диафрагмированные волноводные фильтры / 3df1a9a0-3a2a-4b1d-915a-3efe92f6202e

Abstract—The experimental 6–8.6-GHz five-pole bandpass filter being presented is composed of ridge-waveguide resonator segments, evanescent-mode inter-resonator coupling sections, and planar-circuit impedance-matching port networks. To reduce overall filter size, cavities are filled with a low-loss moldable dielectric material that does not shrink during curing. Good agreement is observed between measured and predicted filter response characteristics. Two additional bandpass filter designs with different fractional bandwidths further highlight the versatility of the design methodology that relies entirely on the use of commercially available general-purpose design software.

Index Terms—Bandpass filter, evanescent-mode waveguide, high power, injection molding, moldable dielectric, ridge waveguide, waveguide filter.

I. INTRODUCTION

IN MANY military and commercial system designs, the physical realization of small microwave filters with low passband loss and good frequency selectivity remains a persistent concern. Among contending solutions are cavity filters that comprise resonated ridge waveguide sections and evanes- cent-mode inter-resonator coupling segments. Such filters are capable of combining, to a large extent, the low insertion loss, high selectivity, and good power handling of single-con- ductor waveguide structures with the broad spurious-free frequency-band coverage of two-conductor transmission-line circuits, while controlling filter size with the help of dielectric

fill materials.

An efficient design methodology for filters of the mentioned genre was introduced in [1]. Among the convenient features of the technique is its full reliance on commercial general-purpose design software, used in conjunction with semiempirical design equations. The objective of the current study was to project beyond the low-frequency example presented earlier, and to experimentally demonstrate the practicability of the approach also at higher microwave frequencies. The primary challenge was the fabrication of the filter’s compound cavity structure, as internal cross-sectional areas shrunk to only a few square millimeters and necessitated key structural changes. Further illustration of the approach is provided by two supplementary numerical-only filter designs with diverse fractional passband widths. The three contiguous-band examples represent channel-filter designs that,

Manuscript received August 19, 2005; revised November 12, 2005. This work was supported in part by the Office of Naval Research.

The authors are with Code 6850, Naval Research Laboratory, Washington, DC 20375-5347 USA (e-mail: rauscher@ieee.org).

Digital Object Identifier 10.1109/TMTT.2005.864106

following adaptation, are to become part of a triplexer for combining the high-power output signals of three solid-state transmitter amplifiers, spanning 6–18 GHz. To avoid duplication, the reader is pointed to [1] for all nonspecific details of the underlying approach, including the rationale behind the technique, the design process, available implementation options, and a set of literature references to relevant work by others, with two of the references, i.e., [2] and [3], reiterated here for the sake of convenience.

II. FILTER DESIGN

Originally, the 6–8.6-GHz five-pole bandpass filter described below was to be derived from the 1–1.45-GHz bandpass filter presented in [1] through simple frequency scaling by a factor of six. The lower frequency structure, with its relaxed dimensional tolerances, was mainly used to verify the design approach, as this did not require special fabrication techniques. Practical considerations, however, forced the envisioned simple scaling process to be modified. Pertinent changes involved not only cavity aspect ratios, but also dielectric fill materials and matching circuit topologies. Cross-sectional drawings of the resultant filter structure are shown in Fig. 1. As in the past, , , and represent ridge-waveguide width, evanescent-mode-waveguide width, and common waveguide height, respectively, , , and , and and denote respective ridge-waveguide and evanescent-mode-waveguide lengths, refers to ridge width, and refers to ridge gap spacing.

The ratio of waveguide height to waveguide width was chosen to be less than in the lower frequency test case to facilitate the physical implementation of the filter as originally envisioned and discussed later. With the filter’s waveguide ridges to be realized by forming precision blind holes within a solid dielectric core and subsequently metallizing the core from the outside, it was advantageous to minimize the depth of the holes—and, thus, the height of the composite filter structure—to keep mechanical-tolerance-induced aberrations within acceptable bounds. With reference to the evanes- cent-mode coupling-gap model depicted in [1, Fig. 4], and the series-connected stub contained therein and described by [1, eqs. (12)–(15)], the height reduction led to a decrease in the equivalent stub electrical length for each of the filter’s coupling gaps. This shifted the associated transmission nulls, akin to those in [1, Fig. 5], to higher frequencies, partially denying stopband benefits that might have been derived from the presence of such nulls. A resultant slight decrease in obtainable

fractional stopband width proved acceptable, however, while still permitting the filter’s upper stopband to extend to 22 GHz, as specified by the application.

