Abstract

In this paper, the efficient full-wave analysis of passivedevices composed of circular and arbitrarily-shapedwaveguides is considered. For this purpose, the well-known Boundary Integral - Resonant Mode Expansion(BI-RME) method has been properly extended. Circularwaveguides are used for the resonant mode expansion,whereas the arbitrary contour is defined by any combi-nation of straight, circular and elliptical segments, thusallowing the exact representation of the most widelyused geometries. The proposed algorithm extends pre-vious implementations of the BI-RME method based oncircular waveguides by considering circular and ellipticalarcs for defining arbitrary geometries. Likewise, it allowsthe efficient analysis of passive devices based on circularwaveguides with arbitrary perturbations, thus providingmore accurate results with less computational effortsthan a rectangular waveguide based BI-RME approach.The extended method has been successfully tested withseveral practical application examples, having comparedits performance with the BI-RME method based on rec-tangular waveguides.

Keywords: Waveguide components, filters, integralequations, circular waveguides, Green function methods

1. Introduction

Nowadays, many waveguide components for satellite ap-plications are based on cylindrical cavities. Examples ofsuch components include dual-mode filters, polarisers,

sidewall-coupled cylindrical cavity filters, etc. (see [1]).The high electrical response sensitivity found in some ofthese components, e.g. dual-mode filters, has encour-aged the development of full-wave electromagneticanalysis tools for its accurate and efficient modelling.The analysis of complex waveguide components hasbeen traditionally carried out by means of segmentingthe structure into simpler building blocks: waveguide sec-tions, discontinuities and planar junctions, as describedin [2]. Instead of considering the structure as a whole, itis simpler and computationally more efficient to analysedifferent types of blocks independently, and eventuallycombine them to obtain the component response. Inorder to perform a high-accuracy analysis, the character-ization of these blocks needs to be multimodal, especiallyif discontinuities are in close proximity. Waveguide sec-tions are characterized by their modal charts. For the full-wave characterization of planar junctions anddiscontinuities, the modal coupling coefficients of the in-volved waveguides are also required. Consequently, full-wave modal analysis methods are generally focused oncomputing these two sets of parameters.

Over the last decades, a wide number of analysis tech-niques have been reported in the technical literature. Onthe one hand, there are techniques based on the solutionof an integral equation by the method of moments (MoM)[3]-[4] which solve a non-linear eigenvalue problem of smallsize. On the other hand, there are techniques based on dis-cretization methods leading to large algebraic problems,such as Finite-Element (FE) [5] or Finite Difference Time Do-main (FD-TD) methods [6]. Recently, hybrid techniques have

5Waves - 2013 - year 5/ISSN 1889-8297

Efficient BI-RME Method Implementation ForThe Full-Wave Analysis Of Passive DevicesBased On Circular Waveguides With ArbitraryPerturbationsC. Carceller1, S. Cogollos1, P. Soto1, J. Gil2, V. E. Boria1, C. Vicente2, B. Gimeno3Correspondence author: carcarc2@upvnet.upv.es

1 Departamento de Comunicaciones, Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universidad Politécnica de Valencia, E-46022, Valencia, Spain.

2 Aurora Software and Testing S.L., E-46022, Valencia, Spain.

3 Departamento de Física Aplicada, Instituto de Ciencia de Materiales, Universidad de Valencia, E-46100, Burjassot, Spain.

been proposed in order to mitigate the drawbacks of bothgroups. Some methods that fall into this category are themode-matching finite-element (MM/FE) method [7], theboundary contour mode-matching (BCMM) method [8],and the combination of the mode-matching, finite-ele-ment, method of moments and finite difference methods(MM/FE/MoM/FD) [9].

In this paper, a technique which combines the flexibilityof discretization methods with the efficiency of modaltechniques is extended, the so called 2D Boundary Inte-gral - Resonant Mode Expansion (BI-RME) method [10].The first original publication of this technique [11] con-sidered its application to the modal analysis of arbitrary-contour waveguide structures by means of thecombination of an integral equation with the modal ex-pansion of a two-dimensional resonant contour. Aftersolving a linear matrix eigenvalue problem, the BI-RMEmethod provides the modal chart of the arbitrarilyshaped waveguide structure.

