диафрагмированные волноводные фильтры / 6d82ecc2-96fb-4b99-a7bf-267e3244082f

Abstract—A new -plane filtering structure suitable for very high-power telecom satellite applications is presented. The conceived configuration exploits the design flexibility provided by cascading highly integrated step/stub resonators with pseudoelliptic frequency responses. Several design examples of filters and diplexers in Ku-, K-, and Q-band are reported and supported by experimental tests campaigns. The components have been designed with a full-wave 2-D spectral element method. Prototypes have been realized in aluminum clam-shell technology. Excellent agreement between the models and the experimental results has been achieved. An alternative manufacturing of the proposed architecture based on the selective laser melting technology is also reported. The attractiveness of the structure in view of this emerging additive manufacturing solution is demonstrated. The main advantages of the proposed filter configuration suitable for components operated in heavily loaded multi-carrier environment are: compact design, very low losses, high rejection, and high power-handling capability.

Index Terms—Additive manufacturing (AM), diplexer, -plane resonator, high power, low-pass filter, multipactor, selective laser melting (SLM), stopband filter.

I. INTRODUCTION

AN INCREASING number of services are currently being accommodated into a single antenna feed-system on

board of telecommunication satellites. Examples are commercial payloads for fixed satellite services (FSS) and broadcast satellite services (BSS) working in the Ku/K-bands [1], [2], and dual-use telecommunication payloads working in K/Ka/EHF bands [3]. Due to their resonant characteristics, filters are usually the most limiting elements in a multiple-band feed-system operated in multiple carrier conditions, owing to their susceptibility to multipaction discharge and passive intermodulation (PIM) products. Although several structures and manufacturing technologies can be used in the design of filters [4], stopband

Manuscript received February 27, 2015; revised June 19, 2015 and July 22, 2015; accepted July 23, 2015.

O.A. Peverini, G. Addamo, R. Tascone, and G. Virone are with the Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni, National Research Council of Italy, Turin 10129, Italy (e-mail: oscar.peverini@ieiit.cnr.it).

P.Cecchiniand R. Mizzoniare with Thales-AleniaSpaceItalia, Rome00131, Italy.

F.Calignano, E. P. Ambrosio, D. Manfredi, and P. Fino are with the Istituto Italiano di Tecnologia, Center for Space Human Robotics, Turin 10129, Italy.

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2015.2462839

structures based on the inline connection of resonators are considered to be optimal candidates in these applications, being characterized by compact size, high power-handling, low insertion losses, and high rejection [5], [6]. Despite this, the interaction between the resonators through higher order modes and small size of the resonator apertures still limit the power handling and the bandwidth of these architectures. This paper presents an advanced configuration of -plane filters consisting of composite step/stub resonators that are directly connected one to each other (Section II-A). The main advantage of the proposed architecture is the maximization of the “frequency distance” product , i.e., maximization of the minimum gap between metallic walls where a high RF field is present. This parameter is directly proportional to the multipaction threshold power level [7]. On the basis of the proposed filter topology, diplexers are designed by connecting Tx and Rx filters through an -plane stepped bifurcation (Section II-B). High-power characteristics of the proposed topology are analyzed and compared with both well-established and novel filter configurations aimed at satellite communications (Section III). Detailed comparison between simulated and measured performance are reported in Section IV for several prototypes of filters and diplexers working in the Ku-, K-, and Q-bands. The prototypes have been built in a clam-shell configuration via milling manufacturing. Additionally, the applicability of the present filter architecture to additive manufacturing (AM) has been investigated for Ku/K-band applications (Section IV-A).