In return, the reduction in waveguide height brought about simpler filter-internal electromagnetic field patterns that translated into enhanced computational efficiency. The fields propagating vertically in a combline-type fashion along the vertical end faces of respective waveguide ridges thus became primarily governed by the fields propagating in the direction of the filter’s main longitudinal axis [1]. This led to a subordinate role for the series-connected stub in the evanescent-mode coupling-gap model.

The experimental filter example presented in [1] pointed to advantages that may be derived from the use of layered dielectric cavity fill materials with substantially different relative dielectric constants. The current filter design might also have theoretically profited therefrom. This option was not pursued, however, due to the small dimensions of the cavity structure and the additional resources that would have been required to implement a composite of multiple dielectric materials. Instead, a single dielectric fill material with a relative dielectric constant of 9.5 was found to offer an acceptable compromise that still allowed the application’s requirements to be met.

Impedance-matching networks are typically used to connect a filter’s ridge-waveguide end resonators to external 50- ports. Planar-circuit configurations offer an effective means for providing both needed impedance transformation and compensation for parasitic reactance effects at transition interfaces. Among the simplest solutions are cascades of strip transmis- sion-line sections with stepped characteristic impedances. In the current filter design, as indicated in Fig. 1, a microstrip format was chosen with pertinent strip widths and lengths

Aside from the mentioned structural details, the design process followed the outline provided in [1]. This included the derivation of equivalent circuits for each of the filter’s main components based on the results of three-dimensional electromagnetic structure simulations, the construction of an equivalent circuit for the composite filter from the derived component equivalent circuits, the equivalent-circuit-based numerical optimization of the filter’s port characteristics, and iterative rounds of refinement that involved convergent reconciliation between results predicted by the electromagnetic structure simulator and results predicted by the filter’s equivalent circuit. The three-dimensional electromagnetic structure analyses were carried out with CST Microwave Studio, which embodies a finite-integral approach, and the linear-circuit analyses and numerical optimizations were performed with AWR Microwave Office, which is a general-purpose microwave design suite. The optimized parameter values thus obtained for the experimental 6–8.6-GHz bandpass filter have been collected in the first numerical column of Table I.

III. FILTER EXPERIMENT

The original idea was to precision machine a replica of the filter’s cavity structure and then use this as a die for casting monolithic filter cores from a moldable dielectric material. All that additionally would have been required, in essence, was to selectively metallize the outer surface of the core and mount it with suitable port transitions on a metal carrier. The approach could provide a cost-effective way to mass-produce miniature high-performance microwave filters. The associated technical challenges that derived from the dielectric core’s small size, its

close tolerances, and its delicate nature, however, would have projected well beyond the scope and available resources of the current assignment. The main shorter term goal thus became simply to demonstrate the practicability of the approach with an experimental proof-of-concept realization of the aforementioned 6–8.6-GHz bandpass filter design.

A first fabrication attempt involved the machining of a filter dielectric core from a slab of magnesium–aluminum–titinate ceramic material in its fully fired state. A laser-based method was initially thought to offer the best chance of success, chosen from a number of contending precision-machining techniques. The most challenging operation, as alluded to earlier, was the machining of blind holes with rectangular cross sections and sharp edges that, following the external metallization of the finished core, would become the filter’s waveguide ridges. The crux was to achieve hole bottoms that were flat and smooth, as these would define critical ridge gap spacings. In the end, despite concerted design efforts to minimize required hole depths, the laser beam could not be focused tightly enough to achieve acceptable bottom surfaces at needed depths in excess of 1 mm.

The approach that was finally taken essentially constituted the inverse of the former, involving wire electric discharge machining to cut the filter’s compound cavity out of solid metal, and using moldable dielectric material as backfill. The structure was actually machined as two separate pieces that were subsequently brazed to form a composite unit. With reference to Fig. 1, the first piece comprised the waveguide cavities’ common roof and the filter’s five stalactite waveguide ridges. The second piece assumed the shape of a frame that defined the

Fig. 2. Filter’s cavity structure, upside down and prior to backfill with moldable dielectric material, together with its carrier plate and positioned port impedance-matching circuits.

