I. INTRODUCTION
Tuning screws are often used in waveguide filters and multiplexers to compensate for small errors produced during the fabrication process. However, the use of tuning screws has some disadvantages. First of all, it is known that, for space applications, fixed structures are generally preferred against others with mobile parts, because non-fixed parts can be moved due to vibration effects (i.e. those generated during the launching operation). As a side drawback, they may cause problems dealing with high-power signals, specially in space applications, since the small gaps along the threads between the screws and the holes, together with the contamination (metal shavings, dirt, etc.) on the surface of the screws, are likely to enhance passive intermodulation (PIM) and multipaction effects [Reference Wu1]. These gaps may also create potential radiation losses in the structure. Furthermore, the second important issue is the tuning process which is usually a time-consuming task, and must be carried out by an expert operator. For all these reasons, many authors have tried to avoid the use of tuning screws in the design and manufacturing of dual-mode filters [Reference Wu1–Reference Accatino, Bertin and Mongiardo3].
In this work, an alternative technique has been developed to correct manufacturing deviations, avoiding the use of tuning screws. Here, the correction is made by means of substituting some pieces of the fabricated devices for new ones, which are able to correct those deviations. These pieces are quite cheap and easy to manufacture with high precision.
In order to find the dimensions of the new pieces, a space mapping (SM) technique is going to be applied. SM techniques were originally introduced to design microwave components in [Reference Bandler, Biernacki, Chen, Grobelny and Hemmers4]. Since then, the idea has been successfully applied in different works with some specific variations [Reference Bandler, Biernacki, Chen, Hemmers and Madsen5–Reference Amari, Ledrew and Menzel9]. SM algorithms are usually employed to design microwave devices in a more efficient way, by combining the efficiency of circuit models with the accuracy of electromagnetic (EM) models. A low-accuracy model which is very fast (usually a circuit model) is used as a “coarse model”, while a high-precision model (usually obtained with an EM simulator) is employed as a “fine model”. The final aim is to obtain an optimal design given by the fine model without performing direct optimization over such expensive model. Instead, many simulations of the coarse model are combined with a few simulations of the fine model, thus establishing a relationship (mapping) between both models.
Here, the SM technique is going to be applied in an alternative way. It will be used to calculate the dimensions of a new set of pieces containing the fixed insertions. The difference between the dimensions of the new pieces and the dimensions of the old ones will be able to compensate for the manufacturing deviations in the whole structure. Therefore, the SM will take place between the measurements of the manufactured device (fine model), and the response simulated by the full-wave EM solver. Hence, by comparing the simulated responses with the measured ones, we will be able to recover the desired measured response using suitable insertion pieces found with the full-wave EM simulator.
In [Reference Brumos, Boria, Guglielmi and Cogollos10], this procedure was particularized for a specific type of filter, the circular-waveguide dual-mode (CWDM) filter. Here, the correction process is going to be generalized for any type of waveguide filter with tuning screws, in which they can be replaced by fixed insertions. The only requirement is that these pieces must be liable to be fabricated as separate pieces. In a similar way, the process will also be extended to correct manufacturing deviations in manifold multiplexers containing channel filters with the same characteristics, where the mentioned filters must also be liable to be fabricated independently of the rest of the structure (which is indeed the most usual way to fabricate waveguide multiplexers).
The rest of the document is organized as follows. In Section II, the procedure to correct manufacturing deviations in any type of waveguide filters is going to be introduced, thus explaining how the dimensions of the new pieces are calculated through an SM technique. In Section III, the method will by applied to correct manufacturing deviations in a specific filter structure, in particular a CWDM filter. After that, in Section IV, the technique will be extended to a more complex case, consisting on a manifold multiplexer whose channel filters are CWDM filters. Finally, after critically discussing the limitations of the proposed method and giving some practical advises in Section V; the main conclusions will be reviewed in Section VI.
II. METHODOLOGY
A) Problem overview
Let us consider a typical situation in which a waveguide filter has been designed, providing a good simulated response, and then, once it is manufactured, the measured response is different from the desired one. Assuming that the full-wave EM solver employed for the design was accurate enough, the deviation in the response will be due to the manufacturing tolerances, which are small errors in the dimensions of the fabricated device, due to inaccuracies in the fabrication process.
