# Optimisation of Segregation Distances between Electric Cable Bundles Embedded in a Structure
## 2 EMC between Two Bundles
### Inter-Compatibility Criterion  
The EM susceptibility of an equipment input, \(S_{A,i}\) (\(S_{B,j}\)), can be defined as a voltage or a current and as a limit below which the equipment operates correctly. As an example, if \(S_{A,i}\) is defined as a threshold current (respectively voltage), the magnitude of the induced current \(I_{A,i}\) (respectively voltage \(V_{A,i}\)) must be compared to \(S_{A,i}\). This is the reason why we introduced \(O_{A,i}\) and \(O_{B,j}\) as either the magnitude of the currents (\(I_{A,i}\) or \(I_{B,j}\)) or the magnitude of the voltages (\(V_{A,i}\) or \(V_{B,j}\)) following the nature of the susceptibility thresholds (\(S_{A,i}\) or \(S_{B,j}\)). \(O_{A,i}\) and \(O_{B,j}\) induced on each elementary cable \(i\) of bundle \(A\) and \(j\) of bundle \(B\) by the source generators depend on the frequency \(f\), the segregation distance \(d\in[d_{\min},d_{\max}]\), the coupling length \(l\in[l_{\min},l_{\max}]\), the heights \(h_{A}\in[h_{\min},h_{\max}]\), \(h_{B}\in[h_{\min},h_{\max}]\), and finally, on the electric characteristics of all elementary cables in each bundle. The computation of \(O_{A,i}\) and \(O_{B,j}\) can be performed with a computer code named CRIPTE [3; 4]. This code developed at ONERA for more than 20 years is dedicated to the evaluation of electromagnetic interferences induced on multiconductor cable networks, for typical applications as lightning indirect effects and internal EMC problems (crosstalk). It is based on a topological formalism associated with the transmission line theory generalised to multiconductor networks. The code is mature enough to model cable networks of industrial complexity such as engine cable architectures [5].  
The next step consists of defining a mathematical scalar criterion to determine if the two bundles \(A\) and \(B\) are EM compatible. For this purpose, we propose to compute a \(G\) function defined as:  
\[G(d,l,h_{A},h_{B})=\max_{f\in F,\ i\in[1,h_{A}],\ j\in[1,n_{B}]}\left(\frac{O_ {A,j}-S_{A,i}}{S_{A,i}},\frac{O_{B,j}-S_{B,j}}{S_{B,j}}\right) \tag{1}\]  
The event \(G(d,l,h_{A},h_{B})<0\) means that both bundles \(A\) and \(B\) are EM compatible, and EM immunity is ensured for all equipment and, conversely, if \(G(d,l,h_{A},h_{B})>0\). Indeed, if \(G<0\), it means that \(O_{A,i}<S_{A,i}\), \(\forall i\) and \(O_{B,j}<S_{B,j}\), \(\forall j\). For instance, if \(S_{A,i}\) is defined in terms of current, it means that \(O_{A,i}\) are the currents induced on bundle \(A\), and these currents are lower than the threshold acceptable by the equipment. Thus, we deduced that the equipment will operate correctly, and we can conclude that \(A\) and \(B\) are compatible.  
The normalisation of the induced currents/voltages to their corresponding susceptibility thresholds enables obtaining a dimensionless \(G\) criterion, which is independent of the nature of the susceptibility thresholds (themselves defined as currents or voltages). Let us remark also that \(G\) in Equation (1) covers the whole frequency band \(F\). The computation time to obtain one evaluation of G with CRIPTE is about 1 min for a thousand frequencies and bundles of about thirty elementary conductors for a given set of \((d,l,h_{A},h_{B})\).