Fig. 3. Fully assembled 6–8.6-GHz filter module with a total length of 18.3 mm.

structure’s vertical outer cavity walls. After brazing, the combined unit was plated with 3-m-thick gold, and the flange area at ground-plane level was resurfaced to achieve a consistent 125-m ridge gap spacing, as required. A photograph of the precision-machined structure lying upside down is provided in Fig. 2, together with the module’s carrier plate and temporarily positioned microstrip port matching networks.

The resultant hollow cavity structure was backfilled with Eccostock-CK, a moldable dielectric material made by Emerson & Cuming Microwave Products Inc., Randolph, MA. The material, which was applied at the factory, was specially formulated to exhibit a desired nominal relative dielectric constant of 9.5. Among the material’s attractive attributes for the current application were its stated loss tangent of less than 0.002, and the absence of shrinkage during the curing process. Excess material was lapped off to establish a flat surface at the ground-plane level. Inadvertently, small glass beads contained in the material broke loose during the lapping process, which left behind tiny voids in the surface. This was a consequence of the improvised use of a material that is designed for casting

with a closed mold, where selective reconditioning of critical surfaces is not normally required. In the current situation, the surface voids were simply filled with compatible epoxy-based Eccostock-HiK Cement obtained from the same company.

Next, the backfilled structure was supplied with a conducting ground plane. This was achieved through e-beam evaporation of a 0.015-m-thick adhesion layer of chromium and a 2-m-thick layer of gold, thereby guaranteeing a solid galvanic connection between ground plane and cavity walls. Resonator end faces were masked off during the evaporation process.

The completed cavity structure and small alumina substrates with microstrip port matching circuits were then attached to a common metal carrier, as indicated in Fig. 1. This was accomplished by applying a constant-thickness layer of conductive epoxy to the carrier’s top surface, and then dropping the cavity structure and microstrip substrates in place. For the application of the conductive epoxy, a framed printing screen supplied by SEFAR Printing Solutions Inc., Burnsville, MN, was employed, comprising a mesh of taught stainless steel wires of 0.0011-in diameter, with a density of 325 wires per inch. The microstrip impedance-matching circuits were connected to the external faces of the filter’s end-resonator waveguide ridges with the help of small pieces of angled gold foil that were ultrasonic-wedge bonded to the microstrip end lines and attached with conductive epoxy to the vertical ridge faces, respectively. The fully assembled filter module, depicted in Fig. 3, was mounted in a special test fixture and connected to coaxial 50- subminiature A (SMA) launchers, as shown in Fig. 4. Predicted and measured port characteristics of the ensemble are compared in Fig. 5.

IV. DISCUSSION

Considering the exploratory nature of the filter implementation, and the fact that the structure did not permit any post-fabri- cation adjustments, the observed agreement between measured and predicted results in Fig. 5 is considered very good. This includes the reproduction of resonances within the upper satellite passband. In trying to determine, for the sake of completeness, the origin of minor discrepancies in the vicinity of the main passband, the filter’s equivalent circuit used in the design was reemployed to help pinpoint specific causes. None such could be identified. Instead, it was concluded that general machining

Fig. 5. Measured and predicted responses of the 6–6.8-GHz experimental bandpass filter.

tolerances were the principal culprit. Even though an effort was made to keep mechanical tolerances below 10 m, actual dimensional deviations turned out to be 25–30 m, and randomly distributed. These, together with the test fixture’s stan- dard-issue SMA port connectors that were not accounted for in the calculations, largely explain apparent frequency shifts in filter reflection-coefficient nulls. The small extra hump in the satellite passband was traced to parasitic signal feed-through within the test fixture, not the filter module itself.

Comparing the predicted midpassband transmission loss of 0.6 dB to the measured value of 1.3 dB, it is believed that at least 0.2 dB of the latter can be attributed to the neglected effects of the two SMA connectors. This leaves 0.5 dB to have been caused by the aggregate effects of tolerance-induced shifts in filter characteristic frequencies, imperfect metal surfaces and ridge edges, fabrication-related lower than anticipated metal conductivities, and a ground-plane metallization thickness of only two skin depths at passband frequencies. Recognizing that these issues remain particular to the current proof-of-concept demonstration and the improvised way in which it was performed, and recalling the excellent agreement observed between measurement and prediction in [1], there is little reason to believe that a new filter, implemented as originally envisioned with a reusable precision mold, should not perform almost exactly as predicted.

