the starting material for preparing ZN using polymer complex method.

The flow chart, in Fig. 1 shows the various steps involved in the synthesis. 3 mol equivalent

of citric acid can be dissolved in 12 mol of ethylene glycol with continuous stirring for 1h to

form a clear solution. 1 mol of zinc acetate can then be added and stirred for several hours at

C to dissolve it completely. 2 mol of Nb(OC

)

can be added to this clear solution with

a stirring speed of 500 rpm until it results in the formation of a thick white gel. The gel can

be sonicated for 2h to obtain the uniform distribution. After sonication the polymeric

precursor can be recovered by desalting with acetone. The dried polymeric precursor can be

calcined at 600

C/4h to obtain the ZnNb

nanopowders.

2.3 Preparation of 60ZnO-30B

-10SiO

(ZBS) glass

High purity ZnO, B

and SiO

(99.9%) can be used as the raw materials for the preparation

of 60ZnO-30B

-10SiO

(ZBS, sintering temperature is <800

C). The raw materials weighed

accurately in the stoichiometric proportion are mixed well in distilled water medium using

zirconia balls for 24 h in a ball mill. The slurry can be dried and the powder can be melted in

a platinum crucible at 1000

C for 2h, and the melt can be quenched into cold distilled water

and powdered. This glass powder can be used for the preparation of glass ceramic

composites.

2.4 Preparation of ZN-ZBS glass composites

Appropriate amounts of ZN and ZBS glass (1,3,5,10 wt%) can be mixed using an agate

mortar for 2 hours in distilled water medium and the slurry can be dried and powdered.

3wt% PVA solution can then be added to this mixture as a binder. The dried powder can be

uniaxially pressed using a tungsten carbide (WC) die in the form of cylindrical discs of