II. COMPONENT TOPOLOGY

Stopband -plane filters based on the inline connection of the resonators through phase shifters are expected to be less sensitive to manufacturing errors than those exploiting a high number of cross-couplings [8]–[10]. Usually, each phase shifter is implemented by inserting a waveguide length between two adjacent resonators placed along the same side of the waveguide. However, the resultant architecture gives rise to a strong interaction between the resonators through the higher order modes that significantly worsens the rejection of the filter. This drawback is commonly overcome by using either waveguide sections with reduced height [4] and/or increased length (with an additional half-wavelength) [9] or symmetric stubs. Any of these solutions can limit filter performances either in terms of power handling, losses, or rejection. Higher order mode interaction between the resonators can be largely reduced by alternating the position of the resonators along the upper and lower sides of the main waveguide [11], [12]. Fig. 1(a) shows

Fig. 1. Longitudinal cross sections of -plane filters based on the inline connection of composite step/stub resonators alternated along the upper and lower sides of the main waveguide channel. Critical gaps for power handling are denoted by . The red dashed–dotted lines indicate the reference planes of themain waveguide channel and of the resonators. (a) Layout with resonators spaced by waveguide lengths . (b) Layout with resonators directly connected.

the longitudinal cross section of an -plane stopband filter based on this arrangement. In the present architecture, each resonator has aperture and height . The internal corners and the sharp edges can be rounded by radii and , respectively. The resonator center can be shifted along the vertical direction with respect to the main waveguide axis by the quantity . A composite stub/step discontinuity is achieved when . This type of discontinuity combines the resonant behavior of stubs with the wideband characteristics of steps, providing higher rejection levels and design flexibility. Indeed, by varying and , it is possible to place a reflection zero at in the passband and a transmission zero at

in the stopband. The design flexibility provided by the composite step/stub architecture of resonators can be further exploited to achieve the phase-matching condition necessary in the cascade of the resonators without inserting additional waveguide lengths. The resultant topology of the proposed filters (i.e., without waveguide lengths and coupling elements, as in [9] and [11]) is clarified in the layout shown in Fig. 1(b). In order to increase the power-handling capability of the filter, a very low voltage standing-wave ratio (VSWR) is needed together with the maximization of the minimum gap where a high RF field is present. Since the phase shift introduced by the waveguide lengths are integrated in the resonator apertures , larger gaps between metallic walls are achieved, enhancing the power-handling capability of the filter.

A. Filters

The design of inline filters exhibiting pseudo-elliptical responses with real transmission zeros can be carried out by analytical synthesis techniques based on equivalent circuit models for the fundamental mode [9], [13], [14]. However,

depending on the filter topology, the filter response can be significantly degraded by spurious multi-mode interaction between the resonators. The filter performance are, hence, recovered by either optimizing the synthesized structure [14] or increasing the lengths between the resonators [9]. Alternatively, filter designs can be carried out by means of optimization procedures based, for instance, on the space-mapping technique [15], [16] or through analytical gradient calculation [17]. Although optimization-based design procedures can be limited by numerical cost and the occurrence of local minima, they are to be preferred when geometrical constraints (e.g., minimum gap between metallic walls) and filter topology have to be strictly enforced, and when the fundamental-mode equivalent circuit provides a poor representation of the actual filter response caused by higher order mode interaction and frequency dispersion. For these reasons, the design of the proposed filter is carried out via a minimax gradient-based technique. To this end, the component frequency response is computed by means of a 2-D spectral-element method implementing a model-order reduction technique [18]. For all the results reported in the paper, the reduced-order model is evaluated by performing the full-wave analysis at 5–10 frequency points, yielding to a very fast evaluation of the filter response (in the order of few seconds). For this reason, a coarse model of the filter (as in the space-mapping technique) is not needed. Instead, the rational multi-port model of the filter fundamental-mode scattering matrix

(1)

is derived by means of the pole-relocating vector-fitting tech-

coefficient matrices of the first-order polynomial direct term in the complex angular frequency . This model provides

the reflection and transmission zeros of the filter response that are controlled in the geometry optimization procedure.