The linear character of the matrix problem offers a greatadvantage over methods that solve integral equationsthrough frequency-dependent eigenvalue problems,which typically result in larger computational efforts. More-over, the moderate size of the matrices involved in the BI-RME method, reduces the amount of required memoryresources, especially when compared with discretizationtechniques. Furthermore, the use of the BI-RME methodwithin optimization procedures offers great advantagessince, from one iteration to the next, only the integrals thatinvolve altered geometries need to be recomputed.

After the first publication of the BI-RME method, thetechnique was revisited to additionally provide the cou-pling coefficients between the arbitrarily shaped wave-guide and the basic resonant contour [12]. For thispurpose, the same matrices involved in the solution ofthe eigenvalue problem were used, thus adding very littlecomputational effort. Further efforts were done in thedirection of extending the original method in order to in-clude circular and elliptical arcs to describe the arbitrar-ily-shaped structure, since the original work [11] onlyconsidered straight segments. In [13], these two kinds ofsegments were added for the BI-RME method formulatedin terms of rectangular waveguide modes. For such case,it was proved that the accuracy can be increased, espe-cially when computing the cut-off frequencies of thelower order modes of such arbitrary waveguides.

However, that work has proven to be inefficient for theanalysis of devices based on circular waveguides. In suchcases the rectangular-based implementation of the BI-

RME method requires a large number of resonant modesto compute the modal chart of the arbitrary waveguidewith a high degree of accuracy. Likewise, the arbitrarywaveguides that typically compose these devices are usu-ally connected to other circular waveguides. Thereforethe rectangular-based implementation does not take ad-vantage of the efficient computation of coupling coeffi-cients provided by the BI-RME method [12]. Thesedrawbacks can be avoided with the new BI-RME imple-mentation presented in this paper, which combines theuse of a circular waveguide as the resonant contour withthe possibility of using circular and elliptical arcs (togetherwith straight segments) for defining the arbitrary geom-etry. With this implementation based on circular wave-guides, many practical passive devices can be analysedand designed more accurately and with less CPU timethan using the rectangular-based algorithm.

2. Arbitrary waveguide analysis bythe BI-RME method

The basic structure under analysis (see Fig. 1) is an arbi-trarily-shaped waveguide whose cross section � is definedby the contour �. In order to analyse this waveguide, itwill be enclosed within a standard circular waveguide S0and the original BI-RME formulation [11] will be applied.

2.1. Computation of the TM modesTo compute the Transversal Magnetic (TM) modes of anarbitrarily shaped waveguide by means of the BI-RMEmethod, it is necessary to compute two matrices, namedL’ and R’ in [11]. The matrix R’ is related to the reso-nant-mode expansion of the basic circular waveguide.The matrix L’ involves the scalar Green’s function g forthe cylindrical resonator. This paper deals only with theL’ matrix, since the computation of the R’ matrix can beeasily performed using standard numerical integrationmethods. The elements of L’ can be expressed as follows:

(1)

6 ISSN 1889-8297/Waves - 2013 - year 5

Use of the BIRME method within optimization procedu-res offers great advantages since, from one iteration tothe next, only the integrals that involve altered geome-tries are recomputed.

Figure 1. Basic contour of the arbitrary waveguide en-closed within a basic circular contour.

L’ij = wi(l)g(s,s’)wj(l’)dl dl’�� ��

where wi,wj are the basis and testing functions relatedto the implementation of the Method of Moments. Thesefunctions are piece-wise parabolic splines defined in twoor three segments of the arbitrary contour �. In our pro-posed enhanced algorithm, these segments can bestraight, circular or elliptical arcs, and the basis functionsare expressed in terms of a suitable variable l defined on�. Furthermore, s = s(l) and s’= s(l’) represent field andsource vectors in the arbitrary contour �, and g repre-sents the scalar Green’s function for two-dimensional res-onators of circular cross section. Since g is singular whens = s’, the diagonal components of L’ manifest a singularbehaviour; in these cases the singularity has to be ex-tracted from the computation of the matrix and solvedanalytically. The non-diagonal components can be easilycomputed using standard numerical integration tech-niques (e.g. the Gauss quadrature).

