\chapter{File Formats} \label{file_formats}

This chapter describes the file formats used as the input to the spice cable bundle model building process.
There are three processes in the creation of a spice cable bundle model. These are:

\begin{enumerate}
\item cable model building process
\item cable bundle model building process
\item spice cable bundle model building process
\end{enumerate}
Frequency dependent parameters

The file formats used to drive each of these processes are described in the following sections.

\section{Cable Specification File Formats} \label{Cable_spec_file_formats}

This section describes the cable specification file formats used as the input to the cable model building process.
Cable specification files have the extension \textbf{name.cable\_spec}.

Models of the following cable types have been developed:

\begin{enumerate}
\item Cylindrical conductor
\item Cylindrical conductor with dielectric
\item Frequency Dependent Cylindrical conductor with dielectric
\item Coaxial cable
\item Frequency Dependent Coaxial cable
\item Frequency Dependent Coaxial cable with transfer impedance
\item Twinax cable
\item Frequency Dependent Twinax cable with transfer impedance
\item Twisted pair
\item Frequency Dependent Twisted pair
\item Shielded twisted pair
\item Frequency Dependent Shielded twisted pair with transfer impedance
\item Spacewire
\item Frequency Dependent Spacewire with transfer impedance
\item Frequency Dependent Overshield with transfer impedance
\end{enumerate}


Frequency dependent parameters may be defined using a rational function form for example a frequency dependent dielectric may
be represented using the following form
\begin{equation} \label{eq:rational_permittivity}
\epsilon_{r}=\frac{a_0+ a_1 \left( \frac{j\omega}{\omega_0} \right) +a_2 \left( \frac{j\omega}{\omega_0} \right)^2 + \cdots}{b_0+ b_1 \left( \frac{j\omega}{\omega_0} \right) +b_2 \left( \frac{j\omega}{\omega_0} \right)^2 + \cdots}
\end{equation}

Within a cable specification file this frequency dependent data is specified in the following format:

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{5cm} |}
    \hline
    Line number & Typical value   & Description \\ \hline
1       & \# dielectric model  & Comment line \\ \hline
2       & 1E8             & $\omega_{0}$ (rad/second)   \\ \hline
3       &  1  & order of numerator \\ \hline
4       &    2.60        2.25  & list of numerator (a) coefficients \\ \hline
5       &  1  & order of numerator \\ \hline
6       &    1.0        1.0  & list of denominator (b) coefficients \\ \hline
    \end{tabular}
\end{center}

In addition to the information required to specifiy a cable, additional flags to control the operation of the software can be
included. These flags consist of text commands. The available flags and their effect are as follows

\begin{enumerate}
\item 'verbose'    output detailed summary of the software operation and calculation results.\\
\item 'use_laplace'    use the numerical Laplace solver to calculate inductance and capacitance matrices where 
appropriate (i.e. where an exact analytic solution is not available.) By default, approximate analytic formulae are used. \\
\end{enumerate}

The file formats required to specify each of these cable types is described in the folllowing sub-sections together with an example.

\subsection{Cylindrical conductor format} \label{Cylindrical_conductor_file_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & cylindrical   & -             & Cable type. Note there should be nothing else on this line \\ \hline
4       & 1             & integer 	& Number of conductors, always 1 for cylindrical cables \\ \hline
5       & 1             & integer 	& Number of parameters, always 1 for cylindrical cables \\ \hline
6       & 0.25e-3       & metre         & parameter 1: conductor radius \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
cylindrical
1		# number of conductors
1		# number of parameters
1.905e-4  	# parameter 1: conductor radius
\end{verbatim}


\subsection{Cylindrical conductor with dielectric format} \label{Cylindrical_conductor_dielectric_file_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & cylindrical\_with\_dielectric   & -   & Cable type. Note there should be nothing else on this line \\ \hline
4       & 1             & integer 	& Number of conductors, always 1 for cylindrical cables with dielectric \\ \hline
5       & 3             & integer 	& Number of parameters, always 3 for cylindrical cables with dielectric \\ \hline
6       & 0.25e-3       & metre         & parameter 1: conductor radius \\ \hline
7       & 0.65e-3       & metre         & parameter 2: outer dielectric radius \\ \hline
8       & 2.25          & -             & parameter 3: realtive permittivity of dielectric \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
cylindrical_with_dielectric
1		# number of conductors
3		# number of parameters
1.905e-4  	# parameter 1: conductor radius
0.5e-3  	# parameter 2: dielectric radius
2.25  	        # parameter 3: dielectric relative permittivity
\end{verbatim}


\subsection{Frequency dependent cylindrical conductor with dielectric coating format} \label{FD_Cylindrical_conductor_dielectric_file_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & FD\_cylindrical\_with\_dielectric   & -   & Cable type. Note there should be nothing else on this line \\ \hline
4       & 1             & integer 	& Number of conductors, always 1 for cylindrical cables with dielectric \\ \hline
5       & 3             & integer 	& Number of parameters, always 3 for frequency dependent cylindrical cables with dielectric \\ \hline
6       & 0.25e-3       & metre         & parameter 1: conductor radius \\ \hline
6       & 0.5e-3       & metre          & parameter 2: dielectric radius \\ \hline
7       & 5e7           & Siemens/metre & parameter 3: electric conductivity \\ \hline
8       & 1             & integer 	& Number of frequency dependent parameters, always 1 for frequency dependent cylindrical cables with dielectric \\ \hline
9      & \# Dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
10      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
11      & 1 & integer & order of numerator model \\ \hline
12      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
13      & 1 & integer & order of denominator model \\ \hline
14      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
FD_cylindrical_with_dielectric
1		# number of conductors
3		# number of parameters
1.905e-4  	# parameter 1: conductor radius
0.5e-3  	# parameter 2: dielectric radius
5E7  	        # parameter 3: conductivity
1		# number of frequency dependent parameters
# dielectric relative permittivity model follows
   1E8        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.60        2.25           
           1   # b order, b coefficients follow below:
  1.0         1.0    
\end{verbatim}