1) Initial Design: For sake of clearness, the design procedure is described by considering a fourth-order low-pass filter

, and a corresponding transition band of 10%. The design starts with the definition of a filter geometry based on the topology shown in Fig. 1(a). For parametric design purposes, Fig. 2 reports the contour maps of the resonator

of the normalized transmission-zero frequency and re- flection-zero frequency for a low-pass filter design in standard waveguide with and . Since each resonator can be designed to exhibit a reflection zero close or inside the passband, the port matching of the entire filter is facilitated and lower VSWR is achieved. A convenient choice consists ofidenticalresonatorsalternated along thewaveguide sides that exhibit normalized transmission zeros at the middle frequency of the stopband , and normalized re-

flection zeros at the middle frequency of the passband ( to 0.875). According to Fig. 2, the height and center shift of each

Fig. 2. Contour maps of the resonator normalized: (a)

(b) center shift as a function of the normalized frequency and reflection-zero frequency

design. Other resonator parameters: , , and .

Fig. 4. Simulated parameter of two fourth-order low-pass filters consisting of identical step/stub resonators equally spaced by . The geometry of the step/stub resonators is reported in Fig. 3. Blue marks: configuration with resonators arranged along the same side of the waveguide channel. Red marks: configuration with resonators alternated along the upper and lower sides of the main waveguide channel [see Fig. 1(a)]. Black marks: both filter configurations when only the fundamental mode is considered in the interaction between the resonators. The red and blue vertical bars indicate the passband normalized passband and stopband .

Fig. 3. Simulated parameter of a single resonator in standard rectangular waveguide with , , , , and . Blue solid line: composite step/stub resonator of the type depicted in Fig. 1(a) with and . Red dashed line: conventional stub resonator aligned with the lower side of the main waveguide and with . The red and blue vertical bars indicate the passband

and stopband .

resonator are and , respectively. Fig. 3 compares the characteristic function of the proposed step/stub resonator with that of a conventional stub resonator aligned along the lower side of the main waveguide and with . The improvement on the resonator response is significant in terms of both the return loss in the passband and the rejection in the stopband.

As a second step, the resonators are connected by means of waveguide lengths equal to . Fig. 4 compares the characteristic function of the resultant filter when the step/stub resonators are arranged inline both on the same waveguide-channel side (blue marks) and alternated according to Fig. 1(a) (red marks). The black marks in Fig. 4 denote the frequency response of the two configurations when onlythe fundamentalmodeis considered in theinteraction between the resonators. In this case, the same equivalent circuit model applies to both filter configurations. It is evident that the evanescent higher order interaction between the resonators not only severely affects the stopband rejection of the filter with resonators along the same side, but also significantly modifies the frequency response of the filter based on the alternated arrangement of the resonators. The simulated scattering parameters of the latter configuration are shown in Fig. 5(a). The initial design of the filter already exhibits four transmission zeros within the

stopband and a reasonable return loss (20 dB) in the passband. Fig. 5(c) shows the complex frequency-plane position of the reflection zeros (red marks) and transmission zeros (magenta marks) of the corresponding rational model (1).

2) Optimization: The first optimization step consists of improving the initial design without setting any mechanical constraint. By duly considering the position of the reflection and transmission zeros in the cost function used in the optimization procedure, the filter geometry whose frequency response is reportedinFig.5(b)isderived.Itcanbenoticedfrom Fig.5(c)that all the three reflection zeros (blue marks) and all the four transmission zeros (black marks) are real and equally spaced in the passband and stopband, respectively. Moreover, the filter exhibits an additional reflection zero at approximately

since all the resonators have a reflection zero in the interval

. The filter geometrical dimensions are

(2)

Starting from this filter structure, the architecture of Fig. 1(b) with resonators directly coupled is derived by iteratively reducing the waveguide lengths during the op-

timization procedure. The values of the optimum geometrical parameters as a function of the upper bound on the waveguide lengths are reported in Fig. 6.

Finally, in order to maximize the power-handling capability of the component, the filter is optimized with constraints on the minimum gap inside the filter and on the position of the

transmission zeros. Fig. 7 shows the values of the optimum geometrical parameters as a function of the upper bound on the minim gap . If is enforced to be larger than 0.5, the

final geometrical values are

(c)

Fig. 5. Simulated scattering parameters (dashed line) and (solid line) of two fourth-order low-pass filters based on the topology shown in Fig. 1(a). Designs in standard rectangular waveguide with normalized passband

design with geometrical parameters (2). (c) Position of the reflection and transmission zeros in the complex frequency-plane. Red marks: reflection zeros of filter (a). Magenta marks: transmission zeros of filter (a). Blue marks:

reflection zeros of filter (b). Black marks: transmission zeros of filter (b). The red and blue vertical bars indicate the passband and stopband.