According to [11], the expression of the scalar Green’sfunction for this structure is:

(2)

where

(3a)

(3b)

(3c)

and a is the radius of the bounding circular contour. Itcan be easily observed that the singular behaviour of g isof the type 1n(R) when the field point s(r,�) ap-proaches the source point s’(r’,�‘) , since R representsthe distance between these two sets of points. To isolatethe problematic behaviour of this term, it is necessary tosplit the Green’s function into a regular and a singularterm, dealing with each of them separately

(4)

where greg is regular since

(5)

Following this division of g into a regular and a singularpart, the double integral of (1) can be split accordingly.On the one hand, the double integral involving greg canbe solved numerically, as it is done with the rest of theintegrals that do not present a singular behaviour (suchas the elements of matrix R’ ). On the other hand, thedouble integral involving gsing can be performed in twosteps. First, the line integral with respect to the primedcoordinates is solved analytically, due to its singular be-haviour. For circular and elliptical arcs, this singular inte-gral can be computed analytically using a proceduretotally equivalent to the one described in [13]. Then, theline integral with respect to the non-primed coordinatesis computed numerically, since it has now a regular form.

2.2. Computation of the TE modesThe accurate computation of the Transversal Electric (TE)modes depends on the capability to evaluate matricesC (not to be confused with variable C defined in (3c))and L , whose elements are [11]:

(6)

(7)

where wn(l) and ∂wn(l)/∂l are, respectively, the basisfunctions and their derivatives, t^=tr r

^+t��^ is the vectortangent to the contour �, and G–st is the solenoidal partof the dyadic Green’s function for the circular cross-sec-tion resonator.

As it can be observed, equation (6) is very similar to (1),with the only difference being the presence of the deriv-atives instead of the basis functions. Therefore, the pro-cedure to solve the singularity inherent to the scalarGreen’s function in the C matrix is completely equivalentto the one previously described for the L’ matrix of TMmodes (1), with the consideration that the derivatives ofthe basis functions are linear splines.

The computation of the Lmatrix requires managing thesolenoidal part of the aforementioned dyadic Green’sfunction, which can be expressed as follows

(8)

where the specific expressions for the dyadic componentscan be found in [11].

This dyadic Green’s function has a logarithmic singularbehaviour equivalent to the one of g. Following a similarprocedure to the one used with the TM modes, G– st canbe split into a regular part and a singular part, being thelatter as shown next:

(9)

where C is defined in (3c) and S is(10)

As it has been done for the TM modes, the double inte-gral of (7) will be split into an inner line integral that willbe solved analytically, due to its singularities, and an outerline integral that will be solved numerically. The singularintegral to be solved analytically is

7Waves - 2013 - year 5/ISSN 1889-8297

Circular-based BI-RME implementation benefits fromlower number of resonant modes required to model ac-curately the arbitrary sections, as well as the efficientcomputation of coupling coefficients between circularand arbitrary-shaped waveguides.

12�

g(r,�,r’,�‘) = 1n(r’Ri/aR)

1/2R=(r2+r’2 -2rr’C)

1/2Ri=(r2+a4/r’2 -2ra2C/r’)

C=cos(� - �’)

1g =greg+gsing= 1n - 1n(R )4�

14�

22r’ Ri

a

(r’2 -a2 )2lim 1n =1n

2r’ Ria a2

G–

st(r,�,r’,�’) = Grr r^r^’ + G�r �

^r^’+Gr� r^�^’+G�� �^�^’

S=sin(� - �’)

g(s,s’) dl dl’Cij =∂wi(l) ∂wj(l’)

∂l ∂l’�� ��

Lij = wi(l)wj(l’)t^(l)•Gst(s,s’)•t

^(l’)dl dl’��

��

G–

st = C1n(R2)r^r^’ - S1n(R2)�^r^’+S1n(R2) r^�^ ’+C1n(R2)�^�^’sing 1

8�

(11)

where t=tr r^+t��^ is the vector tangent to the contour.

Given that

(12a)

(12b)

it is immediate to rewrite the singular integral (11) as

(13)

If the contour � includes circular and/or elliptical arcs, theanalytical computation of this singular integral can be car-ried out using the technique explained in [6] for TE modes.

3. Numerical results

In this section, the proposed implementation of the BI-RME method using a circular resonant contour is vali-dated with results from measurements and the technicalliterature. The results1 obtained with the circular-basedimplementation have proven to be highly accurate whencompared with available numerical or experimental data.This implementation has also shown a more efficient per-formance than the rectangular-based implementation forthe analysis of all the structures considered in this section.

3.1. Elliptical waveguideThe first example involves exclusively elliptical arcs. Anelliptical waveguide with major semi-axis a=20mm and

eccentricity e=0.5 has been analyzed, and the cut-offwavelengths have been compared with those computedin [14], using the classical calculation of the parametriczeros of the modified Mathieu functions. To obtain theresults shown in Table 1, the elliptical waveguide hasbeen segmented into 176 elliptical segments, and thefirst 357 modes have been computed in just 7 s.

