1272 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 6, JUNE 2007 Ka-Band Miniaturized Quasi-Planar High-Q Resonators Kenneth J. Vanhille, Student Member, IEEE, Daniel L. Fontaine, Christopher Nichols, Member, IEEE, Zoya Popović, Fellow, IEEE, and Dejan S. Filipović, Member, IEEE Abstract—Air-filled copper -band resonators with heights between 250–700 m are demonstrated with measured unloaded factors between 440–829. The low-profile quasi-planar resonators are fabricated using a sequential metal deposition process. Miniaturization of up to 70% with respect to a TE101 quasi-planar resonator is accomplished by reducing the footprint of the resonator while maintaining the height. Finite-element simulations predict the measured resonant frequency within less than 1%. Due to fabrication imperfections, un is measured to be approximately 15% less than predicted. The resonators are compatible with air-filled rectangular microcoaxial feed lines fabricated in the same metal-deposition process. Index Terms—Cavity resonator, coaxial transmission line, photolithography, quality ( ) factor. I. INTRODUCTION T HE miniaturization of microwave resonators, including reentrant cavity designs, has been of interest since the development of microwave engineering [1]. Work with filters using evanescent waveguide for miniaturization and suppression of spurious modes with the ability to do wideband filters is presented in [2]. More recently, interest in microfabricated microwave and millimeter-wave resonators using various techniques has been seen. The loading of -band surface micromachined cavity resonators with barium titanate and alumina is examined in [3]; ’s in the hundreds are demonstrated with fabrication tolerances being the most important limiting factor on performance. Silicon micromachining of Ku-band resonators with drain holes used to release the sacrificial material are fabricated as outlined in [4]; the electrical performance is decreased by a small amount of leftover silicon in the resonator after the processing. Silicon micromachined and metal-plated layered polymer resonators with miniaturization factors up to -bands are presented in [5]. More recently, 70% at - and tuning from 5.4 to 10.9 GHz of an evanescent-mode resonator was demonstrated [6]. The resonators presented in [5] and [6] use rib-shaped interdigital capacitor loading (among other Manuscript received September 29, 2006; revised February 3, 2007. K. J. Vanhille, Z. Popović, and D. S. Filipović are with the Department of Electrical and Computer Engineering, University of Colorado at Boulder, Boulder, CO 80309-0425 USA (e-mail: [email protected]; [email protected]; [email protected]). D. L. Fontaine is with the Advanced Systems and Technology Division, BAE Systems, Nashua, NH 03060 USA (e-mail: [email protected]). C. Nichols is with Rohm and Haas Electronic Materials LLC, Blacksburg, VA 24060 USA (e-mail: [email protected]). 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.2007.895232 techniques), and are an excellent starting point for the designs - and -band rectangular coaxial transpresented here. mission line filters with nickel walls using the electrochemical fabrication (EFAB) process have been shown in [7] and [8], respectively. In this study, the resonators are not characterized alone; however, the largest theoretical ’s that can be obtained from nickel coaxial resonators with the same dimensions as in [7] and [8] are less than 80. The same technology with gold plating has recently demonstrated factors near 250 at 60 GHz [9]. Laser etching of copper has been used to fabricate rect-band filters [10]. 2.5-D resonators using angular coaxial U-shaped half-wavelength resonators in a cavity operating band have been fabricated using a low-temperature in the co-fired ceramic (LTCC) implementation [11]. This method allows compact filter design by including multiple resonators in the same cavity. Presented here are loaded-cavity resonators fabricated using a planarizing sequential-layering process that enables simultaneous fabrication of integrated rectangular coaxial transmission lines. Microfabrication of air-filled rectangular coaxial transmission lines and other components allow high isolation, dense circuit integration, multilayer topologies, low-loss performance, and dominant TEM propagation into the 400-GHz range [12]. Rectangular coaxial