10. zyxwvutsrqpon R. Collin. zyxwvutsrqpo Field Theoiy zyxwvutsrqp 01 Guided Wurvs. McGraw-Hill, New zyxwvut York, 1960. 11. E. Kuhn, zyxwvutsrqpo “A Mode Matching Method for Solving Field Problems in Waveguide and Resonator Circuits,” A EU. Vol. 27, December 1973, pp. 511-518. Micronui.e ond Opricul Technolop 1.errer.s. 2/X. 286- 291 J: 1989 John Wilcy & Sons. Inc. CCC 0895-2477/89/$4.CN LOW IMPEDANCE MATCHING: THE RADIAL STUB SOLUTION F. Giannini, M. Auggleri, G. Bartolucci, and C. Paolonl University of Rorna “Tor Vergata” Department of Electronics Engineering Via Orazio Rairnondo 001 73 Rorna Italy KEY TERMS Microstrip rudiul stuh, low impedance. modul theon. sFnthesis, open und shorted straight stuhs ABSTRACT The rudiul stuh zyxwvutsrqponm us zyxwvutsrqp u kec microstrip structure 10 provide IOH. tnipedmce 1ei;el.y with u well-defined insertion point zyxwvutsrqpo is propmed. Its churuc.teri~ution through u plunur upprouch provides u superior uccuruc:r. us conipured with the simulutions uttuinuhle from presentlv ucwiluhle CAD packages. Some experimcnts have fully confirmed the design. Furthermore, the flexibility of radial lines in replacing both open and shorted straight stubs is demonstrated together with somc successful results, athevcd through their use in practical applications. 1. INTRODUCTION In many microstrip realizations, the microwave designer is required to minimize simply and effectively the drawbacks resulting from the use of low-impedance matching elements. zyxwvu In fact, the wide transversal dimension of conventional straight stubs makes it extremely difficult to take proper account of the effective insertion point. As a consequence, highly accurate electromagnetic models and/or timc-consuming optimization procedures are necessary to compensate, for instance, for all the related parasitic effects. Microstrip radial stubs (Figure 1) can represent the proper solution for the preceding kind of problems. The features of thosc structures, in fact, mainly consist of a broadband behav- ior together with a well-defined “low-impedance” insertion point [l, 21. Several circuit applications, such as biasing, filtering, matching networks, and virtual grounds have been succcss- fully demonstrated, adopting radial lines as effective substi- tutes for straight stubs. This was achicved through a proper characterization of the insertion-dependent electromagnetic behavior of radial stubs and the establishment of a relation- ship between them and the corresponding straight stubs. More precisely, the characterization of microstrip radial lines in a frequency range where thc equivalence with an open quarter-wave straight stub can be established, has been invcs- tigated. Both simulation and synthesis procedures have been derived [ 31. Furthermore the equivalence between open radial lines and shorted quarter-wavc straight stubs also can be derived and fully characterized. This paper reports the features of the preceding characteri- zation and points out the superiority of the proposed analysis and synthesis procedures with respect to prcsently available commercial simulation tools. Moreover, some successful applications of radial lines ob- tained through thc replacement of both open and shorted conventional straight stubs are reported in order to confirm the effectiveness of their use. 2. THEORETICAL CHARACTERIZATION The electromagnetic behavior of radial stubs can be charactcr- ized through thc extension of a previously developed theory for planar structures [4]. That analysis, developed for a two-port planar circuit of generic shape. has been previously applied to the rcctangular Figure 1 Single and double radial stub5 in shunt configuration MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol 2 No 8 August 1989 291