If the manufactured filter has tuning screws, this would be the time when they would be used to tune the response. This would be done by moving all the available screws while observing the measured response provided by the network analyzer. If fixed insertions are considered instead of the tuning screws, this correction process is performed in an alternative way, but the final idea will be very similar, since the aim is to obtain the dimensions of the fixed insertions that achieve a response as close as possible to the desired one. In order to find the dimensions of these pieces, more than one iteration (but usually quite a few) may be necessary, as it usually happens with the SM techniques. The whole design procedure is going to be detailed below.
B) SM models and parameters
In the proposed SM application, the coarse model will be a full-wave EM solver. The fine model responses are the measurements of the manufactured filter, which can be obtained with a vector network analyzer.
The SM parameters that are going to be modified during the correction process are the dimensions of the fixed pieces replacing the tuning screws. For example, if each tuning screw is substituted by a rectangular metal insertion, the SM parameters will be the penetrations of these insertions (thus emulating the tuning process of the screws). In that case, there would be as many SM parameters as the number of fixed metal insertions (which is equal to the number of tuning screws in the traditional structure).
C) Formulation
In this case, the aggressive space mapping (ASM) technique has been employed [Reference Bandler, Biernacki, Chen, Hemmers and Madsen5]. The ASM is a version of the classical SM technique [Reference Bandler, Biernacki, Chen, Grobelny and Hemmers4] where less simulations of the fine model are needed, thus resulting in a very efficient algorithm.
Following the method explained in [Reference Bandler, Biernacki, Chen, Hemmers and Madsen5], the dimensions of the fixed insertions (normally the penetration lengths) to be fabricated in each iteration are calculated as follows:
$${\bf L}_f^{(j)} = {\bf L}_f^{(j - 1)} + {{\bf h}^{(j)}}, $$
where L f (j) is a vector with the penetration lengths of the fine model in the jth iteration, and h (j) is the new increment for each new iteration that can be obtained as indicated next
$${{\bf h}^{(j)}} = - {({{\bf B}^{(j)}})^{ - 1}}{{\bf f}^{(j)}}. $$
In the previous equation, B (j) denotes the corresponding Jacobian matrix, also described in [Reference Bandler, Biernacki, Chen, Grobelny and Hemmers4], that can be obtained by means of the classical Broyden update
$${{\bf B}^{(j)}} = {{\bf B}^{(j - 1)}} + \displaystyle{{{{\bf f}^{(j)}}{{\bf h}^{(j - 1)T}}} \over {{{\bf h}^{(j - 1)T}}{{\bf h}^{(j - 1)}}}}, $$
and f (j) can be calculated as
$${{\bf f}^{(j)}} = {\bf L}_c^{(j)} - {\bf L}_c^{(0)}, $$
where L c (j) and L c (0) are the dimensions in the coarse model for the jth iteration and for the optimal solution (the insertion dimensions of the originally designed filter), respectively.
For this particular case of the first iteration, given that there is no information available to build the Jacobian matrix, the identity matrix is used instead.
D) Correction process
Once the original filter has been designed and fabricated, its response is measured. When this response is different from the desired one, the correction process starts. In order to perform the first iteration, the first step is to obtain the new dimensions of the coarse model (L c (1)). This is done by obtaining, with the full-wave EM software code, a response that matches the previously measured response. This can be done by optimizing the original design, only modifying the penetration lengths of the metal insertions. The new penetrations of the coarse model L c (1) obtained after the optimization process are introduced in (1)–(4) to obtain the new penetration values of the fine model L f (1), which correspond with the dimensions of the new pieces that will be manufactured.
The next step is to measure the filter response after substituting the original insertion pieces with the ones obtained after the first SM iteration. If the new measured response is not close enough to the desired one, a second SM iteration can be performed. In this case, the response measured after the first SM iteration will be matched with the optimizer to obtain L c (2). The whole process can be repeated until the desired response is achieved, or until there are no significant improvements between iterations (see Section V).
III. CORRECTION OF MANUFACTURING DEVIATIONS IN CWDM FILTERS
CWDM filters are widely used in payload systems of communication satellites, due to their reduced weight, compact size, and electrical performance [Reference Williams11–Reference Kudsia, Cameron and Tang14]. One of the main problems of these filters is their high sensitivity to manufacturing deviations, which usually involve important degradations of the measured response. This drawback is commonly alleviated by means of tuning screws [Reference Cogollos15].
