\chapter{Shielded Twisted Pair cable models}

The shielded twisted pair models consist of variant 12 STP from the standard  \cite{3901/025} for LF signals and  RS422 cables: variant 24 STP from the standard  \cite{3902/002}.


The process followed to obtain the parameters for the \textbf{.cable\_spec} from information in the ESCC specifications is as follows (where we assume that all dimensions are converted to metres):

 \begin{enumerate}
 \item 
  \begin{equation}
 comnductor\_radius = \sqrt{\frac{nominal\_section}{\pi}}          
 \end{equation}          
 
 \item 
  \begin{equation}
 dielectric\_radius = \frac{core\_max\_diameter}{2}                        
 \end{equation}          
Note that the $core\_max\_diameter$ is not set in the ESCC 3902002 document \cite{3902/002}. In this case it is chosen such that the differential mode impedance of the shielded twisted pair model is the specified 120 ohms. For variant 12 STP from the standard  \cite{3901/025} the dielectric diameter is chosen to be slightly less than the max core diameter from Table 1(a) so that th twisted pair fits inside the shield.

 \item 
 \begin{equation}
 conductor\_separation    = 2* dielectric\_radius + \delta
 \end{equation}          
 where $\delta$ is a small separtion distance, here assumed to be 0.01mm. This is required in order that the dielectric regions do no touch which would cause a problem for the mesh generation.
 
 \item 
 The conductor in the model is a homogeneous cylindrical conductor so we need an effective 
 conductivity. This is based on the maximum resistance (quoted in ohms/km)
 
 \begin{equation}
 Conductivity = \frac{length}{(max\_resistance*nominal\_section)}
 \end{equation}          
 
 \item 
 \begin{equation}
 shield\_radius=\frac{finished\_diameter}{2}-tj
 \end{equation}
 where tj is the outer jacket thickness. This is not specified in ESCC document but a typical value of 0.2mm is used
 
 \item  The shield thickness is set to zero. This indicates to the software that an 'equivalent thickness' should be calculated such that the d.c. resistance of the shield is consistent with the d.c. transfer impedance.
 
 \item The dielectric surrounding each conductor is also assumed to be homogeneous and independent of frequency.
Materials used in the STP cables are:

 Fluoropolymer: $\epsilon_r=2.1$
 
 microporous PTFE $\epsilon_r=1.3$

 \item For RS422 cable, ESCC 3902/002 variant 24, the shield model is based on the shielding effectiveness curve in figure 1b. The usual definition of shielding effectiveness would make this a positive quantity however I am assuming that the curve here is of (1/SE)dB. 

If we assume that the shielding effectiveness can be related to the transfer impedance by the formula 
\begin{equation}
SE(dB)=20log\left(\frac{2Z_0}{Z_T}\right)
 \end{equation}          

where $Z_0$ is the termination impedance in the transfer impedance measurement and $Z_T$ is the transfer impedance, then 

\begin{equation}
Z_T=\frac{2Z_0}{10^{\frac{SE}{20}}}
\end{equation}          

Here it is assumed that $Z_0=50\Omega$.

A value of the shield d.c. resistance is derived from the SE as $f \rightarrow 0$. 

\item For LF signal cable, variant 12 STP from the standard  \cite{3901/025} no shielding effectiveness is specified so a 'reasonable' braid specification has been developed based on the requirement for 90\% coverage and a shield strand diameter of 0.079mm. From this specification the theory of Kley \cite{Kley} in appendix 1 is used to calculate a transfer impedance model of the form $Z_T=R_T+j\omega L_T$. In this case the braid specification is as follows:

\begin{verbatim}
1.4E-3          ! braid diameter, D (m)
8               ! Number of carriers, C
6               ! Number of wires in a carrier, N
0.079e-3        ! diameter of a single wire, d (m)
5E7             ! conductivity of wires (S/m)
52.0            ! pitch angle of the braid (degrees)
\end{verbatim}

$R_T$ 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}

 As an example, the cable specification for the 20AWG cable, variant 24 from \cite{3902/002}
 
 SPICE\_MODEL\_STP\_RS422\_AWG\_26\_ESCC\_3902002\_V24:

\begin{verbatim}
#MOD_cable_lib_dir
LIBRARY_OF_CABLE_MODELS
Shielded_twisted_pair
3                 # number of conductors
8                 # number of parameters
   2.111E-04      # parameter 1: inner conductor radius
   5.000E-04      # parameter 2: inner dielectric radius
   1.010E-03      # parameter 3: inner conductor separation
   1.050E-03      # parameter 4: shield radius
   0.000E+00      # parameter 5: shield thickness
   1.250E-03      # parameter 6:outer dielectric radius
   4.492E+07      # parameter 7: inner conductor conductivity
   4.492E+07      # parameter 8: shield conductivity
2                 # number of frequency dependent parameters
# Inner dielectric relative permittivity model follows
1.0        # w normalisation constant
0   # a order, a coefficients follow below:
   1.300E+00
0   # b order, b coefficients follow below:
1.0     
# Shielded twisted pair outer dielectric relative permittivity model follows
1.0        # w normalisation constant
0   # a order, a coefficients follow below:
   2.100E+00
0   # b order, b coefficients follow below:
1.0     
1                 # number of frequency dependent transfer impedance models
# Shielded twisted pair transfer impedance model follows
1.0        # w normalisation constant
1   # a order, a coefficients follow below:
   1.000E-01   5.035E-10
0   # b order, b coefficients follow below:
1.0     
use_laplace

\end{verbatim}


\clearpage