## Computation

50 100 150 200 250

50 100 150 200 250

Figure 9: Comparison of a voltage measured and computed on 50 Ohm in the caisson placed under the CEG's SSR simulator.

5.3 Applying decomposition into elementary volumes

### 5.3.1 General case

We saw that the number of proper volumes could be limited to the decomposition into the external problem, then into the internal problem where wires are removed, and, finally, into the coupling on wires. Nevertheless, for each shielding level, each associated topological network has to be solved on its global geometry. Generally, these networks may still present a large size, and are characterized by a large amount of unknowns. Particularly, the wiring cannot be spread in independent networks as in the Good Shielding Approximation. Indeed, it is frequent that wires in a piece of cable harness run in other cable harnesses, in other volumes.

Consequently, one could think that the topological analysis of a problem has to be limited to the treatment of the only three steps previously mentioned, what could strongly restrict the interest of the topological decomposition. Fortunately, it is still possible to go on breaking down the problem in sub-problems. For this, the method cannot be based on an approximation. It deals with rigorously concatenating all the network information contained in a piece of network named a "sub-network", in an equivalent junction associated to equivalent voltage generators coming from internal sources distributed on this sub-network. There is no precise rule for defining the limits of sub-networks, but it appears straightforward to delimit one sub-network in each elementary volume. Fig. 10 shows the principle of concatenation of a sub-network with the terminology used in ONERA's CRIPTE code. "Internal junctions" define the equivalent junction: they are junctions localized inside the concatenation limits (in dotted lines). "Internal tubes" relate two internal junctions and "external tubes" relate an internal junction to a non internal junction. In CRIPTE code, the output ports of the equivalent junction are computed at this level. The equivalent junction only characterizes the whole internal scattering inside the sub network and is fully independent of sources applied on it. So, the junction can be described with an S-parameter matrix calculated thanks to the individual S matrices of internal junctions and T matrices of internal and external tubes [Parmantier, 1991]. In a simple way, the equivalent vector generator can be seen as a generalisation of "Thevenin" equivalent generator for multiport system. Consequently, this voltage vector is equal to the open circuit voltage induced on the output port of the equivalent junction. Fig. 10 also shows how the resultant equivalent junction (defined on network A) can be used in other topological networks (for example in network B).

Figure 10: Schematic terminology of a sub-network (cfCRIPTE code terminologyj and principle of the use of the equivalent junction and generators in different topological networks.

5.3.2 Example of cable network concatenation

The following example is an illustration of the sub-network concatenation utility for the treatment of large scale systems. It is taken from a work, performed by ONERA and Labinal companies, and supported by GEC Alsthom company, on the wiring of a subway train project, now in operation in Paris, called "Meteor". The subway train is made of four motor coaches placed in the centre and two slip coaches located at the extremities (see Fig. 11). In each coach, a wiring is installed on the under-frame. Perturbing sources are delivered by internal equipment. This wiring was interconnected from one coach to the neighbourhood coaches. The entire wiring network model for all the subway train was made of 158 tubes, 154 junctions and 1724 unknowns. The biggest junction had 39 ports and the biggest tube had 15 wires. The topological treatment dealt with defining six equivalent junctions limited to the six elementary volumes made by the coaches. In each volume type (motor or slip coaches), the same network could be duplicated because of the similitude of the wiring in each coach. Fig. 12 describes the final equivalent network dealing with the global subway train wiring. Each equivalent junction is related to the other by a simple junction Jc. Satellite junctions around equivalent junctions J1 and J2 are associated to the terminal loads on which an electrical signal had to be calculated. This junction could be used to study different types of connections of wires between two coaches. The important lesson to retain from such a study relies on the methodology: the resulting network is much smaller than the spread network one, and by this way, reveals itself as very well adapted to a modular approach. The final equivalent network contains only

246 unknowns (that is to say, 5 times less than the spread network), and is made of 27 tubes (with 27 Thevenin equivalent generators), and 28 junctions.

Figure 11: Schematic description of the Meteor subway train.

Figure 11: Schematic description of the Meteor subway train.

Figure 12: Resultant network for the under-frame wiring study after sub-network concatenation.

5.3.3 Concatenation with 3D codes

Let us clarify that the concatenation method is also available for networks dealing with physical volumes, different from wires (step 2). Precisely, junctions are like black boxes which summarize the scattering inside the volume. In this way they are similar to equivalent junctions presented before. Nevertheless, in this case, the characteristic of such networks is to contain a small number of tubes and junctions, but with large size matrices.

Until now, such methods have been applied to connect several numerical codes. This is the case for "Gemmacs" environment for which the external problem is treated by TGD, and the internal problem either by a Method of Moments or FDTD method [Coffey et al., 1993]. Nowadays, the use of topological networks is being generalized at ONERA to perform such a numerical code hybridization. The network provides the connections between volumes, but also the coupling of unknowns inside the volumes (especially for asymptotic methods). Particularly, the properties of the scattering matrix of the network is used to reduce the data storage and the computation time and to facilitate the parallelization of calculations [Michielsen, 1993; Ferrieres and Michielsen, 1994],

6 EMT in experimental works: application to EMPTAC aeroplane

### 6.1 Description of the EMPTAC

We previously insisted on the modular interest of EMT. Especially, we mentioned that measurements could be substituted to computations to determine the characteristics of tubes and junctions. Moreover, thanks to a real time analysis of results and their confrontation to measurements, this method can be very useful in experimental works, and can provide significant help for understanding EMC coupling paths inside the system. For the first time, in November 1993, ONERA and CEG, in collaboration with the Philipps Laboratory, had the opportunity to validate all the concepts and apply on an aeroplane, the EMPTAC (EM. Pulse Test Bed Aircraft), available at the Kirtland Air Force Base, in Albuquerque (New-Mexico) \Parmantier et al., 1993, 1995] the methods developed during the last few years.