The corresponding simulated scattering parameters are shown in Fig. 8(a). It has to be noticed that, due to the mechanical constraints set on the design, not all the reflection zeros and transmission zeros can be placed inside the passband and stopband.

The same design procedure can be adopted in order to obtain the fourth-order high-pass filter with flipped passbands and stopbands exhibiting the scattering parameters shown in Fig. 8(b). The geometrical values are

Fig. 6. Optimum geometrical parameters of the symmetric fourth-order lowpass filter as a function of the upper bound on the waveguide lengths (see Fig. 1). Red marks: parameters of the outer resonators (cavities). Blue marks: parameters of inner resonators (cavity).

Since -plane discontinuities are less selective at lower frequencies, wider resonators have to be used in order to achieve a rejection level 35 dB. Hence, the constraint on the minimum

Fig. 7. Optimum geometrical parameters of the symmetric fourth-order lowpass filter as a function of the upper bound on the minim gap (see Fig. 1). Red marks: parameters of the outer resonators (cavities). Blue marks: parameters of inner resonators (cavity).

Fig. 8. Simulated scattering parameters (red dashed line) and (blue solid line) of the lowand high-pass fourth-order filters based on the topology with resonators directly coupled [see Fig. 1(b)]. Final configurations with constraint on minimum gap between metallic walls . (a) Low-pass filter

(3). (b) High-pass filter (4). The red and blue vertical bars indicate the passband and stopband.

Fig. 9. -plane stepped bifurcation used in the diplexers. (a) Longitudinal cross section. (b) Simulated scattering coefficients (black solid line), (red dotted–dashed line), and (blue dashed line) of a normalized design in standard rectangular waveguide.

III. HIGH-POWER BEHAVIOR

gap does not affect the design, and all the transmission zeros and reflection zeros can be placed inside the stopband and passband, respectively.

B. Diplexers

Diplexers consist of a couple of low and high stopband filters that are combined at the common port 1 by means of the stepped bifurcation shown in Fig. 9(a). This junction also provides the necessary clearance between the two filter ports 2 and 3 that are lying in the same longitudinal position and are separated by a gap . In order to facilitate the frequency separation between the

two channels, an asymmetrical architecture is exploited where the bifurcation axis can be vertically shifted with respect to the axis of the input port 1 by a quantity . As an example of the electrical performance achievable by means of this junction, Fig. 9(b), shows the scattering parameters , , and

corresponding to a normalized design in standard waveguide

In the diplexer design, the filters and the junction are designed independently, and subsequently, integrated together. Finally, theresultantstructureisiterativelyoptimized by modifying both the junction and the filters.

In the design stage of the present filter configuration, the maximum single-carrier input power for which the multipactor risk becomes significant is evaluated on the basis of the parallel-plate model (PPM). Although this model proves to be very conservative for waveguide structures with large gaps [22], it can be used to identify the critical regions to be controlled during the design. According to the procedure summarized in [23]–[25], the input power threshold in each gap and frequency is computed as

(5)

where is the peak voltage threshold derived from the surface material susceptibility curves [26], is the input waveguide impedance, and the voltage magnification factor (VMF) is defined as the ratio between the electric field integral across the gap and the incident voltage. Once the minimum value has been determined, the maximum input power per carrier in the multi-carrier condition is derived according to the 20-gap-crossing-rule recommended by the European Space Agency [27].

