The main principles are presented of a method dealing with the resolution of electromagnetic internal problems: Electromagnetic Topology. A very interesting way is to generalize the multiconductor transmission line network theory to the basic equation of the Electromagnetic Topology: the BLT equation. This generalization is illustrated by the treatment of an aperture as a four port junction. Analytical and experimental derivations of the scattering parameters are presented. These concepts are used to study the electromagnetic coupling in a scale model of an aircraft, and can be seen as a convenient means to test internal electromagnetic interference

Aparicio, J. P.

Faure, F.

Parmantier, J. P.

English

NASA Technical Reports Server

I 
ELECTROMAGNETIC TOPOLOGY: CHARACTERIZATION OF INTERNAL 
ELECTROHAGNETIC COUPLING 
J.P. Parmantier" , J.P. Aparicio** and P. Faure** 
*Dassault Aviation, B.P. 300, 92214 SAINT-CLOUD, FRANCE . 
**Office National d'Etudes et de Recherche8 Adrospatiales 
B.P. 72, 92322 CHATILLON CEDEX, FRANCE 
ABSTRACT 
This paper presents the main principles of a method dealing with the 
resolution of electromagnetic internal problems: Electromagnetic Topology. A 
very interesting way is to generalize the multiconductor transmission line 
network theory to the basic equation of the Electromagnetic Topology: the 
B.L.T. equation. 
This generalization is illustrated by the treatment of an aperture as a four 
port junction. Analytical and experimental derivations of the scattering 
parameters are presented. These concepts are used to study the 
electromagnetic coupling in a scale model of an aircraft, and can be seen as 
a convenient means to test internal electromagnetic interference. 
1. INTRODUCTION 
The study of the internal electromagnetic problem should, in the future, lead 
to the development of an electromagnetic design tool. An electromagnetic 
design can be carried out in four phases. The first one is to design a first 
prototype. The second phase is to calculate the interference in the system 
previously defined. In a third phase the system has to be optimized, to be in 
agreement with specific goals such as price, but also weight. The last phase 
is to establish maintenance specifications once the system is entirely 
defined. 
Electromagnetic Topology is a powerful frequency method developed several 
years ago specially for aeronautics by C.E. Baum [l] in the USA, and that 
could answer these four phases. Nowadays, studies are being made to see how 
far this theory can be applied or modified or completed to be successful. 
2, OVERVIEW OF ELECTROMAGNETIC TOPOLOGY 
F ~ D A ~ E N T A L  APPROACH 
The main concept of Electromagnetic Topology, as defined by C.E.  Baum, is to 
divide the space of interest into volumic zones in order to break down a 
total complex electromagnetic problem into a group of small problems 
independent of each other. 
https://ntrs.nasa.gov/search.jsp?R=19910023385 2020-03-17T15:02:43+00:00Z
The topological diagram is a helpful abstract vision of the geometry of a 
system, taking into account the electromagnetic interactions between the 
different volumes. With this diagram, an inventory of all the penetration 
paths into the previous volumes can be made and then an interaction graph 
drawn: this description of the electromagnetic interaction between volumes is 
better suited than the diagram to computerization. Figure 1 represents a 
superimposition of a topological diagram with an associated interaction 
graph. 
According to the theory, the calculation of the interference in the system is 
provided by deriving the topological networkb) associated to the interaction 
graph. Figure 2 is an Clxample of such a network dealing with one external 
penetration path of the interaction graph presented in figure 1. A network is 
constituted by tubes related to each other through junctions. The signal 
propagating on the tubes is understood in terms of wave vectors W(z) and the 
coupling of external sources in terms of source wave vectors Ws. One can then 
derive relations involving all the waves on the network, considering 
supervectors (vectors of vectors) and supermatrices (matrices of matrices). 
The propagation equation relates the wave supervectors at each extremity of 
the tubes W(0) and W(L) by means of a propagation supermatrix r: 
The propagation equation relates the outgoing wave supervectors W(0) and the 
incoming wave supervectors W(L) by means of a scattering supermatrix S: 
Combining (1) and (21 ,  a single equation can then be derived, taking into 
account all the electromagnetic interactions on the network: it is called the 
B.L.T. equation (Baum - Liu - Tesche): 
(1 - sr) w(o) = sws (3 )  
One can already measure how this equation can be useful to perform the 
optimization phase of an electromagnetic design. However, the main problem is 
to express the waves and S and P supermatrices in any coupling configuration. 
Figure 1: Topological diagram and 
associated topological graph. 
72-2 
Figure 2: Topological network. 
,J 
s o u r ce wave- 
/ 
vector 
junction 
/ 
wave vector 
A QUALITATIVE APPROACH 
In this approach, the concepts of topological diagram and graph remain valid. 
The difference is that all the evaluations of the interference are made by 
means of transfer functions. For this, judicious observables must be definied 
at each node of the graph, such as electromagnetic fields or currents and 
voltages and related by means of matricial expressions involving transfer 
operators T, k, as defined in figure 3 .  As an example, the current and 
is given with respect to external electromagnetic voltage at node 3 . 1  
field c} by the relation: fJ3. 1 
n Y 
= T  3 . 1 ; 2 , 2  T 2 , 2 ; 1 , 1  (Lo+ T L )  g}o 
“3.1 
This tool is well suited to evaluate interference on a given structure and to 
propose maintenance specifications. The transfer operators can be measured or 
estimated (defining bounds with matricial norms for example) [1],{3]. The 
main problem is that this approach poorly lends itself to foresee the 
interference value when the geometry of the structure is modified. 
