I. INTRODUCTION
Band-pass filters with excellent performance in terms of loss and power handling are generally realized using waveguide technology. In spite of their advantages, size and mass are well-known considerable drawbacks. Compact and low-loss band-pass filters, instead, are expected to be key elements in future telecommunication systems, especially for satellite and space applications. Many efforts have thus been devoted in the last decades to reduce the size and mass of waveguide filters. Typically, dual- and multi-mode cavities have been proposed and used to this purpose [Reference Williams1–Reference Guglielmi, Jarry, Keherve, Roquebrun and Schmitt6]. Most of such solutions allow for pseudoelliptic filtering functions, but the number and positions of transmission zeros are usually limited, especially as the filter order increases. A novel TM dual-mode cavity capable of realizing Nth-order filtering functions with N symmetrically or asymmetrically located transmission zeros has been proposed and described in [Reference Bastioli, Tomassoni and Sorrentino7–Reference Tomassoni, Bastioli and Sorrentino9].
Another common way to reduce the size and mass of a waveguide filter without significantly reducing its insertion loss (IL) is to load it with a high-permittivity dielectric material (typically ε r > 30). This approach using single- and dual-mode dielectric resonators has been widely used for satellite applications in L-, S-, and C-bands [Reference Cameron, Kudsia and Mansour10–Reference Fiedziuszko12]. In particular, TM010 dielectric cylindrical resonators have been shown to provide considerable volume saving [Reference Kobayashi and Yoshida13] and have been used to realize very compact and low-loss L-, S-, and C-band filters [Reference Hoft14, 15].
In [Reference Pelliccia, Cacciamani, Tomassoni and Sorrentino16], the TM dual-mode rectangular cavity loaded with a high-permittivity cylinder has been proposed for the first time, although without experimental results, to produce ultra-compact Nth-order filters with N symmetric transmission zeros. A generalized coupling topology has been introduced in [Reference Pelliccia, Cacciamani, Tomassoni and Sorrentino17] to achieve Nth-order filtering functions with N symmetric or asymmetric transmission zeros and the results of a fourth-order filter prototype are presented.
In this paper, further investigations on dielectric-loaded TM cavities are presented and new properties related to pass-band reconfigurability and spurious handling are shown and demonstrated through experimental results.
In particular, in Section II the properties of dielectric-loaded TM cavities are compared to those of the conventional cavity resonators. The way to generate a doublet from a single dielectric-loaded TM cavity and the way to realize multi-cavity filters are shown in Sections III and IV. Finally, in Section V results showing the possibility to improve the spurious free band and measurements demonstrating the frequency reconfigurability of a four-pole four-zero filter are shown.
II. TM DUAL-MODE DIELECTRIC-LOADED CAVITY
Figure 1 shows a TM dual-mode dielectric-loaded rectangular cavity, obtained by loading an empty TM dual-mode cavity with a high-permittivity cylinder. As in [Reference Kobayashi and Yoshida13], the cavity is uniform along the z-axis; as shown in the figure, this implies that both circular bases of the dielectric cylinder are in contact with the metallic enclosure. Incidentally, it should be noted that for the practical implementation of this type of filter several mechanical expedients have been proposed to ensure a good and stable metal-to-dielectric contact [Reference Hoft14, 15].
HFSS® model of a TM dual-mode rectangular cavity loaded with a dielectric cylinder.
In contrast to [Reference Kobayashi and Yoshida13] where circular TM modes are employed, two TM degenerate modes are used here. Such a pair of modes corresponds to the TM120 and TM210 modes of the empty cavity [Reference Bastioli, Tomassoni and Sorrentino7, Reference Tomassoni, Bastioli and Sorrentino9] whose cross-sectional H-field distributions (xy-plane) are sketched in Figs 2(a) and 2(b). Contrary to [Reference Kobayashi and Yoshida13], where circular coordinates are used, Cartesian coordinates are adopted here. In fact, for the sake of simplicity, we identify the modes of the dielectric-loaded cavity with the same set of indexes (m, n, p) as the corresponding modes of the unloaded cavity, i.e. with the numbers of half-swings of the EM field along the x, y and z directions. Observe that since both TM120 and TM210 modes are independent of z, the cavity length does not affect their resonant frequency but only the unloaded Q.
