In high ¡Vspeed digital circuits, in order to utilize the space of printed circuit boards(PCB) efficiently, the signal via is a heavily used interconnection structure to communicate different signal layers. However, the interconnection discontinuities will result in the degradation of the signal integrity and become a crucial issue for IC designers. To analyze this problem using finite difference time domain(FDTD) method, the stair case approach of interesting structure with curved metallic surface not only introduce errors due to inaccurate approximation, but consume much simulation time and memory required . In this thesis, a conformal FDTD method of locally distorted contours is presented. By modification of Maxwell¡¦s equations in integration form, we simulate the signal via successfully and discuss several interesting issues such as resonance in power/ground plane, the simultaneous switching noise(SSN), the effect of adding ground vias in PCB, and common-mode and differential-mode drives for source, etc.

FDTD can successfully simulate various kinds of phenomena of electromagnetic waves. Mainly, we use orthogonal Cartesian coordinate in general situations when we deal with the electromagnetic problems, but the curved geometry of the problem makes it difficult to obtain accurate results using conventional FDTD algorithm because of staircasing. To analyze curved geometry using Conformal FDTD can improve this shortcoming. The Conformal FDTD uses the regular FDTD equation for updating the magnetic field by using the electric field values along the distorted contours, that are appropriately weighted with lengths of the contours. The Conformal FDTD technique is well suited for handling such curved geometries. The moment method is used to convert the integral equation into a matrix equation.The major drawback of moment method (MoM) is the full matrix generation and huge computation time. The CFDTD directly approximates the differential operators in the Maxwell curl equation, and avoids using more mathematic formulae. This thesis uses Conformal FDTD to simulate RCS value of the cylinder and sphere and compare Conformal FDTD with Moment Method. We know that Conformal FDTD will save memory requirement and CPU time even more than Moment Method in layered structure.

Many electromagnetic problems can be simulated by FDTD method. Mainly, we use orthogonal cartesian coordinate in normal situations when we deal with the electromagnetic problems. Because in most situations, the structures simulated are simply rectangular. But sometimes we may need to simulate the structures which are not rectangular like the sharps of arc and circle. For this kind of problems, the tranditional FDTD method no longer works, so the tranditional FDTD method must be modified to fit the simulation of irregular structures. Besides the FDTD method we mention above, we even combine it with non-uniform grid method in more applications. And the time to apply it is when the object simulated both has the rectangular and curved structures in the same time like the microstrip fed by the coaxial cable. The situations like that would be a good time to apply it.