диафрагмированные волноводные фильтры / abc3d3e2-3942-486d-896a-577c69d494fa

I. INTRODUCTION

Microwave and millimeter-wave communication systems are expanding rapidly as they offer many advantages over conventional wireless links. They allow the use of wideband radio links suitable for inter-satellite and personal communications. Commercially available systems are under development at 80 GHz. Commercial systems demand high yield and the ability to fabricate large volumes of devices using low cost techniques. One of the major limiting components of millimeter-wave communication systems is the transmit/receive diplexer. This is often implemented in waveguide technology to provide low insertion loss and high channel-to-channel isolation [1]. The more the design frequency increases, the more challenging the accuracy required on the dimensions of the structure becomes.

Such devices are in fact optimized to meet stricter specifications than the required ones, in order to make the design more robust to modeling inaccuracies and fabrication tolerances. A yield analysis is then carried out to estimate the effect of random variations of the physical dimensions. One of the problems often faced at this stage is that the design may be extremely sensitive to such inaccuracies, mostly introduced by milling and galvanic treatment. This in turn requires demanding stricter fabrication

Correspondence to: G. Cannone; e-mail: giandomenico. cannone@siaemic.com

DOI: 10.1002/mmce.20792

Published online 26 December 2013 in Wiley Online Library (wileyonlinelibrary.com).

tolerances, which worsens both the mechanical yield and manufacturing times. This article discusses some practical guidelines applicable to inline diplexers and based on physical considerations concerning the realized structure aimed at addressing sensitivity issues during the design phase.

II. DESIGN WORKFLOW

Thanks to the efficiency of the existing available mathematical tools, the design of waveguide diplexers is nowadays a straightforward process. In our experience, the two filters are usually synthesized as stand-alone components from the ideal Chebychev response, translated to waveguide components (cavities and irises/septa) and optimized to meet the specifications in the filter passband. Local optimization techniques (Nelder–Mead or other simplexbased methods [2]) usually achieve acceptable results, as long as the behavior of the waveguide components resembles that of their lumped counterparts, i.e. the frequency range is not extremely wide with respect to the center frequency.

Once the two filters are ready, one introduces the T- junction. It is typically first designed alone via electromagnetic simulations (a mixed approach combining Finite Element Method and Mode Matching is usually employed for its high efficiency [3]), inserting for instance an inputcompensating iris or a rectangular or triangular septum in the middle to improve the return loss in both passbands.

The junction is then connected to the two filters and their reciprocal loading through the provided junction must be taken into account as it heavily affects the

TABLE I Galvanic Treatment Layers

response of the overall diplexer. Two additional lengths of waveguide can be introduced between the junction and the filters and optimized to meet the specifications on the overall response. One of the techniques used to speed-up this procedure is the fictitious reactive loads method, presented in Ref. 4, which allows to carry out the optimization with a closed-form approximation of the two filters. The resulting design is usually a very good starting point for the final optimization of the complete structure.

Sobj11 (fi) denotes henceforth the goal value of the return loss at the common port at a frequency fi. S11(fi, x) is the TE10 reflection coefficient of the structure to optimize as a function of a given set of geometrical dimensions, gathered in the vector x. fBP is here defined as the set of frequencies of the reflection zeros and of the reflection maxima in the passbands of the two filters. The cost function GF(x) is thus defined as

The geometrical dimensions to optimize in x include the lengths of waveguides from the junction and the size of the input iris or septum. The outcome of this common optimization process is the ideal diplexer, which theoretically fulfills the given specifications. To compensate in advance for the effects of fabrication tolerances and approximate modeling, the ideal diplexer should be optimized to fulfill stricter requirements than the actual ones.

III. ROBUSTNESS/SENSITIVITY CONSIDERATIONS

After the optimization, the diplexer is manufactured. The production process inevitably introduces errors on the geometry. Waveguide diplexers are typically realized by milling a block of prime material (usually aluminum) and, as a consequence, are subject to a number of fabrication inaccuracies concerning in first place the expected geometrical dimensions of irises/septa and cavities. Commercially available milling processes offer an accuracy of 60.02 mm. It can be achieved usually with good repeatability, achieving a mechanical yield close to 100% of the manufactured devices. In our experience, a tolerance of 60.01 mm by contrast may not be industrially available and requires ad-hoc treatment of materials and furthermore exhibit a significantly lower mechanical yield. Moreover, when symmetrical inductive irises are used for the two filters, we may incur in symmetry errors affecting the response.

Another aspect of interest is the thickness of the galvanic treatment layer. Typical values for the considered frequency range (71–86 GHz) are shown in Table I. The

galvanic treatment may also be inhomogeneous and thus unpredictably affect the cavities and septa shape.

In our experience, the sensitivity to fabrication tolerances should be taken into account as design time can be reduced by exploiting the considerations in the following paragraphs.