A. Ku-Band Low-Pass Filter

In order to assess the applicability of the present filter configuration to high-power satellite applications, an eight-order Ku-band low-pass filter based on the layout shown in Fig. 1(b) has been designed targeting a return-loss value of 30 dB in the Tx passband (10.95, 12.75) GHz and a rejection

Fig. 10. Simulated scattering parameters (red dashed line) and (blue solid line) of the Ku-band eight-order filters based on the present topology. (a) Ku-band low-pass filter (6). (b) Ku/K-band stopband filter (7). The black and marks denote the spurious cross-transmissions from the mode at port 1 to the modes at port 2, respectively. The red and blue vertical bars indicate the passband and stopband.

level of 70 dB in the stopband (13.75, 17.7) GHz. The geometrical values of the filter designed in standard WR75 rectangular waveguide are

mm

mm

Similarly to [28], the insertion loss and power-handling capability of the component have been further enhanced by rounding all the sharp edges by mm, apart from the outer ones for which mm (because of geometrical reasons). With reference to Fig. 1(b), no rounding of the internal stub corners is assumed . The corresponding simulated scattering parameters are shown in Fig. 10(a). The filter provides a spurious-free range up to approximately 17.5 GHz corresponding to the cutoff frequency in the WR75 waveguide of the excited by the filter discontinuities. Fig. 11 shows the single-carrier input power threshold as a function of the passband frequency computed according to the PPM (blue marks). The values reported refer to a silver-plated surface. The worst case input power threshold is 14.6 kW (71.6 dBm) at 12.75 GHz. The corresponding critical region is located in the initial part of the second stub where the VMF is approximately 1.4. Since GHz mm, the gap can take up to a 5.1887-V peak threshold

Fig. 11. Input power threshold of the Ku-band eight-order filters based on the present topology. Computations performed with the PPM. Blue marks: Ku-band low-pass filter (6). Red marks: Ku/K-band stopband filter (7).

voltage. The input breakdown power is approximately 10.8 kW for the same filter configuration without sharp-edges rounding.

As highlighted in [22], the PPM provides very conservative input power thresholds for filters with large gaps (high multipactor orders) and smooth profiles. Hence, a more accurate multipaction analysis has been carried out by means of the particle-in-cell (PIC) algorithm that considers the electric field distribution and the dynamic evolution of the electrons inside the component. The analysis has been carried out at the passband frequencies 10.95, 11.85, and 12.75 GHz on the entire filter and in the most critical regions with the software tool Spark3D in conjunction with CST Microwave Studio for the electric field computation. The statistical Spark3D simulations have been repeated several times with a number of electrons ranging from 1000 to 20000, resulting in an input power threshold of 83.7 dBm. This very high value corresponds to the input power threshold computed by Spark3D for the input WR75 waveguide at 10.95 GHz, and is approximately 12 dB higher that the value provided by the PPM model. Similar large deviations between the two models have been reported in [22] for the smooth-wall structures listed in Table I, where the main characteristics of the present configuration are compared with those of both well-established and novel filter topologies aimed at satellite communication. Although the present Ku-band filter design does not exhibit a rejection band as wide as those of the filter designs reported in [28] and [29], it provides a remarkable enhancement in the power-handling capability with respect to the state-of-the-art listed in Table I. Wider spurious-free rejection bands can be achieved as discussed in Section III-B.

B. Ku/K-Band Stopband Filter

The spurious-free range of low-pass filters can be enlarged by combining corrugated low-pass and stopband filters [30], [31]. These building blocks can be integrated in order to achieve more compact designs, as reported in [32], where both passband and low-pass filters are based on quasi-periodic smooth-profile structures.Thelatterconfigurationcanbemodifiedsotoprovide a spurious-free range with higher order mode suppression [22]. In this perspective, the multipaction analysis of a Ku/K-band eight-order stopband filter based on the topology of Fig. 1(b) has been carried out. The stopband filter has been designed in order to providea return loss valueof30 dB intheTx passband (10.95, 12.75) GHz and a rejection level of 70 dB in the stopband (17.5,