\subsection{Coaxial cable format} \label{coaxial_cable_file_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & coaxial   & -                 & Cable type. Note there should be nothing else on this line \\ \hline
4       & 2             & integer 	& Number of conductors, always 2 for coaxial cables \\ \hline
5       & 5             & integer 	& Number of parameters, always 5 for coaxial cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 1.5e-3       & metre          & parameter 2: shield radius \\ \hline
8       & 2.25          &   -           & parameter 3: relative permittivity of inner dielectric \\ \hline
9       & 2.5e-3       & metre          & parameter 4: outer insulation radius \\ \hline
10      & 2.5           &   -           & parameter 5: relative permittivity of outer dielectric \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
coaxial         # cable type
2		# number of conductors
5		# NUMBER OF PARAMETERS
0.00042  	# parameter 1: inner conductor radius (m)
0.00147 	# parameter 2: shield radius (m)
2.25   		# parameter 3: relative permittivity of inner dielectric
0.0025 	        # parameter 4: outer insulation radius (m)
2.50  		# parameter 5: relative permittivity of outer dielectric
\end{verbatim}

\subsection{Frequency dependent coaxial cable format} \label{FD_coaxial_cable_file_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & FD\_coaxial   & -             & Cable type. Note there should be nothing else on this line \\ \hline
4       & 2             & integer 	& Number of conductors, always 2 for FD\_coaxial cables \\ \hline
5       & 5             & integer 	& Number of parameters, always 4 for FD\_coaxial cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 1.5e-3        & metre         & parameter 2: shield radius \\ \hline
8       & 2.5e-3        & metre         & parameter 3: outer insulation radius \\ \hline
9       & 5e7           & Siemens/metre & parameter 4: inner conductor electric conductivity \\ \hline
10      & 2		& integer       & number of frequency dependent parameters \\ \hline
11      & \# Inner dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
12      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
13      & 1 & integer & order of numerator model \\ \hline
14      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
15      & 1 & integer & order of denominator model \\ \hline
16      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
17      & \# Outer dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
18      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
19      & 1 & integer & order of numerator model \\ \hline
20      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
21      & 1 & integer & order of denominator model \\ \hline
22      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
FD_coaxial         # cable type
2		# number of conductors
5		# NUMBER OF PARAMETERS
0.00042  	# parameter 1: inner conductor radius (m)
0.00147 	# parameter 2: shield radius (m)
0.0025 	        # parameter 3: outer insulation radius (m)
5e7             # parameter 4: inner conductor electric conductivity
5e7             # parameter 5: shield electric conductivity
2               # number of frequency dependent parameters
# Inner dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.6        2.0           
           1   # b order, b coefficients follow below:
  1.0         1.0    
# Outer dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.40        2.20           
           1   # b order, b coefficients follow below:
  1.0         1.0    
\end{verbatim}

\subsection{Frequency dependent coaxial cable with transfer impedance format} \label{ZT_FD_coaxial_cable_file_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & ZT\_FD\_coaxial   & -             & Cable type. Note there should be nothing else on this line \\ \hline
4       & 2             & integer 	& Number of conductors, always 2 for FD\_coaxial cables \\ \hline
5       & 5             & integer 	& Number of parameters, always 4 for FD\_coaxial cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 1.5e-3        & metre         & parameter 2: shield radius \\ \hline
8       & 2.5e-3        & metre         & parameter 3: outer insulation radius \\ \hline
9       & 5e7           & Siemens/metre & parameter 4: inner conductor electric conductivity \\ \hline
10      & 2		& integer       & number of frequency dependent parameters \\ \hline
11      & \# Inner dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
12      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
13      & 1 & integer & order of numerator model \\ \hline
14      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
15      & 1 & integer & order of denominator model \\ \hline
16      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
17      & \# Outer dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
18      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
19      & 1 & integer & order of numerator model \\ \hline
20      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
21      & 1 & integer & order of denominator model \\ \hline
22      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
23      & 1		& integer       & number of frequency dependent transfer ipedance models \\ \hline
24      & \# Transfer impedance & - & Comment line Frequency dependent transfer impedance model follows\\ \hline
25      & 1.0 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
26      & 1 & integer & order of numerator model \\ \hline
27      &  0.05  1.6E-9 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
28      & 0 & integer & order of denominator model \\ \hline
29      &  1.0   & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
ZT_FD_coaxial         # cable type
2		# number of conductors
5		# NUMBER OF PARAMETERS
0.00042  	# parameter 1: inner conductor radius (m)
0.00147 	# parameter 2: shield radius (m)
0.0025 	        # parameter 3: outer insulation radius (m)
5e7             # parameter 4: inner conductor electric conductivity
5e7             # parameter 5: shield electric conductivity
2               # number of frequency dependent parameters
# Inner dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.6        2.0           
           1   # b order, b coefficients follow below:
  1.0         1.0    
# Outer dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.40        2.20           
           1   # b order, b coefficients follow below:
  1.0         1.0    
1             & integer       & number of frequency dependent transfer ipedance models 
# Transfer impedance model 
1.0           # angular frequency normalisation
1             # order of numerator model 
0.05  1.6E-9  # list of numerator coefficients a0 a1 a2... 
0             # order of denominator model
1.0           # list of denominator coefficients b0 b1 b2...
\end{verbatim}