H-field distributions of resonant and non-resonating modes of the dielectric loaded cavity: (a) TM120 resonant mode, (b) TM210 resonant mode, and (c) TM110 non-resonating mode.
Besides the resonant TM modes, non-resonating modes, i.e. modes that resonate far away from the operating frequencies, can also be excited in the cavity. Figure 2(c) shows the cross-sectional magnetic field distribution of one of such modes, i.e. the TM110 mode. Non-resonating modes play an essential role as they are used to generate by-pass coupling paths, thus transmission zeros [Reference Bastioli, Tomassoni and Sorrentino7–Reference Tomassoni, Bastioli and Sorrentino9].
The dielectric loading yields a dramatic size and mass reduction of the filter, up to about 90%. In the case of the example presented in following sections, for the same resonant frequency f 0 = 4 GHz, the cavity width (w = h, in Fig. 1) is reduced by 73% (84 mm down to 23 mm) using a dielectric with ε r = 34 and tanδ = 5 × 10−5 [18]. Since the cavity length is unchanged (i.e. 5 mm), the volume saving is about 92%, while the corresponding mass saving can be estimated in 85%. In this example, the Q of the cavity is reduced by less than 15% with respect to the empty cavity (3800 instead of 4400), having assumed silver-plated walls (σ = 6.1 × 107 S/m).
This result is illustrated in general terms in Fig. 3, where the Q S of the loaded and unloaded cavities (Fig. 3(a)) and the frequency of the first higher-order mode (Fig. 3(b)) are shown versus the cavity length l. Indeed, the length is an important parameter that determines the first spurious pass-band. It has been observed that if the cavity length is less than 7.5 mm (roughly λ/8 at f 0) the loaded-cavity has a wider spurious-free range than the empty cavity, while its unloaded Q is close to 5000, just 17% lower than the empty cavity (Q = 6000). On the contrary, when l is close or larger than 7.5 mm, the first higher-order resonant frequency approaches that of the TM120 and TM210 modes. This indicates that the cavity length should be <λ/8 to preserve the out-of-band response of the filter.
Unloaded Q S (a) and first higher-order resonant frequencies (b) of TM dual-mode loaded and unloaded cavities versus cavity length (l) @ f 0 = 4 GHz (C-band), with σ metal = 6.1 × 107 S/m (silver), ε r = 34, and tanδ = 10−5.
Table 1 shows the comparison of the proposed cavity with three other competitive structures: a cavity totally filled with the same dielectric material, a comb-line cavity and a dual-mode dielectric resonator using HE11 degenerate modes [Reference Fiedziuszko12]. All metal surfaces have been assumed to be silver-plated and a dielectric material with ε r = 34 and tanδ = 5 × 10−5 [18] has been adopted in the HFSS® designs of these resonators. All cavities have been sized so as to have the same resonant frequency f 0 = 4 GHz. The comb-line cavity has roughly the same volume as the proposed dual-mode cavity. Compared with the totally filled cavity, the volume saving is around 50%, while the Q reduction is 35% (2500 versus 3800). Compared with the comb-line cavity, the latter has a 25%, lower Q but a wider spurious-free range, since the first higher-order resonant frequency is ~12 GHz instead of ~6 GHz.
Nevertheless, the TM dual-mode loaded cavity has two distinct advantages with respect to comb-line cavity. The first resides in the dual-mode nature that implies a 50% reduction of the filter size. The second one is that, as already pointed out, the TM dual-mode cavity allows two transmission zeros to be realized by exploiting the non-resonating modes. The main advantages with respect to the dielectric HE dual-mode resonators are related to the reduced volume and mass and improved spurious free range, the HE modes allow, instead, for higher Q S. In this manner, by cascading N cavities, 2Nth-order pseudo-elliptic filters with 2N symmetric or non-symmetric transmission zeros can be designed.