A. Resonators

The relative sensitivity to displacements due to finite accuracy can be reduced by using larger cavities. Since typical cavities are designed as resonators at either full or half wavelength, the former exhibits half the sensitivity of the latter and should therefore be the default choice. The lumped equivalent of a kg transmission line section in an inline filter is approximately a shunt-connected parallel resonator. The simplest equivalent lowpass lumped model must thus be devised as a cascade of shunt capacitors and impedance inverters. One of the drawbacks of this choice, however, is that the overall size of the diplexer may increase and that spurious responses may appear below the passbands, which usually does not occur when dealing with kg/2 resonators.

B. Coupling

The choice of coupling types affects the physical size of cavities and the sensitivity, as described in Section IV. The choice of inductive or capacitive coupling is closely related to the slope of the attenuation in the stopbands. In first approximation and without finite transmission zeros, this is controlled mainly by the number of transmission zeros in the origin and at infinity in the lumped bandpass model. The more zeros are in the origin (shunt inductors or series capacitors), the more attenuation in the lower stopband is achieved; by contrast, the more transmission zeros are at infinity (shunt capacitors or series inductors), the more attenuation in the upper stopband is exhibited. For a fixed number of cavities, the repartition of transmission zeros can be controlled as described in Ref. 5.

C. Milling Planes

The technology chosen for the realization of the diplexer affects the milling process, which is typically articulated on different milling planes. The cutter executes a pass in a given plane by removing material along the axis normal to it. Then the piece is rotated to perform milling on a different plane; opposite faces must moreover be milled as different planes. Manufacturing times and displacement errors increase with the number of different milling planes and therefore their number must be kept to a minimum. The practical effects of this are seen in the choice of the junction: an E-plane junction lies on a plane orthogonal to the transverse direction of the ports (see Section IV.A) and requires thus at least one milling plane for the filter structure and another one for the ports. Furthermore, the channel ports require E-plane bends which must be approximated by milled steps. By contrast, an H-plane junction is preferable, as it lies entirely on a plane parallel to the transverse direction of the common port and

therefore only one milling plane is needed. The bends for the channel ports can be precisely milled on the same plane.

D. Milling Depth

Removal of material to create deep shapes may expose the cutter to rupture, due to its small radius. To avoid such an undesirable occurrence, these situations must be dealt with by successive milling passes, each deepening the previous cut, until the desired depth is reached. As evident, this also negatively affects manufacturing times and therefore should be avoided when possible. A typical example of such a necessity is the milling of through-holes for ports in the case of an E-plane junction, which must cut through the whole thickness of the metal base or of the diplexer lid. By converse, a diplexer with an H-plane junction allows milling ports without any through-holes, thus avoiding these deep carves in the prime material.

E. Body-Lid Contact

In order to avoid leakage of microwave or millimeterwave radiation due to a defective contact between the main body of the diplexer and its metal lid, one should typically place the tightening screws in the immediate vicinity of the waveguides. To improve the accuracy of this contact, a narrow (0.1 mm) trench should be cut in the main body following the perimeter of the waveguides.

IV. DESIGN COMPARISON

A set of specifications for a tuning-less E-band diplexer is given in Table II. All the ports are in WR12 waveguides (3.099 mm by 1.549 mm) in TE10 mode. In Section IV.A, a first diplexer has been designed on these specifications with an E-plane junction by following the standard design workflow described in Section II and without specifically addressing the issue of sensitivity to fabrication tolerances. Despite the expected response fulfills the specifications, the manufactured devices (with accuracy of 60.02 mm) exhibit a poor yield. A second design is next discussed in Section IV.B with an H-plane junction and the other considerations discussed in Section III. Manufacturing here has the same tolerance of the previous design, nevertheless this case shows a much higher yield.

The electromagnetic simulations have been carried out by means of Mician Microwave Wizard and Ansoft HFSS. All irises and septa have a thickness of 0.5 mm and both designs are milled with a 0.1-mm deep trench for the closing screws.

Figure 1 Simulated response of the E-plane diplexer.

A. Traditional E-Plane Junction Diplexer

The two filters have been synthesized with the traditional choice of kg0/2 resonators coupled through inductive irises. We chose the symmetric version of inductive irises in order to suppress the TE20 mode and any related spurious response.

The number of required cavities in this setting for the upper-channel filter is found to be 6. Although specifications for the two channels are practically symmetrical, the lower-channel filter is found to demand at least 8 cavities in order to provide the expected rejection in its upper stopband. This asymmetrical number of cavities is to be interpreted as a consequence of the choice of inductive coupling for both filters, as also proven by the example in Section IV.B. The two filters are optimized as stand-alone components to meet the relevant specifications. An E-plane T-junction is chosen to connect the two filters. By using the fictitious reactive loads method, it is optimized in its waveguide lengths on the channel ports. The overall diplexer is finally optimized by adjusting the first cavities toward the junction and introducing the effect of E-plane bends for the channel ports. This final optimization was aimed at achieving a return loss of 20 dB in both passbands (increased by 6800 MHz on the lower channel and by 61000 MHz on the higher one) obtaining the response depicted in Figure 1. The resulting mechanical structure is shown in Figure 2.