21.5)GHz.A WR75 rectangularwaveguidewith reducedheight mm has been used in order to guarantee rejection also to the modes excited by the resonators. The filter

geometrical values are

mm

mm

All the sharp edges have been rounded by mm, whereas no rounding has been applied to the internal stub corners [see Fig. 1(b)]. The simulated scattering parameters of the filter are shown in Fig. 10(b). The spurious cross-trans- missions from the mode at port 1 to the modes at port 2 are also reported. The direct rejection terms to the modes entering in the device are higher than 100 dB. The input power threshold versus frequency computed with the PPM is reported in Fig. 11 (red marks). Due to the large transition band, the VSWR inside the filter is rather low in all the passband. Consequently, the most critical frequency for power handling is 10.95 GHz (i.e., the lowest value of ). Although a reduced-height waveguide has been adopted in the design, an input power threshold of 21100 W (73.2 dBm) has been achieved. The high-power analyses performed with Spark3D have provided a value of 79.6 dBm, corresponding to the value computed by Spark3D for the breakdown power in the reduced-height input waveguide at 10.95 GHz.

Due to the high values of input power threshold provided by both the low-pass and stopband Ku-band filters, the topology of Fig. 1(b) is applicable to the realization of harmonic filters based on the integration of low-pass and stopband structures with the aim of enlarging the spurious-free range while achieving high power-handling capability. Suppression of can be achieved by varying the broad waveguide side along the filter as described in [22] and [33].

IV. COMPARISON BETWEEN SIMULATED AND

MEASURED RESULTS

Several breadboards of filters and diplexers based on the architectures described in Sections II and III have been designed,

manufactured, and tested in the Ku-, K-, and Q-bands. The electrical performance of the components have been measured at room temperature with a vector network analyzer (VNA) calibrated via the thru-reflect-line (TRL) technique. High-power tests to ascertain PIM capability at ambient and versus temperature have been carried out on the most demanding Ku-band diplexers that support third-order PIM.

A.Filters

1)Q-Band Seventh-Order Filter in Clam-Shell Configuration: On the basis of the architecture shown in Fig. 1(b), a Q-band seventh-order filter in WR22 waveguide has been designed to work in the passband [43.2, 44.7] GHz (3.5%) and stopband [36.5, 42.5] GHz (15.2%). The corresponding transition bandwidth is 1.6%. The geometrical values are

mm

mm

mm

(8)

and the internal corners are rounded with a radius mm. No rounding has been applied to the sharp edges . The prototype has been machined out of 6061 aluminum alloy via milling in the clam-shell configuration shown in Fig. 12, and has been passivated with a Surtec 650 surface treatment. A significant correlation between the simulated and measured scattering parameters can be noticed in Fig. 13. The measured rejection in the stopband is higher than 47 dB, the return loss and insertion loss in the passband are better than 34 and 0.3 dB, respectively.

2) Ku/K-Band Fifth-Order Filter for AM: Compared to traditional machining techniques based on metal removal, AM can provide mono-block realizations of complex RF structures, avoiding the use of bulky flanges and mounting screws. Hence, it is a promising manufacturing solution for the development of compact antenna-feed chains to be used in single-feed-per-beam (SFB) and multi-feed-per-beam (MFB) satellite communication systems [34]. Indeed, AM indicates a wide class of layer-by-layer techniques of producing products directly from a digital model, ranging from fused deposition modeling (FDM) or stereolitography (SLA) for polymeric materials, up to the powder bed based processes like selective

Fig. 12. Photograph of the seventh-order Q-band filter.

Fig. 13. Comparison between simulated (blue solid line) and measured (red dots) scattering coefficients and of the Q-band filter in WR22 waveguide shown in Fig. 12. The red and blue vertical bars indicate the passband and stopband. (a) Wideband response. (b) Detail of the parameter in the passband.

