# Prediction Errors due to Ignoring Field Coupling on Printed Circuit Boards

#### Abstract

Boards F. Sabath , H. Garbe University of Paderborn C-LAB, Paderborn, Germany University of Hannover, Hannover, Germany Abstract This paper deals with the coupling between traces on Printed Circuit Boards (PCB). Particularly a method is presented which allows to estimate the deviation of the current distribution on an active trace due to the omission of recoupling by an adjacent trace. An e ective characteristic impedance for the active trace is deduced by the use of the model of capacitive coupling. The comparison with the characteristic impedance of a single trace enables the estimation of the maximum error of the current distribution. The method is examined with real life con gurations on PCB. Introduction Compliance with the legal requirements is in principle a problem of the system design, and therefore, the electromagnetic behaviour of electronic equipment should be considered as early as possible. Ambient electromagnetic elds even of small magnitudes may cause a malfunctioning of a system due to the high sensitivity of modern{day pick{up devices. Therefore, the support of electronic{ and layout{designers with appropriate tools providing the possibility of characterising the electromagnetic behaviour of PCB traces is quite an important task. An analysis of the electromagnetic behaviour can be performed exactly by solving Maxwell's equations. Often and in particular for open area problems these equations are transformed into integral equations which are to be solved numerically. Here, the Method of Moments (MoM) is in widespread use [1]. Since its advent many computer programs have been developed, whereby the transmission lines are often represented via a ' lamentary current model'. Due to the complexity of conducting structures on PCB the MoM leads to matrix equations with large order. As many signal traces can be described using the multiconductor transmission line (MTL) equations there are e orts to combine the MoM with algorithmen based on the MTL-theory. Necessary component of such a hybrid method is an algorithm which decides whether a conducting structure has to be treated using the MoM or MTL{equations. In order to determine the method to be used essential items are the validity of the used model and the computation error which appears by ignoring coupling paths. In this paper a method is presented, which predicts the error of the current distribution on signal traces using the model of capacitive coupling. An example shows the correctness of the method and the e ect of the predicted error on other EMC relevant values. The Multiconductor Transmission Line A Multiconductor Transmission Line (MTL) is considered to be a uniform line in which the n conductors are parallel to each other as shown in Fig. 1, and the cross-sectional dimensions and properties of the conductors are constant along the line. Termination Network Termination Network

### Cite this paper

@inproceedings{Sabath1997PredictionED, title={Prediction Errors due to Ignoring Field Coupling on Printed Circuit Boards}, author={Frank Sabath}, year={1997} }