\chapter{SpaceWire cable models}

 The SpaceWire cable models, gauges 28 and 26 are derived from the standard \cite{3902/003} plus some additional information obtained from samples of cable for the shield transfer impedance specifications.
 
The low mass SpaceWire cable model is derived from the standard \cite{3902/004} plus some additional information obtained from samples of cable for the shield transfer impedance specifications.

The SpaceWire connector model is the 9 contact connector from the standard \cite{3401/071}.

\subsection{SpaceWire cable model}

The SpaceWire cable model parameters have beed determined as follows:

\begin{enumerate}
 
 \item 
 \begin{equation}
 comnductor\_radius = \sqrt{\frac{nominal\_section}{\pi}}          
 \end{equation}          
 DSC07340small.jpg
 \item 
 \begin{equation}
 dielectric\_radius = \frac{core\_max\_diameter}{2}                        
 \end{equation}          


\item  The conductor in the model is homogeneous so we need an effective conductivity. This is based on the maximum resistance (ohms/km). Note this is a single conductor resistance.
 \begin{equation}
 Conductivity = \frac{length}{(max\_resistance*nominal\_section)}
 \end{equation}          

\item  
The dielectric is expanded microporous PTFE whose relative permittivity for the purpose of the calculation of the capacitance matrix for the shielded twisted pair is assumed to be 1.5. This is somewhat higher than the quoted value of 1.3 but the model does not include the dielectric filler or the binder materials so it artificially increased to try and compensate. 

\item  
It is not possible now to use the dimensions in table 1a as these are maximum dimensions so I have an iterative process so as to obtain a viable twisted pair cross section with a differential mode impedance of 100 ohms. (Using the dimensions in table 1a gives an impedance of 140ohms).

It is assumed that the distance between the insulation of the twisted pair is 0.01mm. This ensures that the dielectrics do not touch in the model which will cause the mesh generation to fail.

The adjustable parameters are the inner dielectric radius, and the inner shield radius. 

\item  
The inner conductor separation (here = 2*dielectric radius +0.01mm)

\item  
The inner shield jacket radius is the inner shield radius + the maximum inner jacket wall radius =0.2mm (section 4.4.7.2 from \cite{3902/003}). This and the outer jacket are made of extruded fluoropolymer PFA for which I am using a relative permittivity of 2.1.

\item  
The shielded twisted pair radius and the outer shield radius are chosen to give a sensible looking cable cross section while keeping within the maximum cable diameter (table 1a.)

\item 
The outer jacket thickness is 0.25mm (section 4.4.7.2 from \cite{3902/003})

\item  Shield models.

The shield conductivity is taken to be the same as for the inner wires and the shield thickness is set to zero in the \textbf{.cable\_spec} file - this then allows the software to calculate an 'equivalent thickness' so that the d.c. resistance of the shield is equal to the d.c. transfer impedance. 

The shield transfer impedance models for the inner and outer shields cannot be based on the shielding effectiveness curve in figure 1b as this relates to the shielding effectiveness of the combination of inner and outer shields, connected together.

The shield transfer impedance models are obtained by directly measuring the braid geometry of samples of both AWG28 and AWG26 SpaceWire cables and Low Mass SpaceWire cable. From photographs of both the inner and outer braids, the number of carriers, number of wires in a carrier and the pitch angle of the braid can be determined. 
From this specification the theory of Kley \cite{Kley} in appendix 1 is used to calculate a transfer impedance model of the form $Z_T=R_T+j\omega L_T$.

 
$R_T$ is found as $\Re\left\{{Z_T}\right\}$ as $f \rightarrow 0$ and $L_T$ is found as $\frac{\Im\left\{{Z_T}\right\}}{j\omega}$ at a suitably high frequency (1GHz here).
 

\end{enumerate}

The shielding effectiveness of the SpaceWire models are shown in figures \ref{fig_SE28} and \ref{fig_SE26} respectively. These curves can be compared with figure 1b in the ESCC specification document.

\begin{figure}[h]
\centering
\includegraphics[scale=0.6]{./Imgs/SPICE_MODEL_SPACEWIRE_AWG28_V1_SHIELDING_EFFECTIVENESS_result.jpg}
\caption{AWG 28 V1 SpaceWire Shielding Effectiveness}
\label{fig_SE28}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[scale=0.6]{./Imgs/SPICE_MODEL_SPACEWIRE_AWG26_V2_SHIELDING_EFFECTIVENESS_result.jpg}
\caption{AWG 26 V2 SpaceWire Shielding Effectiveness}
\label{fig_SE26}
\end{figure}


\subsection{Low Mass SpaceWire cable model}

The low mass SpaceWire cable model is derived in exactly the same way as the SpaceWire models. It should be noted that there is no insulation between the inner and outer shields of low mass SpaceWire although the model assumes that there is. This can lead to modes propagating in the model in the region between the inner and outer shields which will not exist in the real cable. This is illustrated in the shielding effectiveness calculation shown in figure \ref{fig_SE_low_mass_1} which shows the shielding effectiveness of 1m of the Low Mass spaceWire cable
model. A model which is more representative of the real cable can be constructed by building the 1m cable from 10cm sections and connecting the inner shields and the outer shield together between each of the sections. The shielding effectivenes obtained from this model is shown in figure \ref{fig_SE_low_mass_2}.

\begin{figure}[h]
\centering
\includegraphics[scale=0.6]{./Imgs/SPICE_MODEL_LOW_MASS_SPACEWIRE_SHIELDING_EFFECTIVENESS_result.jpg}
\caption{Low Mass Spacewire shielding effectiveness}
\label{fig_SE_low_mass_1}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[scale=0.6]{./Imgs/Low_mass_spacewire_SE_10x10cm.jpg}
\caption{Low Mass Spacewire shielding effectiveness which shields connected every 10cm}
\label{fig_SE_low_mass_2}
\end{figure}

\subsection{SpaceWire connector model}

The SpaceWire connector model is specified as a Dconnector in the SACAMOS software. The parameters for the Dconnector model are obtained from the standard  \cite{3401/071} as follows:

\begin{enumerate}
 
 \item   conductor\_radius: fig 2.1 a,b
 
 \item   conductor\_pitch (x\_separation): fig 2.1 a,b
 
 \item   conductor y\_separation: fig 2.1 a,b
 
 \item   offset from conductors to shell:fig 2.1 a,b; 0.5*(G-y\_separation-2*conductor\_radius)
 
\end{enumerate}


\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
Dconnector
10		# number of conductors. This model from ESCC 3401/071, 9 pin connector 
4		# number of parameters
0.43e-3  	# parameter 1: conductor radius: fig 2.1 a,b
1.27e-3  	# parameter 2: conductor pitch (separation in x): fig 2.1 a,b
1.09e-3  	# parameter 3: conductor separation in y: fig 2.1 a,b

1.37e-3  	# parameter 4: offset from conductors to shell:fig 2.1 a,b; 
                               0.5*(G-yseparation-2*rw)

0		# number of frequency dependent parameters
0		# number of transfer impedance models
use_laplace
\end{verbatim}



\clearpage