surface roughness, and electrical conductivity. In order to assess their impact on filter performance, a second-order filter in WR51 rectangular waveguide based on the architecture shown in Fig. 1(a) has been designed. This test cavity exhibits a very high VSWR in order to increase the sensitivity of its scattering parameters to metal losses and mechanical uncertainties. Two prototypes of the test cavity with two different alloy powders (i.e., Ti64 and AlSi10Mg) have been built through an EOSINT M270 xtended direct metal laser sintering (DMLS) machine (DMLS is the trade name by EOS GmbH for SLM) [38]. After the building process, the prototypes have undergone a thermal treatment in order to decrease residual stresses typical of this process. Finally, the components have been detached from the building platform, and subjected to a micro shot-peening post processing to reduce surface roughness (as demonstrated in a previous study [39]). A nonlinearbest fitting procedure between the measured and simulated values of the scattering parameters has been adopted to evaluate geometrical errors and the equivalent surface resistivity of the metal walls. The latter is a combination of the bulk resistivity and the surface roughness. It has been assessed that titanium and aluminum samples exhibit comparable dimensional uncertainties in the range [50, 100] m. However, SLM based on Al compound has to be preferred since it provides an equivalent surface resistivity in the range [10, 40] cm. A value of resistivity higher than 200 cm has been measured for the titanium cavity. In addition, Al alloys exhibit several advantages over titanium: lower density, lower cost, and easier post-processing.

On the basis of these experimental results, a Ku/K-band fifthorder filter in WR51 waveguide with resonators directly coupled [see Fig. 1(b)] has been developed [40]. The passband and stopband are [12.5, 15.3] GHz (20.1%) and [17.5, 21.5] GHz (20.5%). The design has been carried out by taking into account SLM mechanical constraints such as edge and corner rounding mm and discrete layer-thickness (30 m). Although edge rounding is not mandatory in SLM parts such as in other traditional processes, they can be used to reduce thermal stress concentrations. Moreover, the sharp edges can not be accurately built due to the large variation in conductive heat transport caused by a change in local part geometry [41]. In order to achieve a robust design with respect to the mechanical uncertainties of the SLM process (0.1 mm for a worst case design for Al alloys), different filter geometries have been designed and subjected to sensitivity statistical analysis. The final filter dimensions are

laser melting (SLM) and electron beam melting (EBM) for metallic materials [35].

In this paper, the applicability of SLM technology to the manufacturing of filters based on the topology of Fig. 1(b) has been investigated. In [36], the same technology has been applied to the manufacturing of passband filters with shaped cavities and irises. SLM presents significant advantages in comparison with traditional manufacturing techniques [37], including near-net- shape capabilities, superior design and geometrical flexibility, reduced tooling, and fixturing. However, its application to the fabrication of waveguide filters is still limited by some technological issues such as manufacturing accuracy, repeatability,

mm

mm

Thanks to the filter architecture and the robust-design approach adopted, the Al-based prototype manufactured via SLM (shown in Fig. 14) exhibits electrical performance in good agreement with the design values, as illustrated in Fig. 15. The measured values of return-loss (30 dB), insertion-loss (0.08 dB), and rejection (41 dB) meet common specifications set in satellite communication applications. It has to be remarked that these performance have been achieved without any part re-machining

(b)

Fig. 15. Comparison between simulated (solid line) and measured (dots) scattering coefficients and of the Ku/K-band fifth-order filter in WR51 waveguide shown in Fig. 14. The red and blue vertical bars indicate the passband and stopband. (a) Wideband response. (b) Detail of the parameter in the passband.

and/or tuning screws. Moreover, the insertion loss figure corresponds to an equivalent surface resistivity of approximately 10 cm that is comparable with the values measured for aluminum parts machined by milling.

B.Diplexers

1)Ku-Band Diplexer: A diplexer in WR75 rectangular waveguide working in the Tx band [10.7, 12.75] GHz and Rx bands [13.0, 13.25] GHz [13.75, 14.5] GHz has been developed. It has to be noticed that the Tx and Rx bands are very closely spaced with a relative transition bandwidth of 1.94% only. Since the output multiplexer inserted in the TX channel provides the required rejection in the transition band, no requirements have been set on the isolation value between the Tx and Rx ports in the transition band. The diplexer consists of a stepped bifurcation of the type shown in Fig. 9(a) and of two filters with seven and nine resonators directly coupled [see Fig. 1(b)] for the Rx and Tx channels, respectively. In the design, rounded internal corners with mm have been considered in order to simplify the manufacturing process. Indeed, this bending-radius value allows the use of relatively large milling tools, thus, reducing the manufacturing errors and costs. Fig. 16 shows the prototype that has been machined out of 6061 aluminum alloy and silver plated. The overall dimensions