transmission lines, as well as other air-loaded surface-micromachined passive structures, such as high-quality factor inductors, have been demonstrated in the millimeter-wave frequency range [13]. Transmission lines, multiport couplers, and bandpass filters have been fabricated using nickel air-filled coax lines [14]. Quasi-planar microfabricated copper branch-line couplers and transmission-line resonators have been recently presented in -band. [15] with improved electrical properties up to Results for several quasi-planar resonators fabricated using the process presented here are given in [16]. Initial results for a miniaturized quasi-planar resonator are introduced in [17]. This paper gives a comprehensive analysis, design, and measurement study for miniaturized resonators at different frequencies and with different loadings. Sensitivity studies of the release holes, new resonator topologies, and behavioral circuit models are presented. Fig. 1(a) shows an example of a miniaturized cavity resonator with an arbitrary loading mechanism. Two types of predominately capacitive loading are presented in this paper. Fig. 1(b) shows what we refer to as the “puck-loading” used at 26 GHz and Fig. 1(c) shows the 36-GHz “rib-loading” structure, described in detail in Section II. It is worth clarifying the meaning of “quasi-planar” in the for a context of this study. Fig. 2 shows simulated values of 0018-9480/$25.00 © 2007 IEEE VANHILLE et al.: -BAND MINIATURIZED QUASI-PLANAR HIGH- RESONATORS 1273 Fig. 3. Basic fabrication steps for miniaturized quasi-planar resonators. The first eight steps (S1–S8) are identical for the five- and ten-layer structures. Fig. 1. (a) Sketch of a loaded quasi-planar resonator showing the loading, relevant dimensions, and resonator features. (b) Sketch of the metal puck loading in the 26-GHz resonator. The four support posts are also shown. (c) Half-view sketch of the ribs in the 36-GHz loaded cavity resonator. The ribs are cut along the xy -plane to simplify their presentation. The relevant dimensions of the resonators are given in Table I. allows resonators and microcoaxial feeds to be fabricated in the same process, while simultaneously providing factors higher than those of coaxial transmission line resonators of the same height. This paper is organized as follows. • Section II details the design of the resonators. Brief descriptions of the fabrication process, and the resonator feeding and probing structures are also given. • Section III provides a portion of the analysis necessary to understand the various design parameter effects on the performance of the resonators. • Section IV describes a method for deriving a behavioral circuit model of the loaded cavity resonators. • Section V shows the measurement results for the designed resonators. • Section VI discusses a few final points and indicates potential directions for future research. II. FABRICATION-DRIVEN ANALYSIS AND DESIGN Fig. 2. Percentage of Q of a resonator with respect to the maximum Q of metallic resonator as a function of normalized cavity height h =w for a TE several metals. The measured Q values for 26- and 36-GHz fabricated cavity resonators are given. square cavity with a footprint on the side, and with different metal conductivity values. The height of the cavity ( ) is varied from a small value to . The measured unloaded factors for two unloaded quasi-planar cavity resonators are indicated in Fig. 2 for comparison. The normalized heights of the and , justifying the terminology two cavities are “quasi planar.” “Low profile” describes these resonators with regard to their height equally well. The small electrical height The PolyStrata process developed by Rohm and Haas Electronic Materials LCC, Blacksburg, VA, consists of sequentially depositing layers of metal and photoresist with high aspect ratios (2 : 1) [18]. The resonators are fabricated on a low-resistivity silicon substrate using a sequence of standard photolithographic steps, as depicted in Fig. 3. Each copper layer is chemically polished before the next layer is deposited. The final step involves removing the photoresist, leaving microfabricated airfilled copper structures. Devices with up to ten layers are demonstrated in this paper. The fabrication and resulting mechanical parameters dictate the electrical design. The major fabrication-related factors and their influence on component design are as follows. 