3.2. Multi-ridged circular waveguideNext, the modal chart of a multi-ridge circular waveguide(Fig. 2a) is presented. This structure is especially suitableto be analysed by the circular-based implementation.Thus, it serves the purpose of showing how the properelection of the resonant contour has an impact on the

8 ISSN 1889-8297/Waves - 2013 - year 5

Figure 2: a) Dimensions of the multi-ridged circular waveguide as well as the circularand square contours used by the BI-RME method. Red lines indicate those segments thathave to be considered for the application of the BI-RME method in each case. b) Cut-offfrequency for the first two TE modes and the first TM mode of the multi-ridge circularwaveguide for different insertion depths (a). Simulations are compared with [15] andmeasurements of [16].

1 All the CPU times in this section have been obtained using a standard PC with a 2.83 GHz Intel Core 2 Quad processor.

Table 1: Relative error in the cut-off wavelength com-putation of an elliptical waveguide with major semi-axisa=20 mm and eccentricity e=0.5.

trtr’ +t� t�’ =C(txtx’ +ty ty’)+S(ty tx’ - txty’)

- t� tr’ +tr t�’ =S(txtx’ +ty ty’) -C(ty tx’ -txty’)

Lsing= �� wi(l’) (t^ •t^’) dl’1nR

2

8�

Lsing= �� wi(l’) C(trtr’ +t� t�’)+S(-t� tr’ +tr t�’) dl’1nR2

8�

accuracy of the algorithm. This example consists of a cir-cular waveguide of radius b=20 mm with three equidis-tant metal insertions of angular thickness t=20º.Sweeping the inner radius from a=1 to 19 mm, a seriesof simulations have been performed using the circular-based implementation (R=20 mm) and the rectangular-based approach (l=41 mm).

The results of these simulations can be seen in Fig. 2b,where the cut-off frequencies for the first two TE modesand the first TM mode have been computed and success-fully compared with [15] and the measurements of [16].For low order modes, as the ones considered in Fig. 2b,both the circular and the rectangular-based implementa-tions achieve rapidly convergent results. For instance,only 100 resonant modes have been used with both im-plementations, requiring less than 0.65 s per simulationpoint with the rectangular-based code and 0.45 s withthe circular-based one.

However, typical analysis of complex passive devices re-quires the use of higher order modes (usually up to 100modes) for a proper characterization of the structure. Inthose cases, the performance of the circular-based imple-mentation excels that of the rectangular-based approach,since the structure is based on a circular waveguide. Toshow this, we have analysed the multi-ridge waveguide set-ting the inner radius to a=16 mm and studied the conver-gence of both implementations through the computationof the 100-th mode cut-off frequency. The results of thisstudy are summarized in Table 2, where the superior per-formance of the circular-based implementation over therectangular one can be observed. In approximately 0.8 sthe circular-based algorithm computes the cut-off fre-quency of this mode with a relative error smaller than0.1%, while the rectangular-based takes 5.9 s to achieve asimilar level of accuracy. The main reason for this importantimprovement is that the number of segmented portions(red portions in Fig. 2a is smaller since the majority of the

segments are coincident with the outer circular contour,and do no need to be segmented by the circular-based im-plementation. With a smaller number of portions the sizeof the eigenvalue problem decreases, so the time devotedto its construction and solution is drastically reduced.

3.3. Cross-shaped irisIn the previous example, it has been demonstrated howthe election of the resonant contour has an effect on theaccuracy and efficiency of the modal chart calculation.Now, it is shown how this election also affects the com-putation of coupling coefficients, another key factorwhen analysing the electromagnetic response of complexdevices. For such study, a structure consisting of a cross-shaped iris connected to a circular waveguide is consid-ered, as seen in Fig. 3a. On the one hand, this structurehas been analysed with the circular-based algorithm,using the connected circular waveguide (radius R=12mm) as the resonant contour. This analysis has automat-ically provided the desired coupling integrals. On theother hand, the structure has been analysed using therectangular-based algorithm, which computes the cou-pling coefficients as follows:

(14)

where ei� are the modal vectors of the circular waveguideconnected to the iris, en are the modal vectors of the rec-tangular box and ejΔ are the modal vectors of the cross-shaped iris. Note that the first inner product in (14) isanalytical, whereas the second one is provided by BI-RME.