of the diplexer are 145 mm 66 mm 38 mm. According to the worst case PPM analysis, the diplexer designed can handle up to kW input power in the single-carrier

condition, or in a multi-carrier operation, it can sustain 14 equally spaced carriers simultaneously applied with a carrier power W dB margin. These power-handling

values have been obtained by controlling the gaps inside the component. The most critical region is the sixth resonator of the Tx filter, where the peak voltage is higher and the VMF

Fig. 17. Comparison between simulated (blue solid line) and measured (red dots) scattering coefficients of the Ku-band diplexer. The red, blue, and green vertical bars indicate the Tx band [10.70,12.75] GHz, Rx1 band [13.00,13.25] GHz, and Rx2 band [13.75,14.50] GHz. (a) Reflection coefficient at the common port 1. (b) Transmission coefficients and from the common port 1 to the Tx port 2 and Rx port 3. (c) Detail of the transmission coefficients and . (d) Transmission coefficient from the Tx port 2 to the Rx port 3.

is approximately 2.5 at the highest cutoff frequency of the Tx band (12.75 GHz). The aperture of this resonator has been enforced to be 9.5 mm wide, resulting into a peak threshold voltage of 7.6 kV.

The electrical performances of the diplexer are summarized in Table II. The diplexer exhibits high levels of isolation

between the two channels, while presenting low values of reflection coefficients, insertion losses, and phase dispersion. The Tx and Rx bands have been widened by more than 50 MHz in order to compensate for frequency shifts due to temperature variations. Fig. 17 shows the comparison between the measured and computed frequency responses. The reflection coefficient at the common port is reported in Fig. 17(a), whereas Fig. 17(b)–(d) shows the transmission coefficients between the three ports. The excellent fitting between measurements and simulations has been obtained also for the other electrical parameters of the diplexer and demonstrates the low sensitivity of the design to manufacturing tolerances. It also validates the SEM code [18] used in the design. It is worth noting that all of the seven transmission zeros of the Rx filter contribute towards the rejection of the filter in the Tx band. This is not the case for the Tx filter due to the constraints enforced to guarantee the required values of power handling, insertion loss, and phase dispersion.

2) Ku-Band Diplexer With Additional Rejection in K Band:

The second diplexer prototype refers to a Ku/K-band architecture designed to separate the Ku-Tx [10.7,11.7]GHzandKu-Rx [13.0, 14.5] GHz, while providing a high rejection (50 dB) in the Rx channel to signals in the K-band [17.7, 21.2] GHz. The rejection applies to the , , , and modes that are above cutoff in the K-band at the Rx WR75-waveguide port. The mode propagating in the K-band is not considered for symmetry reasons of the overall waveguide plumbing of the antenna-feed system. The component consists of the integration of a Ku-diplexer of the type reported in Section IV-B.1, used to separate the Ku-Tx and Ku-Rx bands, with a further Ku-Rx/K-band diplexer. The latter introduces the required rejection in the Rx channel to K-band signals, and provides an additional K-band port that is terminated into a matched load. This arrangement avoids the generation of spurious peaks caused by internal resonances between the filters. The Ku-Rx/K-band diplexer makes use of a stopband filter design similar to that reported in Section III-B. The overall dimensions of the diplexer are almost the same as the Ku-band diplexer, being 145 mm 80 mm 38 mm. The design of the integrated Ku-Rx/K-band diplexer is carried out by defining a total-power transmission coefficient in the K-band from the common port 1 to the Rx port 3. To this end, the singular value decomposition of the generalized multi-mode scattering matrix block is computed, and the highest singular value (as a function of the frequency) is considered as the characteristic function in the definition of