\subsection{Twinax cable} \label{twinax_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & twinax   & -                  & Cable type. Note there should be nothing else on this line \\ \hline
4       & 3             & integer 	& Number of conductors, always 3 for twinax cables \\ \hline
5       & 6             & integer 	& Number of parameters, always 6 for twinax cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 0.4e-3        & metre         & parameter 2: conductor separation \\ \hline
8       & 1.5e-3        & metre         & parameter 3: shield radius \\ \hline
9       & 2.25          &   -           & parameter 4: relative permittivity of inner dielectric \\ \hline
10      & 2.5e-3        & metre         & parameter 5: outer dielectric radius \\ \hline
11      & 2.5           &   -           & parameter 6: relative permittivity of outer dielectric \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
twinax
3		# number of conductors
6		# number of parameters
0.25e-3  	# parameter 1: conductor radius
1.0e-3  	# parameter 2: conductor separation
2.0e-3  	# parameter 3: shield radius
1.00     	# parameter 4: inner dielectric relative permittivity
3.0e-3     	# parameter 5: outer dielectric radius
1.00     	# parameter 6: outer dielectric relative permittivity
\end{verbatim}


\subsection{Frequency dependent twinax cable with transfer impedance} \label{ZT_FD_twinax_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & ZT_FD_twinax   & -            & Cable type. Note there should be nothing else on this line \\ \hline
4       & 3             & integer 	& Number of conductors, always 3 for frequency dependent twinax cables \\ \hline
5       & 6             & integer 	& Number of parameters, always 6 for frequency dependent twinax cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 0.18e-3       & metre         & parameter 2: inner dielectric radius \\ \hline
8       & 0.4e-3        & metre         & parameter 3: conductor separation \\ \hline
9       & 1.5e-3        & metre         & parameter 4: shield radius \\ \hline
10      & 2.5e-3        & metre         & parameter 5: outer dielectric radius \\ \hline
11      & 5e7           & Siemens/metre & parameter 6: inner conductor electric conductivity \\ \hline
12      & 2		& integer       & number of frequency dependent parameters \\ \hline
13      & \# Inner dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
14      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
15      & 1 & integer & order of numerator model \\ \hline
16      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
17      & 1 & integer & order of denominator model \\ \hline
18      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
19      & \# Outer dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
20      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
21      & 1 & integer & order of numerator model \\ \hline
22      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
23      & 1 & integer & order of denominator model \\ \hline
24      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
25      & 1		& integer       & number of frequency dependent transfer ipedance models \\ \hline
26      & \# Transfer impedance & - & Comment line Frequency dependent transfer impedance model follows\\ \hline
27      & 1.0 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
28      & 1 & integer & order of numerator model \\ \hline
29      &  0.05  1.6E-9 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
29      & 0 & integer & order of denominator model \\ \hline
30      &  1.0   & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
ZT_FD_twinax
3              Number of conductors 
6              Number of parameters
0.25e-3        parameter 1: inner conductor radius 
0.40e-3        parameter 2: inner dielectric radius 
1.0e-3         parameter 3: inner conductor separation 
2.0e-3         parameter 4: shield radius 
2.5e-3         parameter 5: outer dielectric radius 
5e7            parameter 6: inner conductor electric conductivity 
2	       number of frequency dependent parameters 
# Inner dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.6        2.0           
           1   # b order, b coefficients follow below:
  1.0         1.0    
# Outer dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.40        2.20           
           1   # b order, b coefficients follow below:
  1.0         1.0    
1             & integer       & number of frequency dependent transfer ipedance models 
# Transfer impedance model 
1.0           # angular frequency normalisation
1             # order of numerator model 
0.05  1.6E-9  # list of numerator coefficients a0 a1 a2... 
0             # order of denominator model
1.0           # list of denominator coefficients b0 b1 b2...
\end{verbatim}


\subsection{Twisted pair} \label{twisted_pair_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & twisted\_pair & -             & Cable type. Note there should be nothing else on this line \\ \hline
4       & 2             & integer 	& Number of conductors, always 2 for twisted pair cables \\ \hline
5       & 4             & integer 	& Number of parameters, always 4 for twisted pair cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: conductor radius \\ \hline
7       & 0.4e-3        & metre         & parameter 2: conductor separation \\ \hline
8       & 2.5e-3       & metre          & parameter 3: outer dielectric radius \\ \hline
9       & 2.5           &   -           & parameter 4: relative permittivity of outer dielectric \\ \hline
    \end{tabular}
\end{center}


\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
twisted_pair
2		# number of conductors
4		# number of parameters
0.25e-3  	# parameter 1: conductor radius
1.0e-3  	# parameter 2: conductor separation
0.45e-3  	# parameter 3: dielectric radius
2.5     	# parameter 4: dielectric relative permittivity
\end{verbatim}

\subsection{Frequency Dependent Twisted pair} \label{FD_twisted_pair_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & FD\_twisted\_pair & -         & Cable type. Note there should be nothing else on this line \\ \hline
4       & 2             & integer 	& Number of conductors, always 2 for frequency dependent twisted pair cables \\ \hline
5       & 4             & integer 	& Number of parameters, always 4 for frequency dependent twisted pair cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: conductor radius \\ \hline
7       & 0.4e-3        & metre         & parameter 2: conductor separation \\ \hline
8       & 2.5e-3        & metre         & parameter 3: outer dielectric radius \\ \hline
9       & 5e7           & Siemens/metre & parameter 4: inner conductor electric conductivity \\ \hline
10       & 1		& integer       & number of frequency dependent parameters \\ \hline
11      & \# Dielectric & - & Comment line Frequency dependent dielectric relative permittivity model \\ \hline
12      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
13      & 1 & integer & order of numerator model \\ \hline
14      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
15      & 1 & integer & order of denominator model \\ \hline
16      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}