The EMPTAC is a 707 Boeing aeroplane. In the past fifteen years, it has been used to help on the design of specific aeroplane systems, in hardening programs, and was considered as a real laboratory to validate hardening technologies. With this objective, the original 707 aeroplane has been modified applying qualitative EMT rules. The aeroplane contains two volumes especially well shielded: the "lower forward shielded volume", and "the aft shielded volume". Each of these volumes is connected thanks to a specific electrical cable network. Out of both shielded volumes, the wiring is made of over shielded cables, maintaining, by this way, a homogeneous shielding level for the

Figure 13: EMPTAC aircraft after modifications.
Unshielded cables

Figure 14: Topology of the problem understudy and topological network.

During this experiment, the work was restricted to the coupling on a piece of wiring, running inside the cockpit and the forward shielded volume (Fig. 14): this wiring was called "network A". In the cockpit, the wiring under study was made of a 21 wire shielded cable running from the LD5 box, to the "forward shielded volume" with a separating connector J006 between them. At this point, inside the lower volume, the 21 wire cable became unshielded and ran along two paths, connecting LD7 and LD8 boxes. The LD7 box is also connected to J004 by means of unshielded wires.

The preparation of the experiment, held in France, suffered from the limited knowledge on network A: the exact running of the cables, their internal geometry were unknown. Only the load values (spread from 1Q to 1MQ) inside each black box were given in plans. Consequently, a pre-experiment was previously carried out in France by considering a similar network, containing only a few elementary wires, but presenting the same topological characteristics as Network A; that is to say, same running paths, same box location, same lengths. This test wiring was called "Network B". It was made of a 3 wire shielded cable put above a ground plane, corresponding to the cockpit volume, then becoming unshielded as in the forward volume. The connection between the two sides of the volume was made by means of 2 wire cable.

Fig. 15 presents the equivalent topological network associated to this problem. Each elementary volume has been represented with an equivalent junction. Each junction is itself the concatenation of the network existing in the associated volume. On the tube connecting the shielded cable equivalent junction, an equivalent Thevenin source has been placed to represent the coupling in this volume. The wiring inside the forward shielded volume has been designed, separating the terminal loads on which measurements were made. Finally, junction Jc makes simply the connection of junctions equivalent to the cockpit and the forward shielded volumes.

Figure 15: Principle of topological decompositioin for the study of the coupling in the cockpit and the forward shielded volume.
Figure 16: Topological model of network B on the metallic ground plane.

6.2 Test wiring pre-experiment study

The objective of the test wiring experiment was to constitute a large data bank on a wiring, representative of the real cable harness under study. For this, network B was tested after being installed on a metallic ground plane. First, the per unit length impedance and admittance of the elementary cables (that is to say, one, two and three wire cables, shielded and unshielded) were measured very precisely. The interest of taking into account the frequency dependence of these parameters was clearly demonstrated by making comparisons between direct S-parameter measurements and CRIPTE code numerical simulations: thus, a very good agreement was obtained, up to 500 MHz. In this canonical experiment, the "elbows" due to the junction between the cable and the box connector were modelled as an equivalent tube (Fig. 16), [Besnier and Degauque, 1995],

The immunity of the shielded cable was also tested in terms of transfer impedance Zt. The characteristics of the tube, taking Zt into account, were optimized by making comparisons between measurements and numerical simulations performed with CRIPTE code. The first important point in the model is that an injection current probe was used and considered as a transformer, inducing a tangential field in its centre. The second point is that the shield of the cable was considered as a real wire, as the other ones. Both models allowed to take into account all kinds of wire connections by simply changing some junction S-parameters in the topological network model. For example, the same model could be used to determine the response of the shielded cable, whatever the connections of its shield were.

### 6.3 In situ test wiring EM coupling analysis

The pre-experiment held in France allowed to constitute a data bank on network B elementary cables, and on the source generators produced by the current injector. All this data was used to feed the in-situ topological network models during the experiment performed on the aeroplane.

Indeed, the first phase of the in-situ experiment dealt with introducing Network B in the aeroplane and applying the same current injector source as the one applied in France. In fact, the topology inside the aeroplane was quite different from cables laying on a metallic plane (Fig. 17). During the experiment, it was impossible to reach such a detailed modelling as during the pre-experiment. Nevertheless, the cockpit shielded cable was simply decomposed with success into 10 tubes. Their lengths were determined thanks to reflectometry measurements. In the same way, the wiring inside the forward shielded volume was simply modelled by a network including characteristics of flattened and not flattened tubes, previously determined in France.

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