Figure 3 depicts the relative error in the computation ofcoupling integrals between two sets of modes using therectangular-based implementation. In all cases the exactvalue for the coupling integrals is taken as the convergentvalue provided by the circular-based implementation. InFig. 3b the coupling integral between the first mode of

9Waves - 2013 - year 5/ISSN 1889-8297

Table 2: Cut-off frequency of the 100th mode of the triple-ridged circular waveguide (b=20mm, a=16 mm, t=20º) computed with the circular and rectangular-based implementations fordifferent number of resonant modes. The exact cut-off frequency for the computation of therelative error is taken as fc = 34.8788 GHz. This value has been obtained as the convergentcut-off frequency value (difference smaller than 0.1 MHz) of the circular-based implementation.The CPU time required for each analysis is included.

n=1

Nr�ei ,en ej ,enI = �Δ Δ� �

the cross-shaped waveguide and the first mode of thecircular waveguide is shown, for different values of Nr.In Fig. 3c, the coupling coefficient between a high-ordermode (35th) of the cross-shaped waveguide and a high-order mode (257th) of the circular waveguide is depicted.The criteria for choosing these particular combinations ofmodes has been that a significant coupling (I�Δ0.1) be-tween them should exist.

The main conclusion that can be drawn from both graphsis that the rectangular-based implementation, even thoughit provides accurate results when low-order modes are in-volved, lacks some accuracy when dealing with higherorder ones. The reason for this loss in accuracy is that high-order modes have complex field patterns, which are rep-resented in a less accurately way by a series of rectangularwaveguide modes. Meanwhile, the circular-based imple-mentation does not need to represent these arbitrarymodes by any series, but instead defines them by themodal current density computed by the BI-RME method.Therefore, the computation of the coupling coefficients ofthese high-order modes has the same accuracy level as thecorresponding modal chart computation.

Considering high-order modes is important when complexstructures are studied, especially when the arbitrary wave-guide is used as an iris. In such cases, the circular-basedimplementation offers an important advantage over therectangular-based algorithm when some of the intercon-nections involve arbitrary and circular waveguides.

Finally, it is worth noting the oscillatory behaviour of thecoupling integrals with the different number of rectan-gular modes, which may produce inaccurate results if aproper convergence study is not previously carried out.

3.4. Design of a dual-mode filter with cross-shapedirises and tuning elementsThe last example deals with the design of a complex pas-sive device in circular waveguide technology. The struc-ture under consideration is the four-pole dual-mode filterdepicted in Fig. 4, along with its dimensions. It is basedon two circular waveguides coupled through a cross-shaped iris and includes two sets of tuning elements, aclassical structure widely used in satellite communications[17]. After designing the device, a prototype of this dual-mode filter has been manufactured with real rectangular

10 ISSN 1889-8297/Waves - 2013 - year 5

Figure 3: a) Cross-shaped iris of dimensions L1=17.3 mm, L2=15.3 mm, t=2 mm connected to a circular waveguideof radius R=12 mm. Dashed lines represent the contour of dimensions w=15.4 mm, d=17.4 mm used for the appli-cation of the rectangular-based algorithm. b) Relative error in the computation of coupling integrals between the firstcross-shaped mode and the first circular waveguide mode using the rectangular-based implementation. The exact valueto compute the error is taken as the one provided by the circular-based implementation. c) Relative error in the com-putation of coupling integrals between the 35th cross-shaped mode and the 257th circular waveguide mode using therectangular-based implementation.

insets to validate the analysis tool presented in this article.Figure 5 depicts the response of this manufactured pro-totype compared with the simulated response obtainedwith the circular-based and the rectangular-based BI-RMEimplementations. The response simulated with the circu-lar-based code is almost identical to the measured one,confirming the accuracy of this tool when dealing withthese complex devices. Regarding the rectangular-basedresponse, a small frequency shift of approximately 7 MHzis observed. Additionally, the out-of-band response up to20 GHz is successfully compared with measurements.

As far as the computational efficiency of the analysis isconcerned, the circular-based algorithm takes advantageof a more accurate characterization of the tuning sec-

tions, as well as a faster characterization of the differentplanar junctions to achieve convergent results in a shorteramount of time. While the rectangular-based implemen-tation takes 100 s to compute 100 frequency points, thecircular-based implementation takes just 43 s, a consid-erable reduction of the computation time just by usingthe appropriate resonant contour.