1) Total resonator height is limited by the number of layers and thickness of each layer. In our case, with ten layers, a maximal cavity height of 700 m is possible, which will factor as presented in Fig. 2. The electrical limit the height of the tallest resonator presented in this paper is one twelfth of a free-space (TEM) wavelength. 1274 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 6, JUNE 2007 Fig. 5. Normalized Q for different sized release holes on a cavity resonator. The surface area of the release holes is kept constant with respect to the top surface area of the cavity. This is shown for the 250-m-tall cavities at 26 GHz and 700-m-tall cavities at 36 GHz. Fig. 4. (a) Puck-loaded cavity resonator taken from [17]. The ports are indi200 m. (b) Two cavity cated by P1 and P2. The release hole size is 200 resonators fabricated for operation at 36 GHz. The resonator at left (R1) is full sized, and the resonator at right (R2) uses miniaturization. The release hole size is 400 400 m. Probing of the structure is done on the ends of the resonator at ports indicated by P1 and P2. The loading region in each resonator is indicated by the dashed lines. 2 2 2) Photoresist release holes on the top wall and on the sidewalls limit the factor. However, a relatively large number of holes are required to completely evacuate the lossy dielectric from the cavity. The size and number of release holes were carefully examined within fabrication parameters and are described in Section II-A. 3) The design of the loading to reduce the size of the resonator is limited to what can be fabricated with this technology. The main limitation was the size of the loading structure, which needed to be mechanically fixed to the top wall while providing enough loading. We could not use previously published designs, as given the mechanical constraints, they would not provide a sufficiently large loading reactance. This constraint resulted in a 3-D capacitance, which is unique to this paper and differs from the fins presented in [5]. 4) The aspect ratio of a thin cavity is such that the top wall can sag or bulge. The mechanical support posts, which increase the footprint of the 26-GHz loaded cavity, are eliminated in the 36-GHz design because of the miniaturization with the 3-D loading. 5) The inductive coupling between the input -coaxial cable and cavity is constrained by the height of the center conductor and the required impedance match; the analysis is detailed in Section II-C. Results from two sets of wafers are given in order to show the fabrication constraints on the resonator factor, i.e., 1) a wafer with coaxial components fabricated in a five-layer process with design frequencies near 26 GHz and 2) a wafer with 36-GHz components made using a ten-layer process. Resonators from the two wafers are shown in Fig. 4. A. Design of Release Holes In order to remove lossy photoresist after the top metal layer is deposited, release holes in the top layer and on the sidewalls are necessary. Electrically, these holes perturb the current flow and, therefore, affect the resonant frequency, as well as the factor. While no holes or small holes will give the highest factor, many larger holes are needed for high fabrication yield, thus an optimization study is required. The release holes on the sides of these resonators do not have a large effect on the electrical performance because of the cavity heights used so only the effects of the top holes will be examined. Fig. 5 shows the results of a 3-D finite-element method (FEM) study, using the Ansoft High Frequency Structure Simulator (HFSS) version 10, of a cavity resonator versus the number of rows of holes of ). The on the cavity resonator top surface (total holes ratio of the surface area of the release holes to the total top-wall surface area of the resonator is kept constant. For what is fabricated, this ratio is 8.74% for the five-layer 26-GHz designs (250- m cavity height) and 21.80% for the ten-layer 36-GHz designs (700- m cavity height). These numbers are dictated 200 m square release holes at 26 GHz by the use of 200 and 400 400 m square release holes at 36 GHz . Fig. 5 shows curves obtained numerically for both ratios at both design frequencies. The resonant frequency of the resonators changes slightly as the number of holes increases. To for