\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
FD_twisted_pair
2		# number of conductors
4		# number of parameters
0.25e-3  	# parameter 1: conductor radius
1.0e-3  	# parameter 2: conductor separation
0.45e-3  	# parameter 3: dielectric radius
5e7             # parameter 4: inner conductor electric conductivity
# Dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.40        2.20           
           1   # b order, b coefficients follow below:
  1.0         1.0    
\end{verbatim}

\subsection{Shielded twisted pair} \label{shielded_twisted_pair_formats}


\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & shielded\_twisted\_pair & -   & Cable type. Note there should be nothing else on this line \\ \hline
4       & 3             & integer 	& Number of conductors, always 3 for shielded twisted pair cables \\ \hline
5       & 6             & integer 	& Number of parameters, always 6 for shielded twisted pair cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 0.4e-3        & metre         & parameter 2: conductor separation \\ \hline
8       & 1.5e-3        & metre         & parameter 3: shield radius \\ \hline
9       & 2.25          &   -           & parameter 4: relative permittivity of inner dielectric \\ \hline
10      & 2.5e-3       & metre        & parameter 5: outer dielectric radius \\ \hline
11      & 2.5           &   -           & parameter 6: relative permittivity of outer dielectric \\ \hline
    \end{tabular}
\end{center}


\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
shielded_twisted_pair
3		# number of conductors
6		# number of parameters
0.25e-3  	# parameter 1: conductor radius
1.0e-3  	# parameter 2: conductor separation
2.0e-3  	# parameter 3: shield radius
2.25     	# parameter 4: inner dielectric relative permittivity
3.0e-3     	# parameter 5: outer dielectric radius
2.5     	# parameter 6: outer dielectric relative permittivity
\end{verbatim}




\subsection{Frequency dependent shielded twisted pair cable with transfer impedance} \label{ZT_FD_shielded_twisted_pair_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & ZT_FD_shielded_twisted_pair   & -                  & Cable type. Note there should be nothing else on this line \\ \hline
4       & 3             & integer 	& Number of conductors, always 3 for frequency dependent shielded twisted pair cables \\ \hline
5       & 6             & integer 	& Number of parameters, always 6 for frequency dependent shielded twisted pair cables \\ \hline
6       & 0.1e-3        & metre         & parameter 1: inner conductor radius \\ \hline
7       & 0.18e-3       & metre         & parameter 2: inner dielectric radius \\ \hline
8       & 0.4e-3        & metre         & parameter 3: conductor separation \\ \hline
9       & 1.5e-3        & metre         & parameter 4: shield radius \\ \hline
10      & 2.5e-3        & metre         & parameter 5: outer dielectric radius \\ \hline
11       & 5e7           & Siemens/metre & parameter 6: inner conductor electric conductivity \\ \hline
12      & 2		& integer       & number of frequency dependent parameters \\ \hline
13      & \# Inner dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
14      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
15      & 1 & integer & order of numerator model \\ \hline
16      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
16      & 1 & integer & order of denominator model \\ \hline
17      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
18      & \# Outer dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
19      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
20      & 1 & integer & order of numerator model \\ \hline
21      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
22      & 1 & integer & order of denominator model \\ \hline
23      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
24      & 1		& integer       & number of frequency dependent transfer ipedance models \\ \hline
25      & \# Transfer impedance & - & Comment line Frequency dependent transfer impedance model follows\\ \hline
26      & 1.0 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
27      & 1 & integer & order of numerator model \\ \hline
28      &  0.05  1.6E-9 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
29      & 0 & integer & order of denominator model \\ \hline
30      &  1.0   & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
ZT_FD_shielded_twisted_pair
3              Number of conductors 
6              Number of parameters
0.25e-3        parameter 1: inner conductor radius 
0.40e-3        parameter 2: inner dielectric radius 
1.0e-3         parameter 3: inner conductor separation 
2.0e-3         parameter 4: shield radius 
2.5e-3         parameter 5: outer dielectric radius 
5e7            parameter 6: inner conductor electric conductivity
2	       number of frequency dependent parameters 
# Inner dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.6        2.0           
           1   # b order, b coefficients follow below:
  1.0         1.0    
# Outer dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.40        2.20           
           1   # b order, b coefficients follow below:
  1.0         1.0    
1             & integer       & number of frequency dependent transfer ipedance models 
# Transfer impedance model 
1.0           # angular frequency normalisation
1             # order of numerator model 
0.05  1.6E-9  # list of numerator coefficients a0 a1 a2... 
0             # order of denominator model
1.0           # list of denominator coefficients b0 b1 b2...
\end{verbatim}




