Optimised image theory for dielectric layer modelling in PCBs

In the design of PCBs for high frequency applications, it is essential to be able to simulate the electrical behaviour of the PCB layout before it is fabricated to avoid having many expensive design iterations. A powerful CAD tool called FASTERIX is considered. FASTERIX produces an equivalent circuit model for the metallisation and substrate of a PCB. This model is then merged with models for the components attached to the PCB and the combined circuit simulated with a circuit analysis program. Computing the values of the capacitances in the equivalent circuit model of the PCB takes the majority of the CPU time used to generate this circuit in a typical FASTERIX simulation. The time taken for this is, in turn, dominated by the time taken to compute the scalar potential due to a particular charge distribution. Image theory for planar structures (Scott, 1990) shows that the potential due to a point charge in such a structure is the same as that due to an infinite series of point charges in a homogeneous medium. The infinite series is found to converge quite rapidly, and in practice a truncated series has been found to be accurate and fairly efficient. The form of an image series is very convenient for computations, so any method which can reduce the number of terms required for a given accuracy is very valuable in speeding up a simulation. The paper describes a method for reducing the number of terms required in the image series to obtain a given accuracy. The method is demonstrated for a particular PCB geometry, showing that considerable increases in both speed and accuracy are possible at the same time