Here, the correction process explained in Section II is going to be particularized to this type of filters. More specifically, a four-pole CWDM filter with two cavities has been considered, whose structure is depicted in Fig. 1. As it can be seen, it has three fixed rectangular-shaped insertions placed inside each cavity, instead of tuning and coupling screws.
Proposed structure for a four-pole dual-mode filter in circular waveguide. The tuning and coupling screws have been replaced by fixed rectangular-shaped metal insertions.
After designing the filter using an EM solver, it was manufactured. For the fabrication process, the filter was divided into five separate pieces (see Fig. 2), to allow the replacement of two pieces containing the fixed insertions. The manufactured filter can be seen in Fig. 3, whereas the disassembled device is shown in Fig. 4. It has to be stressed that these cuts are located where the currents are minimal, thus producing a structure with very low losses as it was demonstrated in [Reference Cogollos, Boria, Soto, Gimeno and Guglielmi16].
Side cut of the manufactured CWDM filter structure divided into five pieces.
Manufactured CWDM filter with all its pieces assembled together.
Detailed view of the pieces composing the CWDM filter as in Fig. 3.
The ideal response of the filter, obtained with a full-wave EM solver, is shown in Fig. 5 (solid line). After measuring the manufactured filter, the response shown in Fig. 5 (dashed line) was obtained. As it can be seen, due to the manufacturing tolerances, the response of the fabricated filter is quite different from the simulated one.
Ideal response obtained with a full-wave EM solver (FEST3D) compared with the measured response of the manufactured CWDM filter.
In order to improve the response of the manufactured filter, two new insertion pieces (corresponding with pieces two and four in Fig. 2) need to be designed. The SM technique is going to be applied to calculate the penetrations of the three insertions of each piece. Therefore, the only parameters that are going to be modified during the SM process are the penetration depths (L variables in Fig. 6) of the six rectangular-shaped metal insertions.
Pieces with insertions allocated in the middle of each cavity in the CWDM filter.
In this case, the full-wave EM solver FEST3D [17] has been used as a coarse model, but any other software capable of coping with the full-wave EM analysis of the proposed complex structures, within reasonable CPU times, could be used instead. The fine model was the measurement obtained with a vector network analyzer (Agilent E8364B, 10 MHz–50 GHz). A total of three SM iterations have been performed. After each iteration, the length of the six insertions were obtained as indicated in the previous section, and the corresponding two pieces were fabricated. The penetration lengths obtained in the different iterations are detailed in Table 1.
Penetration lengths obtained during the correction process of the CWDM filter.
The measured responses of the filter with the pieces obtained after each iteration are shown in Fig. 7. As it can be seen, the improvement of the response of the first iteration, with regard to the one of the original manufactured prototype, is already considerable. The differences between iterations one and two are also quite important, achieving a better return loss value after the second iteration. Finally, the last iteration has been able to correct almost perfectly the existing frequency shift, thus achieving a response that is very close (almost identical) to the ideal one.
Measured responses after each iteration, compared with the simulated response, and the original fabrication of the CWDM filter.
In order to better verify the effectiveness of the method, the final measured response has been represented together with the ideal EM simulated response and the measurements of the original prototype (see Fig. 8). The improvement between the response of the original manufactured prototype and the response of the last SM iteration is clearly observed. The simulation time of these kind of filters is 4 s in an AMD FX-8350 Eight Core Processor, 4 GHz, 32 GB RAM. This computational effort makes the method very amenable to be used in this kind of designs, because the step related to parameter extraction (obtention of L c (j)) requires several simulations of the coarse model.
Comparison between the responses of the measured original prototype and the last SM iteration, together with the desired ideal response of the CWDM filter.
IV. CORRECTION OF MANUFACTURING DEVIATIONS IN MANIFOLD MULTIPLEXERS
The correction procedure here proposed can also be applied to multiplexers containing channel filters that traditionally have tuning screws. In this section, the method is going to be extended to a manifold waveguide multiplexer with CWDM filters, although the technique could be directly employed with other multiplexer configurations. In particular, a multiplexer with eight contiguous channels has been considered, whose structure can be seen in Fig. 9.
Physical structure of the contiguous eight-channel multiplexer with herringbone configuration, and whose filters are four-pole CWDM filters.
