The Modeling of Lumped Elements Using the Haar Wavelet Multiresolution Time Domain Technique

Abstract

The Finite Difference Time Domain (FDTD) method has been used widely in solving applied electromagnetic problems. Recently, to improve the computational efficiency the multiresolution theory has been applied to the FDTD method and leads to Multiresolution Time Domain (MRTD) techniques (M. Krumpholz and L. P. B. Katehi, IEEE Microwave and Guided Wave Lett., 5, 382-384, 1995). MRTD techniques using the Battle-Lemarie, Daubechies, and Haar wavelets have been applied to analyze various electromagnetic structures with success. Although these techniques need less computational effort than the conventional FDTD method, the latter method is easier to implement boundary conditions than the former methods. Therefore, the MRTD scheme combined with the local FDTD boundary conditions can be used to get the advantages of both the methods. In this work, to analyze the microstrip structure with lumped elements, the conventional FDTD scheme (the physical domain) is used to describe the characteristics of the lumped elements, while the Haar-wavelet MRTD scheme (the wavelet domain) is applied to the remained computational domain. The main distinction between this work and earlier ones is the boundary conditions. The MRTD’s temporal discretization width is twice as large as the FDTD’s one to combine both the methods. To show the validity and the advantage of the proposed scheme, numerical results for microstrip structures with lumped elements (a diode and a capacitor) are presented and compared to those obtained by the use of the conventional FDTD scheme. Fig. 1 shows the 3-D microstrip structure with lumped element of interest. The perfect electric conductor and absorbing boundary condition are treated as described in the previous work (M. Fujii and W. J. R. Hoefer, IEEE Trans. Microwave Theory Tech., 46, 2463-2475, 1998). A microstrip line with a diode (Is = 10 -14 amps) is simulated by the proposed method. For comparison, the conventional FDTD approaches are also applied to the problem. As shown in Fig. 2, the proposed method gives very good results compared with the FDTD fine mesh result. The computation time of the methods is shown in the Table 1.