\subsection{Spacewire} \label{spacewire_formats}


\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .              & -             & Directory to write the cable model file to \\ \hline
3       & spacewire & -  & Cable type. Note there should be nothing else on this line \\ \hline
4       & 13             & integer 	& Number of conductors, always 13 for spacewire \\ \hline
5       & 10             & integer 	& Number of parameters, always 10 for spacewire \\ \hline
6       & 0.1e-3         & metre         & parameter 1: inner conductor radius \\ \hline
7       & 0.4e-3         & metre         & parameter 2: conductor separation \\ \hline
8       & 0.8e-3         & metre         & parameter 3: inner sheild radius \\ \hline
9       & 2.25           &   -           & parameter 4: inner dielectric relative permittivity\\ \hline
10       & 1.0e-3         & metre         & parameter 5: inner shield jacket radius \\ \hline
11       & 2.25           &   -           & parameter 6: inner shield jacket relative permittivity\\ \hline
12      & 2.0e-3         & metre          & parameter 7: shielded twisted pair radius \\ \hline
13      & 4.5e-3         & metre          & parameter 8: outer shield radius \\ \hline
14      & 5.0e-3         & metre          & parameter 9: outer dielectric radius \\ \hline
15      & 2.5            &   -           & parameter 10: outer dielectric relative permittivity\\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
spacewire
13		# number of conductors
10		# number of parameters
0.25e-3  	# parameter 1: inner conductor radius
1.0e-3  	# parameter 2: inner conductor separation
2.0e-3  	# parameter 3: inner shield radius
2.2     	# parameter 4: inner dielectric relative permittivity
2.2e-3  	# parameter 5: inner shield jacket radius
2.5      	# parameter 6: inner shield jacket relative permittivity
4.0e-3     	# parameter 7: shielded twisted pair radius
8.0e-3     	# parameter 8: outer shield radius
9.0e-3     	# parameter 9: outer dielectric radius
2.25     	# parameter 10: outer dielectric relative permittivity
\end{verbatim}



\subsection{Frequency dependent spacewire with transfer impedance} \label{ZT_FD_spacewire_formats}


\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .              & -            & Directory to write the cable model file to \\ \hline
3       & ZT\_FD\_spacewire & -         & Cable type. Note there should be nothing else on this line \\ \hline
4       & 13             & integer 	& Number of conductors, always 13 for ZT\_FD\_spacewire \\ \hline
5       & 9              & integer 	& Number of parameters, always 9 for ZT\_FD\_spacewire \\ \hline
6       & 0.1e-3         & metre        & parameter 1: inner conductor radius \\ \hline
7       & 0.18e-3        & metre        & parameter 2: inner dielectric radius \\ \hline
8       & 0.4e-3         & metre        & parameter 3: conductor separation \\ \hline
9       & 0.8e-3         & metre        & parameter 4: inner sheild radius \\ \hline
10      & 1.0e-3         & metre        & parameter 5: inner shield jacket radius \\ \hline
11      & 2.0e-3         & metre        & parameter 6: shielded twisted pair radius \\ \hline
12      & 4.5e-3         & metre        & parameter 7: outer shield radius \\ \hline
13      & 5.0e-3         & metre        & parameter 8: outer dielectric radius \\ \hline
14      & 5e7           & Siemens/metre & parameter 9: inner conductor electric conductivity \\ \hline
15      & 2		& integer       & number of frequency dependent parameters \\ \hline
16      & \# Inner dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
17      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
18      & 1 & integer & order of numerator model \\ \hline
19      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
20      & 1 & integer & order of denominator model \\ \hline
21      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
22      & \# Outer dielectric & - & Comment line Frequency dependent inner dielectric relative permittivity model \\ \hline
23      & 1E8 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
24      & 1 & integer & order of numerator model \\ \hline
25      &  2.6  2.0 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
26      & 1 & integer & order of denominator model \\ \hline
27      &  1.0  1.0 & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
28      & 2		& integer       & number of frequency dependent transfer ipedance models \\ \hline
29      & \# Inner shield transfer impedance & - & Comment line Frequency dependent transfer impedance model follows\\ \hline
30      & 1.0 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
31      & 1 & integer & order of numerator model \\ \hline
32      &  0.05  1.6E-9 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
33      & 0 & integer & order of denominator model \\ \hline
34      &  1.0   & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
35      & \# Outer shield transfer impedance & - & Comment line Frequency dependent transfer impedance model follows\\ \hline
36      & 1.0 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
37      & 1 & integer & order of numerator model \\ \hline
38      &  0.02  1.9E-9 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
39      & 0 & integer & order of denominator model \\ \hline
40      &  1.0   & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
.
spacewire
13		# number of conductors
9               # Number of parameters
0.25e-3         # parameter 1: inner conductor radius
0.40e-3         # parameter 2: inner dielectric radius
1.0e-3          # parameter 3: inner conductor separation
2.0e-3          # parameter 4: inner shield radius
2.25e-3         # parameter 5: inner shield jacket radius 
3.25e-3         # parameter 6: shielded twisted pair radius 
5.5e-3          # parameter 7: outer shield radius 
6.25e-3         # parameter 8: outer dielectric radius
5e7             # parameter 9: inner conductor electric conductivity
2	       number of frequency dependent parameters 
# Inner dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.6        2.0           
           1   # b order, b coefficients follow below:
  1.0         1.0    
# Outer dielectric relative permittivity model follows
   1E7        # w normalisation constant
           1   # a order, a coefficients follow below:
  2.40        2.20           
           1   # b order, b coefficients follow below:
  1.0         1.0    
2             & integer       & number of frequency dependent transfer ipedance models 
# Inner shield Transfer impedance model
1.0           # angular frequency normalisation
1             # order of numerator model 
0.05  1.6E-9  # list of numerator coefficients a0 a1 a2... 
0             # order of denominator model
1.0           # list of denominator coefficients b0 b1 b2...
# Outer shield Transfer impedance model
1.0           # angular frequency normalisation
1             # order of numerator model 
0.002  2.8E-9  # list of numerator coefficients a0 a1 a2... 
0             # order of denominator model
1.0           # list of denominator coefficients b0 b1 b2...
\end{verbatim}