In this case, due to the complexity of the device, a prototype has not been manufactured. Instead, the errors in the dimensions occurring during the fabrication process have been considered with a full-wave EM solver (i.e. FEST3D). To do so, random deviations of about 10 µm (which is a typical value specified by manufacturers) have been introduced in the dimensions of all the channel filters, manifold waveguide sections, and waveguides connecting the manifold with the filters. Hence, in this example, the coarse model is the ideal EM model (without errors), and the fine model is the EM model with random errors in its dimensions, that models what we would obtain by measuring the fabricated device with a network analyzer. Fig. 10 shows the simulated response of the ideal multiplexer compared with the response of the multiplexer with the simulated errors. In order to make the visualization clearer, only the common port return loss (CPRL) has been displayed in Fig. 10. For validation purposes Fig. 11 shows the transmission response for all channels of the ideal multiplexer simulated with two independent commercial EM solvers (FEST3D and MW Wizard).
Ideal response for the CPRL of a contiguous eight-channel multiplexer obtained with a full-wave EM solver (FEST3D), compared with the response of the same multiplexer considering manufacturing deviations.
Ideal transmission response for all channels of the ideal multiplexer simulated with two independent commercial EM solvers (FEST3D and MW Wizard).
The next step would be to disconnect all the channel filters from the manifold and measure (in our case simulate considering random deviations) each of them separately. After that, following the same procedure as for individual filters, the measured responses of the individual channel filters should be matched with the corresponding ideal simulated prototypes, by optimizing the penetrations of the metal insertions. This is done filter by filter, for the eight channel filters. As a confirmation of the response given by FEST3D, independent simulations with other commercial software tools (i.e. ANSYS HFSS and Microwave Wizard) have been carried out, Fig. 12 shows the second channel response after applying manufacturing deviations and its simulation with FEST3D, HFSS, and Microwave Wizard.
Response of the second channel filter with manufacturing deviations compared with the responses obtained with independent commercial software (HFSS and MW Wizard).
Now, it is important to assure that not only the module of the simulated response perfectly matches the measured one, but also the phase must be exactly the same, since in multiplexer design the phase of the channel filters matter, in order to achieve a certain response of the whole device. Figs. 13 and 14 show the responses (module and phase) of the second channel filter with errors compared with the corresponding optimized responses.
Optimization of the EM model to match the module of the response of the second channel filter with manufacturing deviations.
Optimization of the EM model to match the phase response of the second channel filter with manufacturing deviations.
Once the simulated isolated responses of all the channel filters perfectly match (in module and phase) the corresponding measured ones, a new EM model of the complete multiplexer is created. The next step is to perform a slight general optimization, considering the penetrations of the insertions of all the involved channel filters, in order to match the measured response of the whole multiplexer. That way, the manufacturing errors in the manifold can also be accounted for.
There are several reasons to perform a slight EM optimization of the full multiplexer in each iteration. One is the aforementioned correction of fabrication errors in the manifold. Another reason is the consideration of higher order modes that are very important in the T-junctions of the manifold. This effect is almost negligible for narrowband multiplexers but for wideband applications, the spurious modes of a channel filter can interact with the rest of the filter responses and ruin the whole performance if this fact is not taken into account.
After that, two new insertion pieces for each channel filter are designed, filter by filter, using the formulation detailed in Section II. These pieces are manufactured, and then introduced in the manufactured multiplexer. In our case, we have simulated this step by introducing the dimensions of the new insertion pieces in the EM model of the multiplexer considering manufacturing errors. A good improvement is observed, however, for verification purposes, another iteration has been carried out. The CPRL and transmission (second channel) responses of the corrected multiplexer have been shown in Figs. 15 and 16, respectively, together with the response of the ideal multiplexer, and the one of the original multiplexer with simulated manufacturing deviations. As it can be seen, with just two iterations it has been possible to significantly improve the response of the multiplexer. Nevertheless, successive iterations could also be applied, in order to achieve a more accurate response. However, from the results shown it is clear that the convergence is fairly good (see, for example, in Fig. 16 how close the iterations one and two are).
Evolution in the CPRL response of the corrected multiplexer (including manufacturing errors) for two iterations of the SM algorithm, compared with the simulated response of the original design, and the one of the multiplexer with the simulated errors.