a fixed frequency, it is necescompare these changes in sary to normalize the values. We begin with the formula for due to the conductor losses of a rectangular metallic cavity resonator, as can be found in [19] (1) where is the wavenumber, is the wave impedance of the is the surface resistance of the cavity-filling medium, and cavity walls. The length, width, and height of the cavity are , VANHILLE et al.: -BAND MINIATURIZED QUASI-PLANAR HIGH- RESONATORS 1275 TABLE I DESIGN VALUES FOR THE PARAMETERS AS NOTED IN FIG. 1 , and , respectively. We assume that and are equal and that the cavity is air filled as follows: (2) To compare two resonators with the same size, but different configurations of release holes, it is necessary to normalize the calculated unloaded quality factors based on the frequency of resonance. If the cavity dimensions and materials do not change, we find the ratio of quality factors to be related to a power of the ratio of the resonant frequencies (3) The data shown in Fig. 5 are simulated for two frequencies and two top plate surface area to release hole surface area ratios using the normalization in (3). The cavity is 250- m tall for the 26-GHz resonator and 700- m tall for the 36-GHz resonator. We see that the resonator performance is minimally affected by the release hole size when the cavity is 250- m tall; however, the unloaded of the cavity is large enough in the 700- m-tall case in that an effect on the is seen for large hole sizes. B. Mechanical Support The values of the dimensions labeled in Fig. 1 are given in Table I. The puck-loaded cavity contains four mechanical support posts that connect the top and bottom cavity walls. The added mechanical strength comes with a penalty in size, as the posts behave as inductances in parallel, decreasing the overall inductance of the cavity and increasing the necessary cavity footprint for a given frequency [17]. The metal rib loaded cavity contains two ribs connected to the bottom cavity wall and a single rib hangs from the top cavity wall. A cross configuration is used with the ribs to increase the strength of the connection of the ribs to the top and bottom cavity walls. The ribs have the effect of increasing the capacitance of the cavity, operating much like an interdigitated capacitor. The rib widths that are not explicitly labeled in Fig. 1(c) are 100 m in size. C. Coupling The resonators are measured in a two-port topology with probing structures in the regions marked P1 and P2 in Fig. 4. 150- m-pitch ground–signal–ground (GSG) probes are placed in contact with a short section of vertical rectangular coax, as shown in the figure, where the relatively complex geometry Fig. 6. (a) Top-view photograph of the probing area for the 36-GHz resonator. (b) Cross-sectional view of the port area (courtesy of the Mayo Foundation). (c) 3-D model of the resonator feed. serves for impedance matching by reactively tuning the discontinuity parasitics. The center conductor of the rectangular coax in the probing region bends downwards to connect to the bottom wall of the cavity, resulting in inductive coupling, as shown in Fig. 1(a). A top view of one of the probe structures of the 36-GHz resonator is shown in Fig. 6(a). A wafer is diced down the center line of the rib-loaded resonators to reveal the cross-sectional view shown in Fig. 6(b), giving the sidewall profiles. An indication of the detailed analysis involved in producing high-quality transitions to the on-wafer environment is shown in Fig. 6(c), which gives the computer-aided design (CAD) model of the resonator probe port. III. RESONATOR MINIATURIZATION Comprehensive numerical studies are conducted to examine the effects of several of the design parameters that affect the resonator performance. The more efficient eigenmode analysis is applied to examine parameter effects and trends, while the driven analysis provides frequency-dependent -parameters. The loading effect of the capacitive puck and the more complex 3-D metallic ribs is addressed here. Fig. 7 shows the results of a numerical study of the size of the capacitive loading puck of the 26-GHz resonator for puck heights of 75 m and 175 m, corresponding to the two possible values using the five-layer process. The position and size of the support posts and the overall dimensions of the resonator are kept constant. The fabrication process allows three possible discrete heights (0, 75, and 175 m), as there are three layers that make up the actual cavity (two more layers exist, one for the top wall and one for the bottom wall, making a total of five layers). The tallest height is chosen to maximize the factor, whose theoretical value is less than 2% lower than the highest ideal value for a copper resonator without release holes. 