\subsection{Overshield format} \label{overshield_formats}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to write the cable model file to \\ \hline
3       & overshield    & -              & Cable type. Note there should be nothing else on this line \\ \hline
4       & 1             & integer 	& Number of conductors, always 1 for an overshield \\ \hline
5       & 0             & integer 	& Number of parameters, always 1 for an overshield \\ \hline
6       & 0.005	        & m             & \# parameter 1: overshield radius \\ \hline
7       & 0		& integer       & number of frequency dependent parameters \\ \hline
8       & 1		& integer       & number of frequency dependent transfer impedance models \\ \hline
9       & \# Transfer impedance & - & Comment line Frequency dependent transfer impedance model follows\\ \hline
10      & 1.0 & rad/second & angular frequency normalisation, $\omega_{0}$ \\ \hline
11      & 1 & integer & order of numerator model \\ \hline
12      &  0.05  1.6E-9 & (order+1) reals & list of numerator coefficients a0 a1 a2... \\ \hline
13      & 0 & integer & order of denominator model \\ \hline
14      &  1.0  & (order+1) reals & list of denominator coefficients b0 b1 b2... \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
overshield  # cable type
1	       # number of conductors
1	       # number of parameters
0.005	       # parameter 1: overshield radius
0              # number of frequency dependent parameters
1              # number of frequency dependent transfer impedance models
# Transfer impedance model 
1.0            #  angular frequency normalisation
1              #  order of numerator model
0.05  1.6E-9   #  list of numerator coefficients a0 a1 a2... 
0              #  order of denominator model 
1.0            #  list of denominator coefficients b0 b1 b2... 
\end{verbatim}

\section{Cable Bundle Specification File Formats} \label{Cable_bundle_spec_file_formats}

This section describes the cable bundle specification file formats used as the input to the cable bundle model building process.
Cable bundle specification files have the extension \textbf{name.bundle\_spec}. The inputs required are the cables which constitute the bundle and their configuration in the bundle cross section, an indication of the presence or absence of a ground plane and if a ground plane is present, its configuration in the bundle cross section.

In addition to the data required to specify a cable bundle, additional flags may be specified to influence the operation of the software. These flags are as follows:
\begin{enumerate}
\item 'verbose'    output detailed summary of the software operation and calculation results.\\
\item 'use_laplace'    use the numerical Laplace solver to calculate inductance and capacitance matrices for the external domain and any overshielded domains. By default, approximate analytic formulae are used. \\
\end{enumerate}

\begin{figure}[h]
\centering
\includegraphics[scale=1]{./Imgs/ground_plane_specification.pdf}
\caption{Specification of the ground plane position in the bundle cross section}
\label{fig_ground_plane_specification}
\end{figure}

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to read the cable model file to \\ \hline
3       & \#MOD\_bundle\_lib\_dir & -    & Comment line \\ \hline
4       & .             & -             & Directory to write the cable bundle model file to \\ \hline
5       & 2             & integer 	& Number of cables in the cable bundle \\ \hline
\\ \hline
For each cable: & & & \\ \hline
-       & cable name           & - 	& Name of cable in the cable model directory \\ \hline
-       & 0.02 0.045           & metres metres & x and y coordinates of the centre of the cable in the bundle cross section \\ \hline
\\ \hline
-       & ground\_plane  & - 	& ground\_plane or no\_ground\_plane as required for the bundlle\\ \hline
-       & $\theta$ d           & degrees metres & If a ground plane is specified then propvide the angle of the ground plane normal measured from the x axis and offset from the origin along the normal direction figure \ref{fig_ground_plane_specification} \\ \hline
    \end{tabular}
\end{center}

\vspace{5mm}
\textbf{\underline{Example}}

Bundle model name: two\_wires\_over\_ground 

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
#MOD_bundle_lib_dir
LIBRARY_OF_BUNDLE_MODELS
2    # Number of cables in bundle, cable list follows
single_wire
6.35e-4     -0.001
single_wire
6.35e-4     0.001
ground_plane
0.0  0.0  ! angle and offset of ground plane
\end{verbatim}

\section{Spice Cable Bundle Specification File Formats} \label{Spice_cable_bundle_spec_file_formats}

This section describes the spice cable bundle specification file formats used as the input to the spice cable bundle model building process.
Spice cable bundle specification files have the extension \textbf{name.spice\_model\_spec}.

The input file to the spice cable bundle building processs includes the bundle name, bundle length, incident field specification (if required) and the specification of the validation test configuration.

In addition information regarding the transfer impedance models to be included and also
information to control the transfer function fitting process can be specified. 

The validation test configuration is shown in figure \ref{fig_validation_test_case_config}

\begin{figure}[h]
\centering
\includegraphics[scale=1]{./Imgs/validation_test_case_configuration_portrait.pdf}
\caption{Validation test case configuration}
\label{fig_validation_test_case_config}
\end{figure}

The file format with no transfer impdance models or transfer function fitting information is as follows:

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to read the cable model file to \\ \hline
3       & \#MOD\_bundle\_lib\_dir & -    & Comment line \\ \hline
4       & .             & -             & Directory to read the cable bundle model file from \\ \hline
5       & \#MOD\_spice\_bundle\_lib\_dir & -    & Comment line \\ \hline
6       & .             & -             & Directory to write the spice cable bundle model file to \\ \hline
7       & \# two wires over ground plane, crosstalk model  & -    & Comment line \\ \hline
8       & two\_wires\_over\_ground    & -              & Cable bundle name Note there should be nothing else on this line \\ \hline
9       & \# bundle length  & -    & Comment line \\ \hline
10       & 2.0    & metres              & Cable bundle length \\ \hline
11       & \# incident field specification  & -    & Comment line \\ \hline
12       & 0.0    & V/m          & Amplitude \\ \hline
13       & 90.0  0.0  & degrees          & Wave vector angle k$\theta$ k$\phi$ \\ \hline
14       & 1.0  0.0  & degrees          & Polarisation E$\theta$ E$\phi$ \\ \hline
15       & \# End 1 termination model  & -    & Number of sources and resistances = number of conductors-1 \\ \hline
16       & 1.0    & V          & End 1, conductor 1 voltage source amplitude \\ \hline
-       & 0.0    & V          & End 1, conductor 2 voltage source amplitude \\ \hline
-       & 50.0    & $\Omega$          & End 1, conductor 1 resistance \\ \hline
-       & 25.0    & $\Omega$          & End 1, conductor 2 resistance \\ \hline
-       & \# End 2 termination model  & -    & Number of sources and resistances = number of conductors-1 \\ \hline
-       & 1.0    & V          & End 2, conductor 1 voltage source amplitude \\ \hline
-       & 0.0    & V          & End 2, conductor 2 voltage source amplitude \\ \hline
-       & 50.0    & $\Omega$          & End 2, conductor 1 resistance \\ \hline
-       & 25.0    & $\Omega$          & End 2, conductor 2 resistance \\ \hline
-       & \# Type of analysis  & -    & Comment line \\ \hline
-       & AC    & -          & AC or TRANS \\ \hline
\\ \hline
For AC analysis: & & & \\ \hline
-       & lin    & -          & logarithmic (log) or linear (lin) frequency scale \\ \hline
-       & 1e3 1e8 1000 & Hz Hz integer & min frequency, max frequency  number of frequencies \\ \hline
\\ \hline
For TRANSIENT analysis & & & \\ \hline
-       & 0.01E-9 100E-9  & seconds seconds & \# timestep runtime \\ \hline
-       & 1e-9 50e-9	  & seconds seconds & \# pulse risetime pulse width \\ \hline
\\ \hline
-       & \# Output conductor number and end number  & -    & Comment line \\ \hline
-       & 1   1    & integer integer  & Output conductor number and end number \\ \hline
-       & lin    & -          &  For AC only: Output voltage scaling, linear or dB \\ \hline
 \hline
    \end{tabular}
\end{center}


\vspace{5mm}
\textbf{\underline{AC example}}

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
#MOD_bundle_lib_dir
LIBRARY_OF_BUNDLE_MODELS
#MOD_spice_bundle_lib_dir #LIBRARY_OF_BUNDLE_MODELS/two_wires_over_ground
./
#spice_symbol_dir
SYMBOL_DIR
# Specification for spice model of single wire over ground, no loss
two_wires_over_ground
# cable bundle length (m)
2.0
#Incident field specification
0.0	amplitude (V/m)
90.0 0.0	ktheta kphi (degrees)
-1.0  0.0	Etheta Ephi
# End 1 termination model 
1.0      End 1 voltage source list
0.0
100.0    End 1 impedance list
25.0
# End 2 termination model
0.0      End 2 voltage source list
0.0 
75.0  	 End 2 impedance list
50.0
# Type of analysis
AC
log          # frequency scale (log or lin)
1e3 1e8 1000 # fmin fmax number_of_frequencies
# Output conductor number and end number
1    1   
lin   # output type (lin or dB)

\end{verbatim}



\vspace{5mm}
\textbf{\underline{Transient example}}


\begin{verbatim}
#MOD_cable_lib_dir
.
#MOD_bundle_lib_dir
.
MOD_spice_bundle_lib_dir
.
#spice_symbol_dir
SYMBOL_DIR
2   # number of conductors, n. Conductor n is always the reference conductor
2_wire
# cable bundle length (m)
2.0
#Incident field specification
0.0	amplitude (V/m)
90.0 0.0	ktheta kphi (degrees)
-1.0  0.0	Etheta Ephi
# End 1 termination model
 1      End 1 voltage source list
50.0  	End 1 impedance list
# End 2 termination model
0        End 2 voltage source list
50.0  	 End 2 impedance list
# Type of analysis
TRANS
0.01E-9 100E-9   # timestep runtime
1e-9 50e-9	# pulse_risetime pulse_width
# Output conductor number and end number
1  1     
\end{verbatim}

In the case of frequency dependent models and transfer impedance coupling models then the above file format can be
adapted to include additional information required to drive these models.

A weak form of the transfer impedance is implemented in this work hence the direction of coupling must be specified. 
In order to include a transfer impedance model the conductor number for the shield whose transfer impdeance is required. In addition to
this the direction of the transfer impedance coupling must be specified. The direction is specified as an integer where +1 indicates 
coupling from inside the shield to outside and -1 indicates coupling from the outside to the inside.

The frequency dependent propagation correction takes the form of a s-domain transfer function in the spice model. These propagation
correction transfer functions are derived using a rational function fitting process. This process provides a best fit model of
specified order over a specified frequency range. As a default the model order is 0 i.e. no frequency dependent propagation correction.
The model order can be specified in two ways:

\begin{enumerate}
\item The order is specified as a positive integer and this is the order used
\item A negative integer is specified. In this case the order is chosen using an automatic algorithm which
attempts to choose the best order from 0 up to |specified order|
\end{enumerate}

The frequency range for the model fit may also be specified as can the use of a log or linear frequency scale. If
the frequency range is not specified then it is derived from the definition of the validation test case. 