A total of six samples of this diplexer have been fabricated with a cutter radius of 0.5 mm and a manufacturing process guaranteeing 60.02 mm of milling accuracy. Their insertion loss is shown in Figure 3, where none of the curves fulfill the specifications, with a measured yield of 0% (the simulated yield over 5000 samples is 14%), which is clearly insufficient for industrial applications. With respect to the final optimization return loss target (20 dB), both filters show a peak difference of more than 10 dB in their passband.

B. Improved H-Plane Junction Diplexer

A second diplexer has been designed by facing sensitivity issues from the first step of the design. The two filters are in fact based on full wavelength resonators and the choice of coupling is aimed at improving the isolation slope

between the two passbands: the lower filter employs capacitive septa (allowing to reduce to seven cavities) whereas the upper one uses asymmetrical inductive irises (the cavities remains six).

Next we choose an H-plane junction, so to reduce the number of milling planes, avoid through-holes for the ports, and permit the precise in-plane realization of bends toward channel ports. The junction is optimized with the fictitious load method and the final overall diplexer is then adjusted to obtain 25 dB of return loss in the passbands, a slightly higher value compared to the target used for the E-plane diplexer. Its response and structure are shown respectively in Figures 4 and 5.

This diplexer has been realized in 10 samples, with a mechanical tolerance of 60.02 mm, the same used for the diplexer in Section IV.A. The measured return loss is plotted superimposed in Figure 6, which shows that the number of traces fulfilling all the specifications is 9, which corresponds to a yield of 90% (the simulated yield is actually 87.7% over 5000 samples), now an acceptable for industrial applications.

Moreover, the peak differences of return loss with respect to the target of the optimization can be evaluated

Figure 5 H-plane diplexer structure and picture (lid removed).

as 10 dB for the lower filter (with kg0/2 resonators) and as 5 dB for the upper one (with kg0 resonators).

V. CONCLUSIONS

In order to mitigate the effect of fabrication tolerances on the design of inline E-band waveguide diplexers (71–86

512 Cannone and Oldoni

GHz), we presented some simple considerations concerning the key elements in the design of such devices: resonators type, coupling, and T-junction model. These provide easy rules to support the designer in the choice of technology and components.

An E-band diplexer has been designed by following the discussed considerations and was found, via a number of fabricated samples and electromagnetic simulations, to have a much higher yield with respect to a traditional design, and may thus allow for a cheaper manufacturing process.

ACKNOWLEDGMENTS

Authors wish to thank their supervisors D. Tresoldi and P. Coassini for the support and the suggestions provided to this work. G. Cannone also wishes to extend his gratitude to J.M. Rebollar Machain, C. A. Leal Sevillano, R. Urciuoli, and P. Umeton for the precious skills they conveyed.

REFERENCES

1.Y. Rong, H.-W. Yao, K.A. Zaki, and T.G. Dolan, Millimeterwave Ka-band H-plane diplexers and multiplexers, IEEE Trans Microwave Theory Tech 47 (1999), 2325–2330.

2.J.C. Lagarias, J.A. Reeds, M.H. Wright, and P.E. Wright, Convergence properties of the Nelder–Mead simplex method in low dimensions, Siam J. Optim 9 (1998), 112–147.

3.R. Beyer and F. Arndt, The general scattering matrix separation technique combined with the MM/FE method for the efficient analysis of a comprehensive class of 3D passive waveguide circuits, MTT-S International Microwave Symposium Digest, Orlando, 1995, pp. 277–280.

4.J. R. Montejo-Garai, J.A. Ruiz-Cruz, and J.M. Rebollar, Fullwave design of H-plane contiguous manifold output multiplexers using the fictitious reactive load concept, IEEE Trans Microwave Theory Tech 53 (2005). pp. 2628–2632.

5.G. Macchiarella, M. Oldoni, S. Amari, and F. Seyfert, Synthesis of microwave filters with “reactive” nodes, Proceedings of European Microwave Conference, EuMC 2012, Amsterdam 2012, pp. 467–470.

BIOGRAPHIES

Giandomenico Cannone was born in Bari, Italy, in 1984. He received the M.Sc in Telecommunications Engineering at the Politecnico di Milano, Italy, in July 2009 with a thesis on the design of microwave diplexers for satellite applications with Universidad Politecnica de Madrid (ETSIT). He is currently working as Microwave Engineer at SIAE Microelettronica S.p.A and his activ-

ity is related to the development of waveguide diplexers, hybrid couplers, orthomode transducers and antennae measurement and construction.

Matteo Oldoni was born in Milan, Italy, in 1984 and obtained his B.Sc. degree in Telecommunications Engineering in 2006 from the Politecnico di Milano, Milan, Italy and his M. Sc. Degree in 2009 from the same Polytechnic with a thesis on the synthesis of microwave lossy filters. He received his PhD in Information Technology with a thesis on the design of microwave filters. He is

currently working at SIAE Microelettronica S.p.A and his activities deal mainly with filters synthesis, design and tuning algorithms and numerical methods applied to electromagnetics.