4. Conclusions

In this paper, an important enhancement of previous im-plementations of the BI-RME method has been pre-sented. This new implementation is intended to analysepassive devices based on circular and arbitrarily-shapedwaveguides in a more accurate and efficient way. It com-bines a circular contour as resonant structure with the in-clusion of straight, circular and elliptical arcs for definingthe perturbed geometry. Compared with previous imple-mentations of the same method based on rectangularwaveguides, this implementation takes advantage of alower number of resonant modes for the accurate mod-elling of the arbitrary sections, as well as the efficientcomputation of coupling coefficients between circularand arbitrary-shaped waveguides. Therefore, the analysisof devices based on circular and arbitrary waveguides ishighly improved by the use of the proposed implemen-tation, as it has been shown through some examples. Theaccuracy of this new implementation has also been suc-cessfully verified using several examples of practical in-terest, comparing the simulated responses with datataken from technical literature and experimental meas-urements. Furthermore, a dual-mode filter prototype hasbeen designed and manufactured for this purpose. In allthe examples, the performance of the new implementa-tion has been optimum, especially when compared withthe previous rectangular-based one.

11Waves - 2013 - year 5/ISSN 1889-8297

As shown, the analysis of devices based on circular andarbitrary waveguides is highly improved by the use ofthe proposed implementation.

Figure 4: Physical structure of the designed dual-modefilter in a circular waveguide of radius 13.3 mm. The di-mensions are as follows. Cavities: Lc1=54.4366 mm,Lc2=54.4436 mm. Input and output rectangular irises di-mensions: 10.6441x2 mm, thickness 1 mm. Cross iris:Lc1=7.688 mm and, Lc2=4.407 mm, t=1 mm, t c=1mm. First triple-inset coupling section: t s=ws=2 mmwith screws located at 0º (horizontal), 90º (vertical) and315º of depths, d0º=2.8956 mm, d90º=1 mm andd315º=1.9345 mm, respectively. Second triple-insetcoupling section: ts=ws=2 mm with screws located at0º, 45º and 90º of depths, d0º=2.9023 mm,d45º=2.0364 mm and d90º=1 mm.

Figure 5: In-band and out-of-band response of the designed dual-mode filter. Measurements of a manufactured pro-totype are compared with the simulation of the circular-based implementation.

Acknowledgments

This work was supported by Ministerio de Ciencia e In-novación, Spanish Government, under Research ProjectTEC2010-21520-C04-01.

References

[1] R. J. Cameron, C. M. Kudsia and R. R. Mansour, Mi-crowave Filters for Communication Systems. Hobo-ken, NJ: John Wiley & Sons; 2007.

[2] V. E. Boria and B. Gimeno, “Waveguide Filters forSatellites”. IEEE Microwave Magazine. October 2007;vol. 8, no. 5, pp. 60-70.

[3] W. L. Schroeder and M. Guglielmi, “A contour-basedapproach to the multimode network representationof waveguide transitions”, IEEE Trans. MicrowaveTheory Tech. April 1998, vol. 46, no. 4, pp. 411-419.

[4] A. S. Omar and K. F. Schunemann, “Application ofthe generalized spectral-domain technique to theanalysis of rectangular waveguides with rectangularand circular metal inserts”, IEEE Trans. MicrowaveTheory Tech. June 1991, vol. 39, no. 6, pp. 944-952.

[5] P. P. Silvester and G. Pelosi, Finite Elements for WaveElectromagnetics. New York: IEEE Press; 1994.

[6] A. Taflove, Computational Electromagnetics: The Fi-nite-Difference Time-Domain Method. Norwood,MA: Artech House; 1995.

[7] J. R. Montejo-Garai and J. Zapata, “Full-wave designand realization of multicoupled dual-mode circularwaveguide filters”, IEEE Trans. Microwave TheoryTech., June 1995, vol. 43, no. 6, pp. 1290-1297.

[8] R. H. MacPhie and K. L. Wu, “A full-wave modalanalysis of arbitrarily shaped waveguide discontinu-ities using the finite plane-wave series expansion”,IEEE Trans. Microwave Theory Tech., February 1999,vol. 47, no. 2, pp. 232-237.

[9] F. Arndt, J. Brandt, V. Catina et al. “Fast CAD and op-timization of waveguide components and apertureantennas by hybrid MM/FE/MoM/FD methods State-of-the-art and recent advances”, IEEE Trans. Mi-crowave Theory Tech., January 2004, vol. 52, no. 1,pp. 292-305.