III. GENERATING A DOUBLET
When connected to the external circuit by coaxial connectors as shown in Fig. 4(b), the TM dual-mode cavity of Fig. 1 can be used to realize a second-order filtering function with two symmetric or asymmetric transmission zeros (i.e. a doublet), so implementing the transverse coupling scheme of Fig. 4(a) [Reference Tomassoni, Bastioli and Sorrentino9].
Transverse coupling scheme for second-order filtering functions with two transmission zeros (a); HFSS® model of the proposed architecture (b); geometrical parameters (c).
Let f 1 and f 2 be the resonant frequencies of the TM210 and TM120 modes, respectively. As shown in [Reference Tomassoni, Bastioli and Sorrentino9], to implement the topology scheme of Fig. 4(a), f 1 and f 2 need to be slightly different. This can be obtained by perturbing the cavity geometry, e.g. by letting w ≠ h as in Fig. 4(c).
Short-circuited Sub-Miniature a Connector (SMA) coaxial probes can be used to connect the input and output 50 Ω lines to the cavity. The coaxial connectors are located at the same distance from the cavity center (p), forming an angle θ, as indicated in Figs 4 and 5. In this manner (see Figs 5(a) and 5(b)), the magnetic field of the coaxial TEM mode is coupled to both TM resonant modes, so creating two different paths for the EM energy through the cavity. The direct source-to-load coupling (M SL in Fig. 4(a)), instead, is produced by the non-resonating modes, such as for instance the TM110 mode, that is excited by the coaxial connectors (see Fig. 5(c)).
H-field coupling between coax TEM and cavity modes: TEM–TM210 (a), TEM–TM120 (b), and TEM–TM110 (c)
With reference to Fig. 4(c), the distance p between the coaxial probes and the cavity center controls the amplitude of all couplings. The angle 2θ between the probes affects the ratio between M S1 (=M 1L) and M S2 (=−M 2L): starting from θ = 0° to 90° the value of M S1 (=M 1L) passes from zero to its maximum value, while the value of M S2 (=−M 2L) passes from its maximum value to zero. When θ = 45°, M S1 = M 1L = M S2 = −M 2L.
By properly selecting the location of the feeding connectors it is therefore possible to control the locations of the two transmission zeros. In particular, a ratio M S1/M S2 ≠ 1 (M 1L/M 2L ≠ 1) is required to achieve asymmetric positioning of the zeros [Reference Tomassoni, Bastioli and Sorrentino9].
Figure 6 shows two examples where responses of two coupling matrices are compared to those of the corresponding TM dielectric cavities of Fig 4(b). The two considered coupling matrices are identical except for the fact that the values of M S1 (=M 1L) and M S2 (=−M 2L) are exchanged. This leads to the responses of Figs 6(a) and 6(b) having two zeros in the upper and lower stop-band, respectively. The cavity responses are instead obtained, assuming f 2 < f 1 (thus w < h) and considering that, according to Fig. 5, when θ < 45° M S1 (=M 1L) >M S2 (=−M 2L) while θ > 45° M S1 (=M 1L) <M S2 (=−M 2L).
Positioning the two transmission zeros of the cavity of Fig. 4(b) by changing the angle (2θ) between feeding lines. Comparison between coupling matrix response and full-wave response. FBW (−3 dB) = 11.95%.
Note that this cavity can be seen as a generalization of that presented in [Reference Pelliccia, Cacciamani, Tomassoni and Sorrentino16] having a symmetric response. In fact, as shown in [Reference Tomassoni, Bastioli and Sorrentino9], doublets based on transverse topology are capable of realizing both symmetric and asymmetric filtering functions.