1276 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 6, JUNE 2007 Fig. 7. Results of a parametric analysis of a simplified model of the 26-GHz resonator. The release holes are not included for this analysis. The FEM eigenmode analysis examines how different diameters for the loading puck affect the Q and f of the resonator. Two puck heights (75 and 175 m) corresponding to the two possible heights using the five-layer fabrication process are examined. Values corresponding to the fabricated resonator are indicated on the graph. Fig. 9. Equivalent circuit is generated for the resonator with feed combination for the miniaturized resonator using a loading puck and support posts. (a) Circuit topology used to create the model. (b) Measured input impedance of the resonator/feed combination compared to the input impedance of the circuit model derived from the measured data. IV. CIRCUIT-MODEL DEVELOPMENT Fig. 8. Results of a parametric analysis of the 36-GHz resonator. The analysis examines different spacings of the loading ribs S , as given in the inset. Eigenmode analysis using the FEM is employed, and values corresponding to the fabricated resonator are indicated on the graph. Fig. 8 presents the results of a parametric study examining the effect of the rib spacing on and of the resonator. The values corresponding to the dimensions used for the fabrication are highlighted on the graph. As the rib separation is increased, the capacitance between the ribs diminishes; however, the capacitive coupling from the ribs to the opposite wall of the cavity remains strong. The scaling of the two -axes is the same relative to the first point of each data set, emphasizing the frequency changes more rapidly than over the range of separation values considered. Returning to Fig. 4, the puck-loaded resonator, shown at the top of the figure, has a footprint that is 15% smaller than a normal cavity resonator and 50% smaller than a resonator using the four support posts [17]. A photograph of an unloaded ten-layer 36-GHz resonator is shown on the left in Fig. 4(b). A miniaturized rib-loaded resonator operating at the same frequency, but with a 71% reduction in surface area, is shown on the right-hand side of this figure. Though full-wave FEM simulations are accurate and flexible for detailed studies, they are computationally expensive. For example, on a dual-processor Intel Xeon 3.4 machine, it takes four minutes per frequency point with a 70-k tetrahedron mesh. Therefore, behavioral circuit models are developed for the two loaded resonators and compared with the measured results to validate this approach. A circuit model, as shown in Fig. 9(a), is developed for the two-port resonator. The steps for extracting the model are similar to those outlined in [20]. Once the capacitance of the gap between the puck and top wall is approximated using quasistatic analysis, the other circuit parameters can be determined. The other parameters of interest are the series resistance of the , the turns ratio , which is approximately the coufeed pling coefficient, the total inductance of the support posts , the characteristic impedance of the lines connecting to the resonator , and the nominal capacitance, resistance, and inductance of the cavity , , and , respectively. Starting values for these parameters are found using full-wave analysis, and then the parameters are fit to correspond to the measured results. Good agreement can be seen between the measured response and the derived equivalent circuit [see Fig. 9(b)]. The calculated , , values for the circuit parameters are turns, pF, pF, pH, pH, and k . A similar exercise using the simulated -parameter data from the full-wave response yields a circuit model whose input impedance is indistinguishable from that calculated in the simulation. Fig. 10(a) shows the model and Fig. 10(b) shows the input impedance predicted by the model, as compared with the sim- VANHILLE et al.: -BAND MINIATURIZED QUASI-PLANAR HIGH- RESONATORS 