To further illustrate the approach, the calculated port responses of two additional filter designs with contiguous passbands are given in Figs. 6 and 7, respectively. The associated structural dimensions can be found in Table I. As in the 6–8.6-GHz-passband case, both metal and dielectric losses were included in the calculations, but not the effects of coaxial external connectors. The additional designs also employ a single dielectric material for the sake of expediency.

When contemplating filter configuration options, there is no fundamental prerequisite that the width of the evanes- cent-mode waveguide coupling sections be narrower than the width of adjacent ridge-waveguide segments, as the three design examples might suggest. To substantiate this,

Fig. 6. Calculated response of a 8.6–11-GHz bandpass filter.

Fig. 7. Calculated response of a 11–18-GHz bandpass filter.

numerical designs for five-pole ridge-waveguide filters that did not utilize constrictions in the coupling areas were derived, using the exact same design methodology. Associated performance characteristics were found to be consistent with those of the examples reported here. However, in order to maintain proper inter-resonator coupling, increases in the lengths of the evanescent-mode waveguide sections were required, adding noticeably to the overall length of each filter. In return, respective passband insertion-loss numbers were projected to be slightly lower. Within practical bounds, this offers an opportunity for tradeoffs among filter size, circuit performance, and manufacturing effort. In the cited application, size reduction was an important concern, for which the inclusion of width-constricted coupling areas was indicated.

As for alternative ways of fabricating ridge-waveguide filters designed in accordance with the methodology presented in [1],

low-temperature cofired ceramic (LTCC) processes, such as used in [3], deserve special mention. Such processes are well established and can be quite cost effective. An often-expressed concern, though, relates to the accuracy with which a filter design can be reliably reproduced. The concern is of a compound nature, as it encompasses the necessity to dependably predict the amount of substantial shrinkage that occurs during the firing of the material, deal with a degree of uncertainty surrounding the exact value of the fired material’s dielectric constant, and accommodate relatively large fabrication tolerances on the placement of via-holes. This last issue can pose a particular problem when using arrays of vertical via-holes in conjunction with buried conductive strips to approximate waveguide ridges. Designers are often encouraged to slightly offset via-hole arrays toward the centers of respective strips to facilitate the definition of critical ridge edges, but at the risk of increasing a structure’s dissipation loss and reducing its power-handling capability due to potentially higher strip-edge current concentrations. LTCC-implemented ridge waveguide that employs via-hole arrays already tends to exhibit higher dissipation loss than is encountered in comparable ridge waveguide with solid-metal walls. In addition, LTCC processes do not lend themselves well to the practical realization of commonly desired rounded ridge edges for the reduction of dissipation loss, something that is simple to accommodate in structures that utilize moldable dielectric materials.

The ultimate goal remains the production of cost-effective filters in the form of monolithic ridge-waveguide structures made of cast dielectric material with selective external metallization. The approach would, in fact, permit a filter’s planar-circuit port impedance-matching networks to also be included as part of the monolithic unit by extending connected end-resonator ridges out to respective external port reference planes and designing the footprints of the ridge extensions to coincide with desired matching-circuit strip patterns. The casting of the dielectric core would be followed by the evaporation of a thin layer of precious metal onto the core’s entire outer surface and the fortification thereof through electroplating. After mounting the unit on a metal carrier to ascertain structural integrity, excess material would be removed from areas above prospective port-matching circuits, leaving low-profile metallized channels to function as strip conductors, and residual dielectric material to serve as substrates. The process would simultaneously expose the dielectric material at the filter’s resonator end faces and at its port reference planes, in accordance with design requirements.

The top portion of an applicable die might look similar to the empty cavity structure depicted in Fig. 2, augmented at both ends to accommodate filter port matching networks. Naturally, the design would have to be modified to include holes for injecting the moldable material, and slanted sidewalls to facilitate the release of molded cores after curing. Mechanical tolerances would again be a critical issue. Fortunately, precision milling machines are commercially available that are said to be capable of maintaining a general tolerance of 2.5 m. This would be more than sufficient to realize, with good reproducibility, filters of the type being proposed. Other established techniques, such as the use of LIGA molds, could be applied to the fabrication of precision dielectric cores as well.