It is also possible to use rectangular irises as coupling elements. Coupling mechanisms are depicted in Fig. 7, where the magnetic field distributions in the iris and the cavity are shown. According to the figure, irises are oriented so as to be orthogonal to the line connecting iris center to cavity center. As in the coaxial case, the angle θ affects the ratio between M S1 (=M 1L) and M S2 (=−M 2L) and does not affect M SL, while the distance p from the cavity center affects all coupling amplitudes. In this case however, taking advantage from the rectangular geometry, a further parameter (iris width a) can be used as a further degree of freedom allowing a better control of the response parameters. As an example we can change M SL leaving M S1 (=M 1L) and M S2 (=−M 2L) unchanged. In fact, shifting the rectangular iris from the cavity center (p = 0) to the edge of the dielectric (p = dielectric cylinder radius), according to Fig. 7(c), M SL passes from 0 to its maximum value. In the meanwhile, according to Figs 7(a) and 7(b), M S1 (=M 1L) and M S2 (=−M 2L) decrease, but the decrease can be compensated by increasing the iris width a.
H-field coupling between iris TE10 mode and cavity modes: TE10–TM210 (a), TE10–TM120 (b), and TE10–TM110 (c)
The possibility to control M SL independently of all others couplings leads to a better control of the position of transmission zeros.
Figure 8 shows three examples where the responses of three coupling matrices are compared to those of the corresponding TM dielectric cavities with rectangular irises. While rectangular irises are used, according to Fig. 8(d), it is convenient to use rectangular waveguides as input and output. In the examples considered, input and output waveguides are dielectric filled in order to reduce their dimensions. In any case, the choice of input and output waveguides affects the in-band response but has no impact on the position of the transmission zeros. As we will see later on, the positioning of the zeros is a key point in the proposed filter design procedure.
Number and position of the transmission zeros by changing the angle (2θ) between feeding lines and the distance p of irises from the center. Comparison between coupling matrix response and full-wave response. FBW (−3 dB) = 4.5% (a), (b), FBW (−3 dB) = 3% (c).
Analogously to Figs 6(a) and 6(b), also in the case of Figs 8(a) and 8(b) the zeros in the upper stop-band are obtained for θ > 45° and those in the lower stop-band for θ < 45°. Note that, in contrast to the coax coupling section, the lack of the short-circuited connectors allows the rectangular irises to be easily positioned in correspondence of the dielectric cylinder. Taking advantage from this flexibility, in Fig. 8(c) the irises have been positioned at the center of the cavity (p = 0). In that position, the non-resonating mode is not excited (M SL = 0). Furthermore, considering that θ = 45° (thus M S1 = M 1L = M S2 = − M 2L.), the resulting response is symmetric with no transmission zeros.
IV. DESIGNING MULTI-CAVITY FILTERS
This section illustrates how a 2Nth-order filter with a number of transmission zeros up to 2N can be obtained by cascading N cavities.
Such a filter can be designed according to the following four steps [Reference Bastioli, Tomassoni and Sorrentino7, Reference Tomassoni, Bastioli and Sorrentino9]:
A) Design each doublet of the filter
Number and position of the transmission zeros of each doublet are chosen considering that they become the zeros of the whole filter.
B) Cascade all doublets through NRNs
With reference to Fig. 9(b), doublets are cascaded through non-resonating nodes (NRNs). The resulting topology has the property of maintaining number and position of the zeros of each cascaded doublet [Reference Guglielmi, Jarry, Keherve, Roquebrun and Schmitt6, Reference Bastioli, Tomassoni and Sorrentino7]. In the final cascaded filter, the positions of the transmission zeros will be slightly different with respect to the original positions in the non-cascaded doublets, but such differences will be not significant and do not need to be compensated for. The pass-band return loss is not preserved, instead, and slight tuning of the couplings is needed to recover it.
Cascade of TM dual-mode dielectric-loaded cavities. Connection through a thick iris (a) and its equivalent coupling scheme (b). Connection through a thin iris (c) and its equivalent coupling scheme (d).
C) Implement the topology by using TM dielectric-loaded cavities
According to Section III, each doublet is realized with a TM dielectric-loaded cavity. NRNs can be realized by thick irises. This leads to a filter composed of cavities cascaded through thick irises, as shown in Fig. 9(a) for a two-cavity filter.