1277 TABLE II SUMMARY OF THE SIMULATION AND MEASUREMENT RESULTS IS GIVEN FOR THE TWO RESONATORS Fig. 10. Equivalent circuit is generated for the resonator with feed combination for the miniaturized resonator using three ribs for miniaturization. (a) Circuit topology used to create the model. (b) Simulated input impedance of the resonator/feed combination and the input impedance of the circuit model derived from the simulated data. ulated input impedance for the rib-loaded resonator. A comparison with the simulated results demonstrates that the circuit model predicts the measured response and agrees with the full-wave simulations. The circuit model has one inductor less than the model in Fig. 9(a), as there are no support posts in this , is caldesign. The loading capacitance from the ribs, i.e., culated using Ansoft’s Maxwell 3D, as the approximation of the capacitance is more involved than what was done for the loading puck. This method calculates the electrostatic capacitance, but this is a good approximation since the dimensions of at the resonant frequency. the loading ribs are less than is 0.068 pF. The nominal capacitance of the resonator is pF, the nominal inductance is nH, k , the turns ratio is the nominal resistance , and the series resistance of the feed is . An examination of the derived circuit models of the two miniaturized resonators presented in Figs. 9(a) and 10(a) reveals that quite similar behavioral models describe the two resonators with seemingly different loading topologies. This approach can be generalized to other possible quasi-planar loading topologies. V. MEASUREMENT RESULTS The resonators are measured using 150- m-pitch probes from Cascade Microtech on a Cascade Summit 9000 probe station connected to an HP-8510C network analyzer. An external short-open-load-thru (SOLT) calibration on an alumina substrate is performed. A comparison of the measured and simulated results for the two miniaturized resonators is given for the in Table II. The simulated and measured values of puck-loaded resonator are 508 and 442, respectively. Compared Fig. 11. S -parameter transmission data for the 26-GHz resonator taken from [17]. A comparison of measured, circuit model, and simulated results is shown. The simulated resonator is modeled using HFSS. The offset in frequency between the measured and simulated results is less than 0.7%. Fig. 12. S -parameter transmission data for the 36-GHz resonator. A comparison of measured, circuit model, and simulated results is shown. The simulated resonator is modeled using HFSS. The offset in frequency between the measured and simulated results is less than 0.4%. to a cavity resonator with four support posts, but no capacitive loading, the 50% reduction in footprint results in virtually no for a cavity resreduction in quality factor. The simulated onator using this technology is 541; therefore, a 15% footprint reduction with four supporting posts is realized by sacrificing . The values of for the rib-loaded resonator 6% of are 995 and 829 for the simulated and measured results. This of 1308 for a full-sized cavity compares to a simulated resonator with the same cavity height. A 71% reduction in . footprint is thus achievable for a 25% reduction in The measurement results of the puck-loaded 26-GHz resfrom the full-wave simulation onator are shown in Fig. 11. 1278 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 6, JUNE 2007 and the equivalent-circuit model of Fig. 9(a) are also plotted for comparison. The resonant frequency of the measured resonator differs by less than 0.7% from the predicted value. The for the rib-loaded 36-GHz resonator measurement results of are given in Fig. 12. Again, a comparison is made between the full-wave simulation and the derived equivalent-circuit model; the deviation of the measured from predicted resonant frequency is less than 0.4%. VI. CONCLUSION Results from two miniaturized resonators have been presented and their performance and size has been compared to that of full-sized cavity resonators operating at the same frequencies. The puck-loaded resonator achieves a 15% miniaturization in the footprint of the resonator, while including mechanical supporting posts (this gives a 50% reduction in footprint compared to a cavity with just the support posts). The rib-loaded resonator has a 71% miniaturization in the cavity footprint