5. K. Hirayama, E.N. Glytsis, and T.K. Gaylord, Rigorous analysis of diffractive cylindrical lenses, J Opt Soc Am A 13 (1996), 2219 –2231. 6. Y.J. Guo and S.K. Barton, Flat printed lens and reflector antennas, Proc IEE 9 th Int Conf Antennas Propagat, Eindhoven, The Nether- lands, 1995, pp. 253–256. 7. D.M. Pozar, Flat lens antenna concept using aperture-coupled micros- trip patches, Electron Lett 32 (1996). 8. S. Chandran and J.C. Vardaxoglou, Experimental results on the focus- ing properties of tapered frequency-selective surfaces, Microwave Opt Technol Lett 11 (1996), 277–279. 9. D.M. Pozar and T.A. Metzler, Analysis of a reflectarray antenna using microstrip patches of variable size, Electronic Lett 29 (1993), 657– 658. 10. J.A. Encinar, Design of two-layer printed reflectarrays using patches of variable size, IEEE Trans Antennas Propagat 49 (2001), 1403–1410. 11. J.A. Encinar and J.A. Zornoza, Broadband design of three-layer printed reflectarrays, IEEE Trans Antennas Propagat 51 (2003), 1662– 1664. 12. B.A. Munk, Frequency-selective surfaces: Theory and design, Wiley– Interscience, New York, 2000. 13. C.A. Moses, A theoretical study of electromagnetic feedforward/feed- back media and wire media, Ph.D. dissertation, University of Penn- sylvania, 1997. 14. C.A. Moses and N. Engheta, Electromagnetic wave propagation in the wire medium: A complex medium with long thin inclusions, special issue on electrodynamics in complex environments, Wave Motion 34 (2001), 301–318. 15. C.A. Balanis, Advanced engineering electro-magnetics, Wiley, New York, 1989. 16. J.A. Stratton, Electromagnetic theory, McGraw-Hill, New York, 1941. © 2004 Wiley Periodicals, Inc. CHARACTERISTICS OF MICROFABRICATED RECTANGULAR COAX IN THE Ka BAND E. R. Brown, 1 A. L. Cohen, 2 C. A. Bang, 2 M. S. Lockard, 2 B. W. Byrne, 2 N. M. Vandelli, 2 D. S. McPherson, 2 and G. Zhang 2 1 University of California Los Angeles Los Angeles, CA 90095 2 MEMGen Corporation Burbank, CA 91506 Received 13 August 2003 ABSTRACT: Miniature rectangular coaxial transmission line (with a 300  300 m outer conductor) is simulated, fabricated, and tested up to the Ka band. It is made by the electrochemical fabrication (EFAB™) of nickel such that the center conductor is supported primarily by /4 stubs that also establish a resonant passband. The minimum insertion loss of a 1.67-cm-long test structure is found to be 1.74 dB at the pass- band center of 29 GHz. This is within 0.57 dB of the lowest insertion loss predicted by full-wave numerical simulations, indicative of the high precision and smooth surface morphology of the EFAB process. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 365–368, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11383 Key words: rectangular coaxial transmission line; electrochemical fab- rication; Ka band; nickel RF properties; resonant passband INTRODUCTION AND BACKGROUND Various 3D microfabrication techniques have improved in preci- sion and yield to the point where they can be considered for producing passive RF components on the deep submillimeter-size scale. A technique familiar to the MEMS community is silicon bulk micromachining, which has already been utilized to make several RF components, including resonators and filters [1–3]. The technique utilized in the present work is electrochemical fabrica- tion (EFAB™) [4]—a process that allows for the selective depo- sition of metals using a conformable polymeric mask that is patterned lithographically. A promising building block for the generation of passive RF components by EFAB™ is rectangular coaxial transmission line (“rectacoax”). Like its popular counterpart— circular coax, rectan- gular coax offers several advantages over other high-frequency transmission lines. For example, if uniformly filled with a low-loss dielectric material, it supports a purely TEM dominant mode over a very broad bandwidth, determined by the turn-on of the first TE mode. If the filler material has a frequency-independent real part of the dielectric constant and a small loss tangent, the TEM modal dispersion will be negligible over this bandwidth. Also, because of the peripheral distribution of surface current on the inner and outer conductors, the microwave specific attenuation from skin-effect absorption will be much less significant at the miniature scale than in printed-circuit transmission lines, such as microstrip and copla- nar waveguide. Furthermore, losses from substrate-mode excita- tion, so pervasive in printed-circuit lines, are nonexistent in rec- tacoax or any other TEM-coax for that matter. The disadvantages of rectacoax pertain mostly to the practical issues of design and fabrication. Although analytic solutions for the fundamental properties (for example, the characteristic imped- ance) of rectacoax do exist, they are in the form of infinite-series or integral solutions that are not amenable to simple design rules [5]. Therefore, fast full-wave techniques (such as transmission-line matrix) have been developed, particularly for designing junctions and other discontinuities [6 – 8]. And to fabricate “precision” mul- tiport passive components such as directional and hybrid couplers, the rectacoax must be made by expensive machine-shop tech- niques [9]. Because of these drawbacks, rectacoax has not yet been applied to RF integrated circuits (RFICs), particularly not with semiconductor monolithic microwave integrated circuits (MMICs). Two incentives for pursuing rectacoax in RFICs are its small allowable turn radius and its high isolation. Because the turns are made during the fabrication, their radius can be very small and still cause little insertion loss for the dominant TEM mode. This is in contrast to circular coax, such as UT-08 (the smallest known commercial coax), which has a very small center conductor (0.05-mm diameter) and outer conductor (0.167-mm inner diam- eter) but has a minimum turn radius of 0.8 mm [10]. This mini- mum radius is determined more by mechanical failure (collapse of the outer conductor) than by electromagnetic effects. The high isolation of rectacoax means that two side-by-side lines will have negligible crosstalk if the outer wall thickness is just a few tens of microns or more. This is because the skin depth in good metals is very small at microwave and mm-wave frequen- cies (for example, 1 m in copper at 10 GHz). And it allows one to reduce the footprint of distributed passive components by wind- ing straight sections of rectacoax back-and-forth in a serpentine fashion. These advantages are exploited in the design of the present rectacoax test structure. FABRICATION OF MINIATURE RECTACOAX The retrocoax in this work was made by EFAB™, a fabrication technology developed by MEMGen Corporation. It is beyond the scope of this discussion to illustrate the EFAB process in detail, however, it can be briefly described through the following steps: (i) MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 5, March 5 2004 365