D) Optimization
The structure so obtained is a good starting point for the optimization. During the optimization process it is recommended to reduce the iris thickness in order to obtain shorter filters.
Note that when the irises are thin (Fig. 9(c)), the relevant topology is that of Fig. 9(d) [Reference Guglielmi, Jarry, Keherve, Roquebrun and Schmitt6, Reference Bastioli, Tomassoni and Sorrentino7]. This is due to the fact that thin irises allow the direct coupling between resonant modes of adjacent cavities as well as the direct coupling to filter input and output.
Even though the cavities can be cascaded through coaxial irises, as shown in Fig. 9, only rectangular irises have been taken into consideration in this paper, with the purpose of simplifying the manufacturing process. Furthermore, as explained in the previous section, rectangular irises allow a better control of the position of the transmission zeros in the doublets and, consequently, in the whole filter.
V. RESULTS
A) 4-pole 4-zero filter
The procedure illustrated in the previous section has been applied to the design of the fourth-order filter shown in [Reference Pelliccia, Cacciamani, Tomassoni and Sorrentino16] centered at 4.35 GHz having 3% fractional bandwidth (FBW) with four transmission zeros. According to Step 1 of Section IV, the first doublet has been designed so as to obtain two transmission zeros in the lower stop band. In order to maintain the structure symmetry, first and second doublets are chosen identical. According to Step 2, doublets have been cascaded through NRNs and, after a slight tuning of the couplings, the following coupling matrix has been obtained.
In the coupling matrix, the two cascaded doublets can easily be recognized. The unity elements represent the coupling between the two NRNs. The relevant filtering function is shown in Fig. 10(a). As shown in the figure, two double zeros are obtained, resulting from the cascade of two identical doublets.
fourth-order filter response (S parameters): response from coupling matrix related to Fig. 9(b) (a); comparison among measurement (solid lines), HFSS® simulations (dotted lines) and response from coupling matrix related to Fig. 9(d) (b); in-band IL, comparison between measurement (solid line) and HFSS® simulations (dotted lines) (c); in-band Group-delay, comparison between measurement (solid line) and HFSS® simulations (dotted lines) (d).
Following Step 3, doublets have been realized according to Section III, but replacing one of the two coaxial pins by a rectangular iris. Cavities have then been cascaded through the rectangular (thick) iris.
According to Step 4, the structure obtained has then been optimized obtaining the response of Fig. 10(b). Note that in this response four single zeros in the lower stop band are present. This is due to the fact that during the optimization the thick iris has been forced to become a thin iris, moving from the topology of Fig. 9(b) to that of Fig. 9(d). This topology preserves the number of zeros but does not preserve their positions, leading to a separation of the double zeros.
In Fig. 10(b) simulated results (HFSS) have been compared to measured results, showing very good agreement. Figs 10(c) and 10(d) show the comparison in terms of in-band IL and Group Delay.
The HFSS® model and a picture of the fabricated filter are shown in Fig. 11. The filter size is 40 × 40 × 12 mm3 without including the input/output SMA connectors. The cavity length is 5 mm. Aluminum is used as the metal and the dielectric material is NGK/NTK-F31 (ε r = 34 and tanδ = 5 × 10−5) [18].
HFSS® model and two picture of the measured prototype of a fourth-order band-pass filter at 4.35 GHz [Reference Pelliccia, Cacciamani, Tomassoni and Sorrentino17].
The in-band measurements show a Return Loss (RL) better than 14 dB and an IL of 0.38 dB. Tuning screws (shown in Fig. 11) have been used to tune the filter response to compensate for manufacturing tolerances. The tuning screws placed as in Fig. 11 can provide a maximum frequency shift of 30 MHz (<1%) of each mode frequency. They are placed out of the dielectric cylinders, orthogonally along the side walls, two for each cavity (i.e. one for each resonant TM mode of the filter).
