## 2 The Concept of an EMC Topological Model
### A Ship's EMC Topological Structure  
As already mentioned, a typical ship structure consists of a specified number of shielding walls, i.e., shielding planes, that influence the EM disturbance distribution. A disturbance interaction of an EM signal is related to its electrical component E, i.e., the electrical field strength. In practice, the disturbance distribution is described by effective values of the electrical component E of the propagating EM field, which mainly depends on the localization and value of its source and the properties of the shielding planes. The arrangement of the shielding planes results from the ship's internal structure. Figure 1 shows a ship's general topological structure, where:  
* _EuT_ is the equipment under test that is affected by all existing disturbing signals;
* _Sp_ is the \(p\)-th shielding plane, such as a deck or walls, and \(p\in(1,2,\ldots,P)\);
* \(D_{m}^{(i)}\) is the \(m\)-th internal (i.e., under the main deck) EM field source (disturbance source) that radiates the \(E_{m}^{(i)}\) disturbing signal, where \(m\in(1,2,\ldots,M)\);
* \(D_{j}^{(o)}\) is the \(j\)-th external (i.e., above the main deck) EM field source (disturbance source) that radiates the \(E_{j}^{(o)}\) disturbing signal, where \(j\in(1,2,\ldots,J)\); and
* \(D_{k}^{(e)}\) is the \(k\)-th extraneous external EM field source (disturbance source) that radiates the \(E_{k}^{(e)}\) disturbing signal from another ship or aircraft, where \(k\in(1,2,\ldots,K)\). Using the above-presented topological structure of a ship's environment, the value of the total disturbing signal at a given equipment under test (EuT) device, taking into account the arrangement of the signal sources and the location of particular shielding planes, can be calculated. An effective value \(E_{l}^{(i)}\) of the total disturbing signal at the selected \(l\)-th EuT can be calculated in the following way,  
Figure 1: The topological form of a ship’s structure with shielding planes (walls), S, and electromagnetic (EM) disturbance sources, D, equipment under test (EuT). due to the resultant disturbing signals that are radiated by transmitting antennas, with other sources of disturbing signals being classified into three groups, namely, internal, external, and extraneous external, i.e.,  
\[E_{l}^{(t)}=\sqrt{\left(E_{l}^{(i)}\right)^{2}+\left(E_{l}^{(o)}\right)^{2}+ \left(E_{l}^{(e)}\right)^{2}}, \tag{1}\]  
in which  
\(\bullet\)\(E_{l}^{(i)}\) is the resultant value of the sum of the ship's own internal disturbing signals, which equals  
\[E_{l}^{(i)}=\sqrt{\sum_{m=1}^{M}\left(E_{lm}^{(i)}\right)^{2}}, \tag{2}\]  
\(\bullet\)\(E_{l}^{(o)}\) is the resultant value of the sum of the ship's own external disturbing signals, which equals  
\[E_{l}^{(o)}=\sqrt{\sum_{j=1}^{l}\left(E_{lj}^{(i)}\right)^{2}}, \tag{3}\]  
\(\bullet\)\(E_{l}^{(e)}\) is the resultant value of the sum of extraneous external disturbing signals, which equals  
\[E_{l}^{(e)}=\sqrt{\sum_{k=1}^{K}\left(E_{lk}^{(i)}\right)^{2}}. \tag{4}\]  
Equations (1)-(4) describe the summation of disturbing signals, which indicate the measured effective scalar quantities; these powers are expressed by squares of electric field strength of the electromagnetic signal. As can be seen, the disturbing signal values depend on their source values, the space attenuation of the disturbing signals along the paths between their sources and the EuT's location, and the attenuation of the shielding planes that are located on the propagation paths of the disturbance signals. Otherwise, the total value of \(E_{l}^{(t)}\) does not exceed its accepted (limited) value of \(E_{l(\text{lim})}^{(t)}\), ensuring the correct operation of the \(l\)-th EuT, i.e.,  
\[E_{l}^{(t)}\leq E_{l(\text{lim})}^{(t)}. \tag{5}\]  
Verification of Equation (5) is one of the main goals of EMC analysis. This requires calculating the abovementioned sums of the disturbing signals, i.e., \(E_{l}^{(i)}\), \(E_{l}^{(o)}\), and \(E_{l}^{(e)}\), for which the topological model of the ship's EMC environment is proposed.