V. SUMMARY

Three ridge-waveguide bandpass filter designs have been presented, spanning passband frequencies from 6 to 18 GHz, with fractional passband widths ranging from 25% to 50%. One of these examples, a 6–8.6-GHz bandpass filter, was reduced to practice, displaying very good agreement between predicted and measured results. The examples aim to reaffirm the practicability of the underlying design approach, which relies on equiv- alent-circuit representations of key filter subcomponents, used in conjunction with commercial software for linear-circuit and three-dimensional electromagnetic analyses. A perceived benefit of the approach is its potential to realize miniature filter modules from monolithic dielectric cores that are fabricated with the help of injection-molding techniques and metallized selectively to form conductive cavity boundaries. By adhering to the inline format, resultant filters would retain an intrinsic structural simplicity that should prove attractive in a variety of practical system applications.

ACKNOWLEDGMENT

The authors extend special thanks to R. Stanford and his colleagues, Applied Physics Laboratory, The Johns Hopkins University, Baltimore, MD, for their help with the machining of the filter cavity structure, M. Osward and J. DelPrete, both of Emerson and Cuming Microwave Products Inc., Randolph, MA, for the custom formulation and application of the dielectric material used in the experiment, B. Fruehling, SEFAR Printing Solutions Inc., Burnsville, MN, for supplying the screen used to deposit conductive epoxy, and D. Jachowski, Naval Research Laboratory, Washington, DC, and J. Willhite, Sonnet Software Inc., North Syracuse, NY, for constructive discussions and assistance.

REFERENCES

[1]C. Rauscher, “Design of dielectric-filled cavity filters with ultrawide stopband characteristics,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1777–1786, May 2005.

[2]J. Bornemann and F. Arndt, “Transverse resonance, standing wave, and resonator formulations of the ridge waveguide eigenvalue problem and its application to the design of e-plane finned waveguide filters,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 8, pp. 1104–1113, Aug. 1990.

[3]Y. Rong, K. A. Zaki, M. Hageman, D. Stevens, and J. Gipprich, “Lowtemperature cofired ceramic (LTCC) ridge waveguide bandpass chip filters,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2317–2324, Dec. 1999.

Christen Rauscher (S’73–M’75–SM’84–F’89) received the Diploma degree in electrical engineering and Doctorate degree from the Swiss Federal Institute of Technology, Zürich, Switzerland, in 1969 and 1975, respectively.

From 1976 to 1978, he studied the nonlinear behavior of GaAs field-effect transistors (FETs) at Cornell University, Ithaca, NY, and at the Naval Research Laboratory (NRL), Washington, DC. He subsequently joined the NRL, where he is currently Staff Consultant to the Microwave Technology

Branch, after having spent a sabbatical year with the Los Alamos National Laboratory, Los Alamos, NM, from 1985 to 1986, and having served from 1986 to 2002 as Head of the NRL Solid-State Circuits Section. His current research interests are centered on the pursuit of new concepts for realizing miniature high-frequency filters and the exploration of nonlinear signal interaction in semiconductor devices at microwave, millimeter-wave, and optical frequencies.

Dr. Rauscher served as an IEEE Distinguished Microwave Lecturer from 1997 through 1999. He was the recipient of a 1976 International Fellowship presented by the Swiss National Science Foundation, the 1987 IEEE Microwave Prize, the 1991 NRL Sigma Xi Applied Science Award presented by the Scientific Research Society of America, the 1999 IEEE Microwave Application Award, and the 2002 Engineering Sciences Award presented by the Washington Academy of Sciences.

Steven W. Kirchoefer (S’80–M’82) received the B.S., M.S., and Ph.D. degrees from the University of Illinois at Urbana-Champaign, in 1978, 1979, and 1982, respectively, all in electrical engineering.

Since 1982, he has been with the Naval Research Laboratory, Washington, DC. His research has involved the application of compound semiconductors and other materials to high-speed devices. He has fabricated and demonstrated a wide variety of prototype device concepts. These include semiconductor quantum-well devices utilizing real space transfer

and confined particle effects. Recently, he has been involved in the investigation of microwave properties ferroelectric of thin films and strain effects in such films. This research includes the study of interdigital capacitors for varactor applications, as well as the fabrication and measurement of distributed coplanar waveguide structures for phase-shifter applications.