compared to a stanresonator. The electrical effects of release holes and dard their size and placement are studied. The electrical phenomena resulting in the miniaturization of the resonators are explored and the quality factors and cavity footprints are compared to standard cavity resonators. Behavioral equivalent circuits are derived and their usefulness validated by measurements. From here, one could develop filters, using the circuit models as the building blocks for rapid synthesis. Such resonators can also be integrated with rectangular coaxial lines and active elements for circuits that require high- factors such as low phase-noise oscillators and frequency diplexers. ACKNOWLEDGMENT The authors would like to thank G. Potvin, BAE systems, Nashua, NH, D. Sherrer and the Rohm and Haas Microfabrication Team, Blacksburg, VA, W. Wilkins and her measurement team, Mayo Clinic, Rochester, MN, Dr. J. Evans, Defense Advanced Research Projects Agency (DARPA), Arlington, VA, and E. Adler, Army Research Laboratory (ARL), Adelphi, MD, for their support. The authors would also like to thank M. Lukić, and Dr. S. Rondineau, both with the University of Colorado at Boulder, for helpful technical input. REFERENCES [1] G. L. Ragan, Ed., Microwave Transmission Circuits, ser. MIT Radiat. Lab. New York: McGraw-Hill, 1948, vol. 9. [2] R. V. Snyder, “New application of evanescent mode waveguide to filter design,” IEEE Trans. Microw. Theory Tech., vol. MTT-25, no. 12, pp. 1013–1021, Dec. 1977. [3] C. A. Tavernier, R. M. Henderson, and J. Papapolymerou, “A reducedsize silicon micromachined high-Q resonator at 5.7 GHz,” IEEE Trans. Microw. Theory Tech, vol. 50, no. 10, pp. 2305–2314, Oct. 2002. [4] K. Strohm, F. Schmuckle, O. Yaglioglu, J.-F. Luy, and W. Heinrich, “3D silicon micromachined RF resonators,” in IEEE MTT-S Int. Microw. Symp. Dig, Philadelphia, PA, Jun. 2003, pp. 1801–1804. [5] A. Margomenos, B. Liu, S. Hajela, L. Katehi, and W. Chappell, “Precision fabrication techniques and analysis on high-Q evanescent-mode resonators and filters of different geometries,” IEEE Trans. Microw. Theory Tech, vol. 52, no. 11, pp. 2557–2566, Nov. 2004. [6] S. Hajela, X. Gong, and W. J. Chappell, “Widely tunable high-Q evanescent-mode resonators using flexible polymer substrates,” in IEEE MTT-S Int. Microw. Symp. Dig, Long Beach, CA, Jun. 2005, pp. 2139–2142. [7] R. Chen, E. Brown, and C. Bang, “A compact low-loss Ka-band filter using 3-D micromachined integrated coax,” in Proc. IEEE Int. MEMS Conf., Maastricht, The Netherlands, Jan. 2004, pp. 801–804. [8] J. Reid and R. Webster, “A compact integrated V -band bandpass filter,” in Proc. IEEE AP-S Int. Symp., Monterey, CA, Jul. 2004, pp. 990–993. [9] E. D. Marsh, J. Reid, and V. S. Vasilyev, “Gold-plated micromachined millimeter-wave resonators based on rectangular coaxial transmission lines,” IEEE Trans. Microw. Theory Tech, vol. 55, no. 1, pp. 78–84, Jan. 2007. [10] I. Llamas-Garro, M. Lancaster, and P. Hall, “Air-filled square coaxial transmission line and its use in microwave filters,” Proc. Inst. Elect. Eng.—Microw. Antennas Propag., vol. 152, pp. 155–159, Jun. 2005. [11] L. Rigaudeau, P. Ferrand, D. Baillargeat, S. Bila, S. Verdeyme, M. Lahti, and T. Jaakola, “LTCC 3-D resonators applied to the design of very compact filters for Q-band applications,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 6, pp. 2620–2627, Jun. 2006. [12] M. Lukić, S. Rondineau, Z. Popović, and D. Filipović, “Modeling of realistic rectangular -coaxial lines,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 5, pp. 2068–2076, May 2006. [13] I. Jeong, S.-H. Shin, J.-H. Go, J.-S. Lee, and C.-M. Nam, “High-performance air-gap transmission lines and inductors for millimeter-wave applications,” IEEE Trans. Microw. Theory Tech, vol. 50, no. 12, pp. 2850–2855, Dec. 2002. [14] J. Reid, E. D. Marsh, and R. T. Webster, “Micromachined rectangular coaxial transmission lines,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 8, pp. 3433–3442, Aug. 2006. [15] D. S. Filipović, Z. Popović, K. Vanhille, M. Lukić, S. Rondineau, M. Buck, G. Potvin, D. Fontaine, C. Nichols, D. Sherrer, S. Zhou, W. Houck, D. Fleming, E. Daniel, W. Wilkins, V. Sokolov, and J. Evans, “Modeling, design, fabrication, and performance of rectangular -coaxial lines and components,” in IEEE MTT-S Int. Microw. Symp. Dig, San Francisco, CA, Jun. 2006, pp. 