\chapter{Introduction}\label{introduction}

\section{Overview}

This manual describes the theory which underlies the Spice cable bundle modelling software SACAMOS. The SACAMOS software generates a Spice subcircuit which models the propagation of signals on multi-conductor transmission lines i.e. cables and bundles of cables. The models include the effects of crosstalk, transfer impedance coupling and incident field excitation as required by the user. The frequency dependence of the transmission line parameters is taken into account in the model. The resulting models take the form of Spice sub-circuits which may be linked to arbitrary termination circuits. The use of the SACAMOS software and the resulting cable models is described in the accompanying user guide \cite{sacamos_UG}.

The document is structured as follows:

Chapter \ref{MTLtheory} describes the multiconductor transmission line equations which form the basis for the Spice cable bundle model. The chapter includes a discussion of the per-unit-length paramters which characterise a multi-conductor transmission line, the solution of the transmission line equations and the inclusion of termination conditions into the solution. The method for including the effect of a plane wave incident field illuminating a transmission line into the multi-conductor transmission line equations is also described. 

Following this review of the theory of multi-conductor transmission lines, the Spice multi-conductor transmission line model is derived in chapter \ref{spice_cable_model}. The chapter provides an overview of the Spice model structure before describing the different aspects of the Spice cable bundle model; the domain decomposition approach to deal with shielded cables , the model for twisted pairs, the implementation of modal decomposition and the propagation model using method of characteristics (the technique used to incorporate the frequency dependent propagation model) and finally the transfer impedance coupling and incident field excitation models.

The ways in which the per-unit-length parameters of multi-conductor cables are calculated using a Finite Element method are described in chapter \ref{Laplace}. The 'filter fitting' process which is used to create s-domain transfer functions for frequency dependent aspects of the model is described in chapter \ref{fd_transfer_functions}. Following this the types of cable implemented in the software are described and the approximations made for each cable type are described in chapter \ref{cable_types}. Finally the implementation of frequency dependent transfer functions using passive circuit elements through a network synthesis process is described.

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