The measured unloaded Q is 1750, i.e. roughly 60% of the simulated one. Such a decrease is ascribed to the loose contacts in the connections between the different filter blocks (Fig. 11) of this first prototype. The Q is expected to increase up to 3000 by silver-plating the metallic surfaces. Measurements over temperature variation from 20°C up to 70°C showed negligible changes of the filter response, while the theoretical maximum RF input power that can be handled by the filter is 700 W. This value has been calculated using the formula presented in [Reference Schettini19] and is an estimate at environmental conditions (1 atm and 20°C). Such a theoretical analysis will be validated in the future by experimental results.
The relative spurious-free range is ~40% for the lower stop band and ~25% for the upper stop band. The transmission spike at 2.5 GHz is due to input/output couplings and inter-cavity coupling of the TM110 resonant mode. The upper frequency transmission spikes at 6.3 GHz are due, instead, to the couplings of the first higher-order cavity modes, while the spike at 5.5 GHz is ascribed to the first resonance of the coupling slot. The slot is placed between the dielectric cylinders and because of the high permittivity (ε r = 34) the λ/2 transverse resonance of the slot is very close to the filter pass-band.
B) Improving the spurious-free range
A possible way to increase the upper spurious-free range is described here. In the right-hand side of Fig. 12 an alternative HFSS® design of a fourth-order filter is proposed: the coupling slot, properly re-sized, is partially placed out of the dielectric cylinders so as to avoid its resonance below 6 GHz. If the slot is placed out of the dielectric, the λ/2 transverse resonance of the slot is moved away from 5.5 GHz. As shown in the graph of Fig. 12, the slot resonance below 6.25 GHz is avoided in the second design (dotted lines). In this way, the new upper relative spurious-free range is increased to ~43%.
Alternative HFSS® design (right-hand side and dotted lines) to increase the upper stop-band in the case of a fourth-order filter at 4.35 GHz. Solid lines refer to the filter of Fig. 11.
C) Shifting the filter response
In this section, a simple way to shift in frequency the response of a filter based on TM dual-mode dielectric-loaded cavities is proposed. The fourth-order filter prototype presented above is used as an example.
Using full-wave simulations, it can be shown that in the interval ε r = 25–50 the filter response remains practically unchanged except for a frequency shift from +750 MHz (+17%) to −720 MHz (−16.5%), as shown in Fig. 13. The FBW change is indeed <± 6% and the RL response remains still above 11 dB.
HFSS-simulated responses (S parameters) of the same filter enclosure model are shown in Fig. 11, using different cylinders of different dielectric permittivity (ε r = 34: solid lines; ε r = 50: dotted lines; and ε r = 25: dashed lines).
The invariance of the shape of the filter response over the variation of the relative permittivity is due to the electromagnetic field in the cavity being mainly confined within the dielectric cylinder, so that the filter enclosure only slightly affects the resonant frequencies and the filter couplings. Tuning screws, already present in the filter case, can be used to adjust the filter response after tuning when it is necessary.
This behavior has been experimentally verified by simply replacing the dielectric cylinders of the filter of Fig. 11 with another of same size (d = 10 mm, l = 5 mm), but different ε r. As shown in Fig. 14, by increasing the relative permittivity from 34 to 45, the shape of filter response and its FBW are almost unchanged, while the pass-band is downshifted by more than 500 MHz (11.5%). The dielectric materials are NGK/NTK -F31 and -E43 (tanδ = 5 × 10−5) [18] and the tuning screws are in the same position in both the measurements.
Measured responses (S parameters) of the same filter fabricated enclosure are shown in Fig. 11, using different cylinders of different dielectric permittivity (ε r = 34: solid lines; ε r = 45: dotted lines).
The proposed ultra-compact pseudo-elliptic filters and their simple mechanical tunability, can provide significant benefits in saving design effort, manufacturing time, and cost in those telecommunication front-end applications where several band-pass filters with similar response but shifted frequency are required (e.g. in multiplexer systems).