Evolution in the transmission response of the second channel of the corrected multiplexer (including manufacturing errors) for two iterations of the SM algorithm, compared with the simulated response of the original design, and the one of the multiplexer with the simulated errors.
V. ADDITIONAL CONSIDERATIONS
The proposed method is intended for the correction of the filter response, which has been deteriorated due to the manufacturing deviations in the whole structure. However, the insertion pieces fabricated in each iteration are not perfectly fabricated either. Because of that, a totally perfect response is never going to be achieved (except for a matter of chance). Nevertheless, due to mechanical reasons, the accuracy that can be obtained in the fabrication of the pieces with insertions is significantly higher than the accuracy that can be achieved in the rest of the structure, so the final result, if not perfect, can be very close to the ideal one.
Apart from that, this technique will only be able to correct those manufacturing problems that can be compensated with the circuit parts considered in the process (in this case the rectangular metal insertions). Therefore, the best achievable result will be similar to the one obtained in the tuning process of a filter or multiplexer, where real tuning and coupling screws are used instead of fixed metal insertions. This means that if, for example, there are important errors in the fabrication of the irises, which could lead to a significant variation of the bandwidth, it may not be possible to correct the related response deviations perfectly. For sure this limitation also applies to the case of using tuning screws. Nevertheless, given that case, the technique would be able to significantly improve the initial response of the original manufactured device.
A possible solution for strong deviations in the fabrication of the irises would be to add insertions in the irises themselves, because a deviation on the input iris can have a big impact in the filter performance. However, adding an insertion in the input iris could be critical for high-power handling, because it is well known that the input iris is the weakest point in the filter for multipaction tests. Therefore, considering this new optimization variable, we can use it to control strong deviations with the restriction of high-power issues.
Finally, the beauty of the SM technique is that the method will tend to obtain the desired response even if the coarse model cannot perfectly simulate the real structure. Indeed, instead of insertions we can use real screws in the physical filter. The SM algorithm will give at each iteration the penetrations of the screws to improve the overall performance. Additionally, if the EM solver allows the simulation of the insertions with arbitrary profiles, any shape can be checked as a potential correction structure. Moreover, if the simulator cannot account for strange shapes, the method will work in any case because the SM will try to obtain the approximate mapping through the Broyden matrix in order to match the response of both models (probably more iterations will be needed). The practical limit is how far are both spaces, how many variables are handled, and how many iterations are allowed.
VI. CONCLUSIONS
A novel technique to correct manufacturing tolerances in the production of waveguide filters and manifold multiplexers has been proposed, which allows to avoid the inclusion of tuning screws, replacing them by fixed rectangular-shaped metal insertions. In this case, the tuning process of the screws is substituted by the manufacturing of these insertion pieces in an iterative process. The aggressive SM technique is employed to design these pieces, thus being able to finally achieve the desired response.
The procedure has been initially validated with a CWDM filter. A total of three SM iterations have been performed. A significant improvement has been observed between the measurements of the original prototype and the measured results corresponding to the third SM iteration. Additionally, the correction process has also been applied to a manifold multiplexer with eight CWDM filters, showing very good results after performing just two iterations. The same technique could be easily extended to other type of waveguide filters and multiplexers.
Santiago Cogollos received his degree in Telecommunication Engineering in 1996 and the Ph.D. degree in 2002 from the Universidad Politécnica de Valencia, Valencia, Spain. In 2000 he joined the Communications Department of the Universidad Politécnica de Valencia, where he was an Assistant Lecturer from 2000 to 2001, a Lecturer from 2001 to 2002, and became an Associate Professor in 2002. He has collaborated with the European Space Research and Technology Centre of the European Space Agency in the development of modal analysis tools for payload systems in satellites. In 2005 he held a post doctoral research position working in the area of new synthesis techniques in filter design at University of Waterloo, Waterloo, Ontario, Canada. His current research interests include applied electromagnetics, mathematical methods for electromagnetic theory, analytical and numerical methods for the analysis of waveguide structures, and design of waveguide components for space applications.
