 = 3  10 7 S/m, and the input modulated Gaussian pulse is V 0 = 1.0 V,  = 16.68 ps, and t 0 = 66.68 ps. As in Figure 4, the attenuation of the propagating sinusoidally modulated Gaussian pulse is due mainly to the ohmic loss of both the center strip and ground planes. Also, the attenuation is more rapid at the start of the pulse propagation distance. 4. CONCLUSIONS Based on an improved empirical formula to calculate the ohmic loss of CPWs, the lossy effects in coplanar waveguides on the pulse propagation have been studied. These CPWs are assumed to be fabricated on single-layer, low-dispersion and low-loss LTCC. For normal LTCC CPWs, it is shown that the total loss is contrib- uted mainly by the ohmic loss of the conductive planes in the frequency range up to 40 GHz. The ohmic loss can lead to nearly 50% pulse magnitude attenuation at the start of the propagation distance of less than several millimeters. REFERENCES 1. M. Riaziat, R. Majidi-Ahy, and I. Jaung Feng, Propagation modes and dispersion characteristics of coplanar waveguides, IEEE Trans Micro- wave Theory Tech MTT-41 (1993), 1499 –1510. 2. G. Gihione, A CAD-oriented analytical model for the losses of general asymmetrical coplanar lines in hybrid and monolithic MICs, IEEE Trans Microwave Theory Tech MTT-41 (1993), 1499 –1510. 3. H. Klingbeil and W. Heinrich, Calculation of CPW A.C. resistance and inductance using a quasi-static mode-matching approach, IEEE Trans Microwave Theory Tech MTT-42 (1994), 1004 –1007. 4. C.L. Hollowy and E.F. Kuester, A quasi-closed form expression for the coplanar loss of CPW lines, with an investigation of edge shape effects, IEEE Trans Microwave Theory Tech MTT-43 (1995), 2695– 2701. 5. K.C. Gupta, R. Grag, I. Bahl, and P. Bhartia, Microstrip lines and slotlines, 2 nd ed., Artech House, Boston, 1996. 6. D. Lederer and J.P. Raskin, Substrate loss mechanisms for microstrip and CPW transmission lines on lossy silicon wafers, 2002 IEEE MTT-S Dig, 2002, pp. 685– 688. 7. D.S. Phatak and A.P. Defonzo, Dispersion characteristics of optically excited coplanar striplines: pulse propagation, IEEE Trans Microwave Theory Tech MTT-38 (1990), 654 – 661. 8. C.L. Liao, Y.M. Tu, J.Y. Ke, and C.H. Chen, Transient propagation in lossy coplanar waveguides, IEEE Trans Microwave Theory Tech MTT-44 (1996), 2605–2611. 9. G.E. Ponchak, M. Magloubian, and L.P.B. Katehi, A measurement- based design equation for the attenuation of MMIC-compatible copla- nar waveguide, IEEE Trans Microwave Theory Tech MTT-47 (1999), 241–243. 10. D. Heo, A. Sutono, E. Chen, Y. Suh, and J. Laskar, A 1.9-GHz DECT CMOS power amplifier with fully integrated multilayer LTCC pas- sives, IEEE Microwave Wireless Compon Lett 11 (2001), 249 –251. 11. K. Kageyama, K. Saito, H. Murase, H. Utaki, and T. Yamanoto, Tunable active filters having multilayer structure using LTCC, IEEE Trans Microwave Theory Tech MTT-49 (2001), 2421–2424. © 2003 Wiley Periodicals, Inc. A HYBRID IMPLICIT-EXPLICIT FDTD SCHEME WITH WEAKLY CONDITIONAL STABILITY Binke Huang, 1 Gang Wang, 2 Yansheng Jiang, 1 and Wenbing Wang 1 1 Department of Telecommunication Engineering Xi’an Jiaotong University Xi’an 710049, P.R. China 2 Department of Telecommunication Engineering Jiangsu University Zhenjiang 212013, P.R. China Received 13 March 2003 ABSTRACT: A hybrid implicit-explicit FDTD (HIE-FDTD) algorithm is proposed in this paper. In the HIE-FDTD algorithm, semi-implicit- and explicit-difference schemes are imposed on two different field com- ponents, respectively, and the field component with implicit difference is updated by solving simple tridiagonal matrix equations. The HIE-FDTD method, although conditionally stable, allows for larger time-step size than the conventional FDTD method because the stability condition of the HIE-FDTD method is weaker than that of the conventional Yee’s FDTD algorithm. The demonstrated numerical dispersion relation of the HIE-FDTD method is found to be identical to that of the ADI-FDTD method. The accuracy and efficiency of the HIE-FDTD are verified by numerical simulation results. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 97–101, 2003; Published online in Wiley Inter- Science (www.interscience.wiley.com). DOI 10.1002/mop.11138 Key words: implicit difference; explicit difference; weakly conditional stability; FDTD; tridiagonal matrix equations Figure 6 Propagation of a sinusoidally modulated Gaussian pulse in LTCC CPWs: (a) (  r , tan ) = (4.2, 0.003); (b) (  r , tan ) = (7.8, 0.0015) and (10.6, 0.001) MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 2, October 20 2003 97