The format is descibed below followed by an example.

\begin{center}
    \begin{tabular}{ | p{1.5cm} | p{4.5cm} | p{2.5cm} | p{5cm} |}
    \hline
    Line number & Typical value & Unit  & Description \\ \hline
1       & \#MOD\_cable\_lib\_dir & -    & Comment line \\ \hline
2       & .             & -             & Directory to read the cable model file to \\ \hline
3       & \#MOD\_bundle\_lib\_dir & -    & Comment line \\ \hline
4       & .             & -             & Directory to read the cable bundle model file from \\ \hline
5       & \#MOD\_spice\_bundle\_lib\_dir & -    & Comment line \\ \hline
6       & .             & -             & Directory to write the spice cable bundle model file to \\ \hline
7       & \# two wires over ground plane, crosstalk model  & -    & Comment line \\ \hline
8       & two\_wires\_over\_ground    & -              & Cable bundle name Note there should be nothing else on this line \\ \hline
9       & \# bundle length  & -    & Comment line \\ \hline
10      & 2.0    & metres              & Cable bundle length \\ \hline
11      & \# incident field specification  & -    & Comment line \\ \hline
12      & 0.0    & V/m          & Amplitude \\ \hline
13      & 90.0  0.0  & degrees          & Wave vector angle k$\theta$ k$\phi$ \\ \hline
14      & 1.0  0.0  & degrees          & Polarisation E$\theta$ E$\phi$ \\ \hline
15      & \#Transfer impedance terms  & - & this line must inlcude the words 'transfer impedance' 
                                           to indicate that transfer impedance information follows \\ \hline
16      & 1 & integer  &    \# number of transfer impedances to include in the model \\ \hline
-       & 3 +1 & integer integer & \# shield conductor number and coupling direction for transfer impedance model 1 + is inside to out \\ \hline
-       & \# End 1 termination model  & -    & Number of sources and resistances = number of conductors-1 \\ \hline
-       & 1.0    & V          & End 1, conductor 1 voltage source amplitude \\ \hline
-       & 0.0    & V          & End 1, conductor 2 voltage source amplitude \\ \hline
-       & 50.0    & $\Omega$          & End 1, conductor 1 resistance \\ \hline
-       & 25.0    & $\Omega$          & End 1, conductor 2 resistance \\ \hline
-       & \# End 2 termination model  & -    & Number of sources and resistances = number of conductors-1 \\ \hline
-       & 1.0    & V          & End 2, conductor 1 voltage source amplitude \\ \hline
-       & 0.0    & V          & End 2, conductor 2 voltage source amplitude \\ \hline
-       & 50.0    & $\Omega$          & End 2, conductor 1 resistance \\ \hline
-       & 25.0    & $\Omega$          & End 2, conductor 2 resistance \\ \hline
-       & \# Type of analysis  & -    & Comment line \\ \hline
-       & AC    & -          & AC or TRANS \\ \hline
\\ \hline
For AC analysis: & & & \\ \hline
-       & lin    & -          & logarithmic (log) or linear (lin) frequency scale \\ \hline
-       & 1e3 1e8 1000 & Hz Hz integer & min frequency, max frequency  number of frequencies \\ \hline
\\ \hline
For TRANSIENT analysis & & & \\ \hline
-       & 0.01E-9 100E-9  & seconds seconds & \# timestep runtime \\ \hline
-       & 1e-9 50e-9	  & seconds seconds & \# pulse risetime pulse width \\ \hline
\\ \hline
-       & \# Output conductor number and end number  & -    & Comment line \\ \hline
-       & 1   1    & integer integer  & Output conductor number and end number \\ \hline
-       & lin    & -          &  For AC only: Output voltage scaling, linear or dB \\ \hline
-       & -10    & integer  &  \# order for transfer function fit model \\ \hline
-       & log   & -          & logarithmic (log) or linear (lin) frequency scale for transfer function fitting \\ \hline
-       & real real integer & 1e5 1e9 200 & \# fmin fmax number\_of\_frequencies for transfer function fitting \\ \hline
 \hline
    \end{tabular}
\end{center}


\vspace{5mm}
\textbf{\underline{AC example for a frequency dependent coaxial cable with a transfer impedance model plus a single wire}}


\begin{verbatim}
#MOD_cable_lib_dir
./
#MOD_bundle_lib_dir
./
#MOD_spice_bundle_lib_dir
./
#spice_symbol_dir
./
# Specification for spice model of two wire transmission line, no loss
zt_test
# cable bundle length (m)
1.0
#Incident field specification
0.0	amplitude (V/m)
90.0 0.0	ktheta kphi (degrees)
-1.0  0.0	Etheta Ephi
#Transfer impedance terms
1    # number of transfer impedances to include in the model
3 +1 # conductor number and coupling direction for transfer impedance model 1 + is inside to out
# End 1 termination model
 0.02      End 1 voltage source list
 0.5
300.0  	End 1 impedance list
20.0
# End 2 termination model
0.03        End 2 voltage source list
1.0
1000.0 	 End 2 impedance list
150.0
# Type of analysis
AC
log          # frequency scale (log or lin)
1e5 1e9 1000 # fmin fmax number_of_frequencies
# Output conductor number and end number
1    2
lin   # output type (lin or dB)
-10     # order for transfer function fit model 
log          # frequency scale for transfer function fit (log or lin)
1e5 1e9 200 # fmin fmax number_of_frequencies for transfer function fit
\end{verbatim}


In addition to the data required to specify a spice cable bundle model, additional flags may be specified to influence the operation of the software. These flags are as follows:
\begin{enumerate}
\item 'verbose'    output detailed summary of the software operation and calculation results.\\
\end{enumerate}



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