VI. CONCLUSIONS
A new ultra-compact pseudo-elliptic waveguide filter using TM dual-mode dielectric-loaded cavities has been presented in detail to achieve Nth-order filtering functions with symmetric or asymmetric positioning of N transmission zeros. Each TM dual-mode dielectric-loaded cavity provides two transmission poles and two transmission zeros. Higher-order filters can be realized by cascading several cavities and coupling such cavities using slots. Up to 50% volume saving is achievable compared to a coaxial comb-line filter of the same order.
The experimental results of a fourth-order filter at 4.35 GHz (3% FBW) with four transmission zeros below the pass-band have been analyzed. A 73% linear size reduction, corresponding to more than 90% volume saving, is obtained compared to an equivalent filters using empty TM cavities, while the Q decrease is only 15%. Furthermore, a strategy to increase the upper stop-band has been illustrated. Finally, reconfigurability properties of the filter have been experimentally demonstrated obtaining a frequency shift of about 11% just by changing the dielectric cylinder material (i.e. the relative permittivity) without changing the filter enclosure.
Luca Pelliccia was born in Foligno, Italy, in 1984. He received the Master Laurea degree (with distinction) in Electronic Engineering from the University of Perugia, Italy, in April 2009. In 2008–2009, he carried out his master thesis research in Ericsson AB, Mölndal (Sweden), where he was involved with the design of innovative concepts of waveguide filters for microwave applications at E-band frequencies (71–86 GHz). In May 2009, he joined the Department of Electronic and Information Engineering of the University of Perugia. His research activities include the development and design of new solutions for high-Q tunable filters, micro-machined filters and miniaturized waveguide filters and diplexers. His research involvement has resulted in the publication of several papers. In November 2012, he received his Ph.D. degree under the advice of Prof. Roberto Sorrentino. He is currently working at RF Microtech (Perugia) as a microwave engineer.
Fabrizio Cacciamani was born in San Benedetto del Tronto, Italy, in 1981. He received the Master Laurea degree in electronic engineering from the University of Perugia, Italy, in 2009. In February 2010, he joined the Department of Electronic and Information Engineering (DIEI) of University of Perugia (Italy) under the advice of Prof. Roberto Sorrentino. His research activities include: development and design of reflectarray antennas radiating element and microwave filters. For the last 3 years, he has collaborated with RF Microtech (spin-off of Perugia University, Italy) in several international research projects concerning RF MEMS, microwave band-pass filter and antenna design.
Cristiano Tomassoni received the Laurea degree and Ph.D. degree in electronics engineering from the University of Perugia, Italy, in 1996 and 1999, respectively. His dissertation concerned the mode-matching analysis of discontinuities involving elliptical waveguides. In 1999, he was a Visiting Scientist with the Lehrstuhl für Hochfrequenztechnik, Technical University of Munich, Germany. From 2000 to 2007 he was a postdoctoral research associate with the University of Perugia. In 2001, he was a Guest Professor with the Fakultät für Elektrotechnik und Informationstechnik, Otto-von-Guericke University, Magdeburg, Germany. Since 2007 he is an assistant professor with the University of Perugia, Italy. His main area of research concerns with the modeling and design of waveguide devices and antennas and the development of reduced-size cavity filters, reconfigurable filters, and printed reconfigurable antenna arrays. He was the recipient of the 2012 Microwave Prize presented by the IEEE Microwave Theory and Technique Society (IEEE MTT-S).
Roberto Sorrentino is a Professor at the University of Perugia, Italy. His research activity deals with the analysis and design of microwave and millimeter-wave circuits and antennas. He is the author or co-author of more than 150 technical papers in international journals, 300 refereed conference papers and three books. Roberto Sorrentino is an IEEE Fellow (1990), recipient of the MTT-S Meritorious Service Award (1994), the IEEE Third Millennium Medal (2000), Distinguished Educator Award from IEEE MTT-S (2004). He was the Editor-in-Chief of the IEEE Microwave and Guided Wave Letters (1995–1998) and was among the founders and President of the European Microwave Association (1998–2009).