[10] G. Conciauro, M. Guglielmi and R. Sorrentino. Ad-vanced Modal Analysis - CAD Techniques for Wave-guide Components and Filters. Chichester, England:John Wiley & Sons; 2000.

[11] G. Conciauro, M. Bressan and C. Zuffada, “Wave-guide modes via an integral equation leading to a lin-ear matrix eigenvalue problem”, IEEE Trans.Microwave Theory Tech., November 1984, vol. 32,no. 11, pp. 1495-1504.

[12] P. Arcioni, “Fast evaluation of modal coupling coef-ficients of waveguide step discontinuities”, IEEE Mi-crowave Guided Wave Lett., June 1996, vol. 6, no. 6,pp. 232-234.

[13] S. Cogollos, S. Marini, V. E. Boria et al. “EfficientModal Analysis of Arbitrarily Shaped Waveguides Com-posed of Linear, Circular, and Elliptical Arcs Using theBI-RME Method”, IEEE Trans. Microwave Theory Tech.,December 2003, vol. 51, no. 12, pp. 2378-2390.

[14] S. Zhang and Y. Shen, “Eigenmode sequence for anelliptical waveguide with arbitrary ellipticity,” IEEETrans. Microwave Theory Tech., January 1995, vol. 43,no. , pp. 227-230.

[15] U. Balaji and R. Vahldieck, “Radial mode matchinganalysis of ridged circular waveguides”. IEEE Trans.Microwave Theory Tech., July 1996, vol. 44, no. 7, pp.1183-1186.

[16] B. M. Dillon and A. A. P. Gibson, “Triple-ridged cir-cular waveguides”. J. of Electronmag. Waves Appli-cat., January 1995, vol. 9, no. 1-2, pp. 145-156.

[17] C. M. Kudsia, R. J. Cameron and W. C. Tang, “Inno-vations in Microwave Filters and Multiplexing Net-works for Communications Satellite Systems”, IEEETrans. Microwave Theory Tech., June 1992, vol. 40,no. 6, pp. 1133-1149.

Biographies

Carlos Carceller was born in Villar-real, Spain, in 1986. He received anIngeniero de Telecomunicación de-gree in 2010 and a Máster Universi-tario en Tecnologías, Sistemas yRedes de Comunicación degree in2012, both from the UniversidadPolitécnica de Valencia (UPV), Valen-cia, Spain. He is currently working

toward a Ph.D. degree in telecommunications at the sameinstitution. In 2009 he attended the University of Maryland(College Park MD, USA) through the PROMOE (UPV) pro-gram, where he worked in the design of microwave filtersin LTCC technology. In 2010 he joined the Grupo de Apli-caciones de Microondas where he currently develops soft-ware tools for the electromagnetic analysis of passivemicrowave components in waveguide technology. His cur-rent research interests include numerical methods in elec-tromagnetics and its application to CAD tools for passivemicrowave devices.

Santiago Cogollos was born in Va-lencia, Spain, on January 15, 1972.He received the degree in telecom-munication engineering and the Ph.D. degree from the Polytechnic Uni-versity of Valencia, Valencia, Spain,in 1996 and 2002, respectively. In2000, he joined the Communica-tions Department of the Polytechnic

University of Valencia where he was an Assistant Lecturerfrom 2000 to 2001, a Lecturer from 2001 to 2002, and be-came an Associate Professor in 2002. He has collaboratedwith the European Space Research and Technology Centreof the European Space Agency in the development ofmodal analysis tools for payload systems in satellites. In2005, he held a post doctoral research position working inthe area of new synthesis techniques in filter design at Uni-versity of Waterloo, Waterloo, Ont., Canada. His currentresearch interests include applied electromagnetics, math-ematical methods for electromagnetic theory, analytical andnumerical methods for the analysis of waveguide struc-tures, and design of waveguide components for space ap-plications.

12 ISSN 1889-8297/Waves - 2013 - year 5

Pablo Soto was born in 1975 inCartagena, Spain. He received theM.S. degree and Ph.D. degree (cumLaude) in Telecommunication Engi-neering from the Universidad Po-litecnica de Valencia in 1999 and2012, respectively. In 2000 hejoined the Departamento de Co-municaciones, Universidad Politec-

nica de Valencia, where he is Associatte Professor since2012. In 2000 he was a fellow with the European SpaceResearch and Technology Centre (ESTEC-ESA), Noord-wijk, the Netherlands. His research interests comprise nu-merical methods for the analysis, synthesis andautomated design of passive components in waveguideand planar technologies. Dr. Soto received the 2000COIT/AEIT national award to the best Master Thesis inbasic information and communication technologies.

