Analytic formulas for calculating the quasistatic parameters of a multilayer cylindrical coplanar strip line

Abstract

ABSTRACT: Fast, simple, and accurate analytic expressions are deri ¤ edfor calculating the quasistatic TEM parameters of a multilayer cylindricalcoplanar strip line MC CPS . The effects of the dielectric materials on()the quasi-TEM characteristics are in ¤ estigated using the conformalmapping method. The deri ¤ ed results are compared with those of acorresponding planar CPS. The cur ¤ ature effects on the quasistaticparameters are also discussed. In addition, it has been obser ¤ ed that theeffect of the inner substrate on the quasistatic parameters is much lessthan the outer substrate. Q 1999 John Wiley & Sons, Inc. MicrowaveOpt Technol Lett 22: 432]436, 1999. Key words: cylindrical CPS; conformal mapping; CAD-orientedformulas INTRODUCTION To date, many authors 1wx]5 have extensively studied sym-metric coplanar strip lines CPSs on planar-shaped sub-.strates due to the flexibility in the design of complex mi-crowave circuitry requiring shunt and series connections. Dueto these properties as well as several advantages, such asexcellent propagation with linear dispersion, less sensitivity tosubstrate thickness, small discontinuity parasitics, and elimi-nating the need of via holes, the coplanar strip line is suitablefor the emerging wireless communications industry, and forthe design of low-cost uniplanar microwave circuits such asmixers, filters, antennas, and optoelectronic devices 6 .wxBriefly, the CPS supports all of the advantages of a coplanarwaveguide CPW , which is complementary to CPW, and also,.it is efficient in the use of wafer area. In addition, the CPS isuseful in manufacturing lines with high characteristicimpedances as it is easier to realize a high impedance withCPS than with CPW. Furthermore, due to its balanced con-figuration, it is also useful for balanced circuits such asmixers and for differential drivers such as those used in somehigh-speed digital applications. Unlike these structures, thereis only a limited number of publications dealing with qua-sistatic parameters of CPS on cylindrically shaped substrates.We have reported the analytic expressions for quasi-TEMparameters of the single-layer cylindrical CPS 7 . However,wxaccording to our knowledge, there is no study on cylindricalCPS with multilayered dielectrics, whereas, in practice, thereare many circumstances in which the substrates are multi-layer, for example, in MICs, connection lines are either on orburied between dielectric layers. Here, the multilayer cylin-drical CPS MC CPS is analyzed using the conformal map-.ping technique. As is well known, the quasi-TEM approxima-tion is valid only at low frequencies. However, Bedair andWolff 8 have shown that a simple quasistatic approximationwxcan be used in the design of coplanar monolithic microwaveintegrated circuits MMICs up to 40 GHz because of their.very low dispersion. Furthermore, Goverdhanam, Simons,and Katehi 4 have shown, for conventional CPS structures,wxthat there are no higher order modes up to the millimeter-wave frequency range. The CPS with smaller line dimensionsand thinner substrates can increase the cutoff frequency tohigher frequencies, thus extending the operating range.Namely, due to the fewer dispersion characteristics of CPS,the quasi-TEM approximation can be used to discuss the CPSpropagation characteristics, at least up to the millimeter-wavefrequency range. In this case, the characteristic impedanceand effective dielectric constant may be calculated by theformulas based on the conformal mapping method becauseconformal mapping techniques lead to closed-form analyticalsolutions suitable for CAD software packages. Also, full-wavemethods, such as spectral-domain analysis, the integral equa-tion method, and the finite-difference method, are mathemat-ically complex and require time-consuming numerical calcu-lations, and so they are not very attractive for the interactiveCAD. Therefore, the aim of the study is to present fast,simple, and accurate CAD-oriented analytic expressions forthe quasistatic parameters of the MC CPS.