Carlos Carceller was born in Villarreal, Spain, in 1986. He received the Ingeniero de Telecomunicacion degree in 2010 and Master Universitario en Tecnologias, Sistemas y Redes de Comunicacion degree in 2012, both from the Universidad Politécnica de Valencia (UPV), Valencia, Spain. He is currently working toward the Ph.D. degree in Telecommunications at the same institution. In 2010 he joined the Grupo de Aplicaciones de Microondas where he currently develops software tools for the electromagnetic analysis of passive microwave components in waveguide technology. In 2009 and 2013 he was with the University of Maryland at College Park. Within the framework of his thesis, he collaborates actively with Aurora Software and Testing S.L. in the EM modeling of passive waveguide components. His current research interests include numerical methods in electromagnetics and its application to the development of CAD tools for passive microwave devices.
Mariam Taroncher was born in Lliria, Valencia, Spain, on October 8, 1979. She received her Telecommunications Engineering degree from the Universidad Politécnica de Valencia (UPV), Valencia, Spain, in 2003. From 2002 to 2004, she was a Fellow Researcher with the UPV in the field of analysis methods for waveguide structures, and is currently working toward the Ph.D. degree at UPV. Since 2004, she has been a Technical Researcher in charge of the experimental laboratory for high-power effects in waveguide devices at the Research Institute iTEAM, UPV. In 2006 she was awarded a Trainee position at the European Space Research and Technology Centre, European Space Agency (ESTEC-ESA), Noordwijk, The Netherlands, where she worked in the Payload Systems Division Laboratory in the area of Multipactor, Corona Discharge, and Passive Intermodulation (PIM) effects.
Vicente E. Boria was born in Valencia, Spain, in 1970. He received his Telecommunication Engineering degree (with first-class honors) and the Ph.D. degree from the Universidad Politécnica de Valencia, Spain, in 1993 and 1997, respectively. In 1993 he joined the Communications Department, Universidad Politécnica de Valencia, where he has been Full Professor since 2003. In 1995–1996, he was holding a Spanish Trainee position with the European Space Research and Technology Centre, European Space Agency (ESTEC-ESA), Noordwijk, The Netherlands, where he was involved in the area of EM analysis and design of passive waveguide devices. He has authored or co-authored seven chapters in technical textbooks, 75 papers in refereed international technical journals, and over 150 papers in international conference proceedings. His current research interests are focused on the analysis and automated design of passive components, left-handed and periodic structures, as well as on the simulation and measurement of power effects in passive waveguide systems.
Marco Guglielmi received his Electronics Engineering degree in 1979 from the University of Rome “La Sapienza”, Italy. In 1981 he was awarded a Fulbright Scholarship in Rome and an HISP (Halsey International Scholarship Programme) from the University of Bridgeport, Connecticut, USA, where in 1982 he obtained an M.S. Degree in Electrical Engineering. In 1986 he received a Ph.D. degree in Electrophysics from the Polytechnic University, Brooklyn, New York, USA. From 1984 to 1988 he was Associate and Assistant Professor at the same institution. From 1988 to 1989 he was the Assistant Professor at the New Jersey Institute of Technology, USA. In 1989 he joined the European Space Agency in the RF System Division of the European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands, where he was in charge of the development of microwave filters and EM simulation tools. In 2001 he was appointed Head of the Technology Strategy Section in the Technology Programmes Department of ESTEC.
Carlos Vicente was born in Elche, Spain, in 1976. In 1999, he received his Dipl. degree in physics from the University of Valencia, Valencia, Spain and the Dr.-Ing degree in Engineering in 2005 from the Technical University of Darmstadt, Germany. From 1999 until the beginning of 2001, he worked as a Research Assistant at the Department of Theoretical Physics of the University of Valencia. From 2001 until 2005 he was an Assistant Professor at the Institute of Microwave Engineering at the Technical University of Darmstadt. From 2005 he is with the Microwave Applications Group, from the Technical University of Valencia, Spain. In 2006, he co-founded the company Aurora Software and Testing S. L. devoted to the telecommunications sector. His research concerns the analysis and design of passive components for communications satellites with special emphasis in high-power practical aspects such as Passive Intermodulation, Corona Discharge and Multipaction.
Maria Brumos was born in Teruel, Spain, on February 17, 1986. She obtained the Telecommunication Engineering degree from Universidad Politécnica de Valencia, Spain, in 2009. At the end of 2014, she received her Ph.D. degree from the same university. Her thesis was focused on the design of waveguide filters and multiplexers for satellite communications. In 2015, she joined the company Thales Alenia Space in Tres Cantos, Madrid, where she is working in the design of passive microwave components for space applications.