Vicente E. Boria received the Inge-niero de Telecomunicación and theDoctor Ingeniero de Telecomuni-cación degrees from the UniversistatPolitècnica de València, València,Spain, in 1993 and 1997. In 1993he joined the Universistat Politècnicade València, where he is Full Profes-sor since 2003. In 1995 and 1996

he was held a Spanish Trainee position with the EuropeanSpace research and Tecnology Center (ESTEC)-EuropeanSpace Agency (ESA). He has served on the Editorial Boardsof the IEEE Transactions on Microwave Theory and Tech-niques. His current research interests include numericalmethods for the analysis of waveguide and scatteringstructures, automated design of waveguide components,radiating systems, measurement techniques, and powereffects in passive waveguide systems.

Carlos Vicente was born in Elche,Spain, in 1976. In 1999, he re-ceived the Dipl. degree in physicsfrom the Universidad de Valencia,Valencia, Spain, and the Dr. Ing. de-gree in engineering from the Tech-nical University of Darmstadt,Darmstadt, Germany, in 2005.From 1999 to the beginning of

2001, he was a Research Assistant with the Departmentof Theoretical Physics, Universidad de Valencia. From2001 to 2005, he was an Assistant Professor with the In-stitute of Microwave Engineering, Technical University ofDarmstadt. Since 2005, he has been with the MultimediaApplications Group, Universidad Politécnica de Valencia,Valencia. In 2006, he cofounded the Aurora Softwareand Testing S.L., which is devoted to the telecommuni-cations sector. His research interests include passive in-termodulation, corona discharge, and multipaction incommunications satellite applications.

Benito Gimeno was born in Valen-cia, Spain, on January 29, 1964. Hereceived the Licenciado degree inPhysics in 1987 and the PhD degreein 1992, both from the Universidadde Valencia, Spain. He was a Fellowat the Universidad de Valencia from1987 to 1990. Since 1990 heserved as Assistant Professor in the

Departamento de Física Aplicada y Electromagnetismoand ICMUV (Instituto de Ciencia de Materiales) at theUniversidad de Valencia, where he became Associate Pro-fessor in 1997 and Full Professor in 2010. He was work-ing at ESA/ESTEC (European Space Research andTechnology Centre of the European Space Agency) as aResearch Fellow during 1994 and 1995. In 2003 he ob-tained a Fellowship from the Spanish Government for ashort stay at the Universita degli Studi di Pavia (Italy) as aVisiting Scientific. His current research interests includethe areas of computer-aided techniques for analysis ofmicrowave and millimetre-wave passive components forspace applications, waveguides and cavities structures in-cluding dielectric objects, electromagnetic band-gapstructures, frequency selective surfaces, and non-linearphenomena appearing in power microwave subsystemsand particle accelerators (multipactor effect, corona ef-fect and passive inter-modulation phenomena).

Jordi Gil was born in Valencia,Spain, in 1977. He received the Li-cenciado degree in physics from theUniversidad de Valencia, Valencia,Spain, in 2000, and the Ph.D. de-gree in telecommunications engi-neering from the UniversidadPolitécnica de Valencia, Valencia,Spain, in 2010. From 2001 to 2004,

he was Researcher with the Aerospatiale Italian Company,Ingegneria Dei Sistemi-S.p.A., under the frame of the VEuropean Framework Programme. From 2004 to 2006,he joined the Microwave Applications Group, UniversidadPolitécnica de Valencia, under the frame of a Europeanreintegration grant funded by the VI European FrameworkProgramme. In 2006, he cofounded the company AuroraSoftware and Testing S.L. which is devoted to the spacesector. He is currently the Managing Director of the com-pany, where he also continues his research activities. Hiscurrent research interests include numerical methods incomputer-aided techniques for the analysis of microwaveand millimeter passive components based on waveguidetechnology, and nonlinear phenomena appearing inpower microwave subsystems for space applications. Hewas the recipient, in 2011, of the PhD Thesis ExtraordinaryAward at the Universidad Politécnica de Valencia.

13Waves - 2013 - year 5/ISSN 1889-8297