# Model-Based Analysis and Improvement of Vehicle Radiation Emissions at Low Frequency
## 3 Topological Modelling Process
### Decoupling of Vehicle Radiation Problem  
In essence, the objective of decoupling is to decompose the entire problem into several sub-ones. Each subsystem is comparatively easier to be modelled by the appropriate method. The following vehicle's characteristics make it suitable to use the decoupling method:  
1. Most components are electrical small and wrapped in metal shells, which are well grounded. Such components can be considered as lumped parameter systems when studying the vehicle-level radiation emissions. 2. Vehicle manufactures focus on the system design, while the detailed design of components is carried out by the supplier. Considering both the demand for secrecy and the concerns of different roles, a decoupling structure is required to make each supplier responsible for their own parts. 3. Though there exist nonlinear materials and devices in components, their connection cables and surroundings are linear. These linear systems with their internal couplings can be described by such methods as the multi-port network, transfer function, etc. Accordingly, the suggested decoupling process is depicted in Figure 2, where the subsystems are labeled as \(V_{i,j}\). The principles for the conversion of the original vehicle-level radiation problem to a topological model are:  
1. The parts without direct radiation coupling with others can be considered as a separate subsystem. The direct radiation coupling means that interferences flow into and out of a part through space. At this condition, it is hard to separate the propagation of electromagnetic wave further. On the contrary, if there is no such direct radiation coupling, the part can be considered as a separate subsystem. For example, in Figure 2b, since the boundaries are metal materials which shield the radiation effectively, \(\mathrm{V2},3\sim\mathrm{V2},5\) and \(\mathrm{V3},1\sim\mathrm{V3},3\) only receive the conduction interference  
Figure 2: Decoupling process of vehicle radiation problem: (**a**) Original system; (**b**) Equivalent system; (**c**) Topological connection. and there is no direct radiation coupling among them. As a result, they are considered as separated subsystems as shown in Figure 2c. 2. Conduction and radiation coupling paths that belong to the same volume should be integrated into one network. As shown in Figure 2b, the transfer paths between V2, \(3\sim\) V2, \(5\) are conduction couplings in the volume V1, \(1\). But in the same volume, there also exist other radiation couplings. These radiation and conduction paths should be integrated into one network, i.e., V1, \(1\) in Figure 2c, unless it is ensured that the coupling among the radiation and conduction paths is negligible. By this way, the requirement of prior knowledge about the radiation problem is reduced. Meanwhile, each subsystem can be modeled separately and the radiated emissions can be solved by solving an algebraic equation (see Section 3.2). The consumption of calculation resources is greatly reduced. 3. Electrical large and small subsystems are described by multi-port networks and circular nodes, respectively. The subsystems are denoted by circles in Figure 2c, and the lines represent their subordinate relationships. For an electrical large subsystem, the interference interactions among different devices are very complicated and it is difficult to find out that required to be modeled properly. To reduce the requirement of engineer's experiences and the priori knowledge of the concerned problem, the multi-port network is adopted to describe electrical large systems denoted by the blue circles in Figure 2c. It includes all possible coupling paths and is easily to be solved numerically. The electrical small subsystems are modeled by circuit nodes (Yellow circles in Figure 2c) connected to the multi-port network. Particularly, the subsystems acting as the interference sources or sensitive equipments have to be modeled as circuit nodes. It should be noted that the determination of interference sources or sensitive equipment depends on the type of studied problems.