1393–1396. [16] K. J. Vanhille, D. L. Fontaine, C. Nichols, D. S. Filipović, and Z. Popović, “Quasi-planar high-Q millimeter-wave resonators,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 6, pp. 2439–2446, Jun. 2006. [17] ——, “A capacitively-loaded quasi-planar Ka-band resonator,” in Proc. 36th Eur. Microw. Conf., Manchester, U.K., Sep. 2006, pp. 495–497. [18] D. Sherrer and J. Fisher, “Coaxial waveguide microstructures and the method of formation thereof,” U.S. Patent 7 012 489, Mar. 14, 2006. [19] D. Pozar, Microwave Engineering, 2nd ed. New York: Wiley, 1998, pp. 300–350. [20] F. Gardiol, Introduction to Microwaves. Norwood, MA: Artech House, 1983, pp. 136–142. Kenneth J. Vanhille (S’00) received the B.S. degree in electrical engineering from Utah State University, Logan, in 2002, the M.S.E.E. degree from the University of Colorado at Boulder, in 2005, and is currently working toward the Ph.D. degree at the University of Colorado at Boulder. From 2000 to 2003, he was with the Space Dynamics Laboratory, Logan, UT, where he designed space science instrumentation for sounding rocket campaigns. In 2002, he was a member of the National Aeronautics and Space Administration (NASA) Academy, Goddard Space Flight Center. His current interests include millimeter-wave components and antenna design. Daniel L. Fontaine was born in Holyoke, MA, on February 17, 1966. He received the B.S. and M.S. degrees in electrical engineering from the University of Massachusetts at Amherst, in 1988 and 1991, respectively. From 1988 to 1996, he was a Senior Design Engineer with the Raytheon Company, Tewksbury, MA. Since 1996, he has been a Principal Design Engineer with the Advanced Systems and Technology Division, BAE Systems, Nashua, NH. His professional design experience and interests include microwave and millimeter-wave patch antennas and arrays, quasi-optical feed networks, transmit/receive (T/R) modules, and frequency-selective surfaces. VANHILLE et al.: -BAND MINIATURIZED QUASI-PLANAR HIGH- RESONATORS Christopher Nichols (M’03) received the B.S. degree in physics from Arkansas State University, State University, in 1990, and the M.S. degree in physics and Ph.D. degree in applied science from The College of William and Mary, Williamsburg, VA, in 1992 and 1996, respectively. His doctoral dissertation involved the engineering of a novel hyperthermal neutral stream etch process tool for charge-free wafer stripping. Prior to graduation, he was with IBM, Yorktown Heights, NY, where he was involved with ionized physical vapor deposition. He is currently a Senior Engineer and Microfabrication Program Manager with Rohm and Haas Electronic Materials LLC, Blacksburg, VA. Zoya Popović (S’86–M’90–SM’99–F’02) received the Dipl.Ing. degree from the University of Belgrade, Belgrade, Serbia, in 1985, and the Ph.D. degree from the California Institute of Technology, in 1990. She is currently the Hudson Moore Jr. Chaired Professor of Electrical and Computer Engineering with the University of Colorado at Boulder. Her research interests include high-efficiency and low-noise microwave circuits, quasi-optical millimeter-wave techniques, smart and multibeam antenna arrays, intelligent RF front ends, RF optics, and wireless powering for batteryless sensors. 1279 Dr. Popović was the recipient of the 1993 and 2006 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Microwave Prize for best journal papers. She was also the recipient of the 1996 URSI Issac Koga Gold Medal, a 2000 Humboldt Research Award for Senior U.S. Scientists, and a 1993 National Science Foundation (NSF) Presidential Faculty Fellow Award. Dejan S. Filipović (S’97–M’02) received the Dipl. Eng. degree in electrical engineering from the University of Nis, Nis, Serbia, in 1994, and the M.S.E.E. and Ph.D. degrees from The University of Michigan at Ann Arbor, in 1999 and 2002, respectively. From 1994 to 1997, he was a Research Assistant with the University of Nis. From 1997 to 2002, he was a Graduate Student with the University of Michigan at Ann Arbor. He is currently an Assistant Professor with the University of Colorado at Boulder. His research interests are in the development of millimeter-wave components and systems, multiphysics modeling, antenna theory and design, as well as in computational and applied electromagnetics.

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