Figure 3: Transfer functions on 
a topological graph. 
72-3 I 
A NEW APPROACH COMBINING QUANTITATIVE AND QUALITATIVE ASPECTS 
The two previous fundamental approaches must progress each in its own way, 
but it must always be kept in mind, that they must meet and merge in a single 
approach in the future. 
Today, an approach conciliating the two is developed, based on the fact that 
a very important way to propagate the interference is constituted by cables. 
As a matter of fact, the multiconductor transmission line network theory is 
well suited to the B.L.T. equation formalism because all the quantities 
defined in (3) can be easily expressed with respect to current I(z) and 
voltage V(z) observables all along the lines [2],[5]. Figure 4 shows the 
electrical modeling of a multiconductor line cell where Z and Y are the 
distributed shunt impedance and parallel conductance matrices respectively. 
Vsand Is shunt voltage and parallel current generators dealing with 
the coupling of external sources'on the wires. 
A Zcmatrix can be defined on each transmission line by: 
are the 
zc= (Z.Y)% (3) 
which allows to express the waves W(z) as: 
W(z) = V(z) + ZCI(Z) (4) 
r and Ws quantities can also be easily derived from Z and Y matrices and Vs 
and Isvectors. 
To obtain a generalization of this network transmission line formalism for 
the treatment of a global electromagnetic internal problem, one may think of 
integrating other forms of electromagnetic couplings into this theory. 
Effectively, apertures, joints, seams, antennas are very common and important 
penetration points in aeronautical vehicles. 
- .-. 
Z '  z+dzl 
Figure 4: Electrical modeling of a multiconductor cell. 
This can be done in two ways. The first one deals with distributing Vsand Is 
generators all along the lines, using direct measurements or 3-dimensional 
codes. The second one consistsin characterizing the coupling in terms of a 
network junction. This is what will be discussed now. 
I 
72-4 
3. ELECTROMAGNETIC COUPLING THROUGH AN APERTURE DESCRIBED AS A JUNCTION 
3.1. COUPLING OF TWO WIRES LOCATED ON BOTH SIDES OF AN APERTURE 
Geometrical configuration 
The configuration is represented in figure 5. The aperture is circular, with 
a diameter d, but the study remains valid for any shape, Both wires of length 
1 are parallel to a ground plane at heights hiand h,respectively. The main 
hypothesis here is that conducting wire paths always prevail on any external 
radiation field. 
A 
Figure 5: Coupling 
on both sides 
of 
of 
two wires located 
an aperture. 
Electrical modeling and scattering parameters for small apertures 
This model is valid insofar as the resonances of the aperture are not 
involved. The electrical scheme associated with this configuration is shown 
in figure 6 (the reaction of the inner wire is not taken into account). It 
can be shown that current I and voltage V in the upper volume, create in the 
lower wire shunt current Ieqand serial voltage Veqgenerators [3], defined as: 
V = jwaI (5 )  
(6) 
One can consider this configuration as a four port junction. The scattering 
parameters determination implies that each port is loaded on the 
characteristic impedance of the lines connected to ZcIand ZcIIrespectively 
(see figure 6). 
A 4x4 matrix [SI is then derived and can be divided into four blocks as 
follows 141: 
eq 
Ie = jwPV 
72-5 
port, I Port2 ------------------- 
zc, 
Figure 6: Electrical modeling of the 
junction dealing with the coupling of 
two wires through an aperture. z c a  
I I V,, = joal ! 
Junction Port 3 
port4 1. _----------------..I 
are 2x2 matrices dealing with the scattering parameters of a 
transmission line and are only slightly affected by the presence of the 
aperture. More important are the 2x2 blocks SIJIIand SI, dealing with the 
signal transfer from one side of the structure to the other. The expression 
of S - -  _components is given by: 
111 and S I I , I I  
1 1  
1 1 1 1  
Scattering parameters Eor large apertures 
It must be noted that the relation (8 )  still remains valid for low 
frequencies (before the resonances of the wires) and can inspire an efficient 
way to go back to 01 and P values. 
However, when the frequency increases, the best way to characterize the 
aperture coupling is the measurement. The scattering parameter determination 
is not made directly. The first step of the work generally consists in 
measuring parameters So of the 4-port junction with a network 
analyser [ S I .  These parameters have the same definition as the "topological" 
S parameters except the load impedance is fixed at Zcogenerally equal to 
50 42. 
The second step is to go back to the Y parameters of the junction with such a 
rnatricial relation: 
the microwave 
1 
CY1 = - (C11 + (C11 - P o l )  (9 )  
c o  
Z 
with [l]: the unit matrix. 
One can then derive the [SI  topological matrix, considering the local 
characteristic impedance matrix [Zc] of the connected lines: 
(10) [ S I  = (111 - C Z C l  CY])= (C11 + CzclCyl)-l 
72-6 
Figures 7a,7b,7c illustrate as an example the variation of So,Y and S 
parameters between port 1 and port 3. 
It must be specified that when the length of the lines becomes greater than 
the aperture size, the B.L.T. equation formalism gives the opportunity to 
find the parameters in the actual reference plane of the junction. 
So in d6 
i 
-30 
-40 
-50 
-60 
-70 
7 
60v 
II I W 
.Figure 7: Evolution of electrical 
parameters between port 1 and port 3. 
a) Microwave parameter. 
b) Admittance parameter. 
c) Scattering parameter. 
3.2. MODELING OF THE FIELD TO WIRE COUPLING 
For this case, one must consider the geometrical configuration represented in 
figure 8. The upper wire in volume I has disappeared and has been replaced by 
an external electromagnetic plane wave. If the aperture is short circuited, 
this wave creates, short circuit electric Escand magnetic Hscfields on it, 
The aperture must be supposed small enough to consider that the distribution 
of the fields is homogeneous. 
Then the question can be asked what should the characteristic of the fictive 
wire in volume 1-be to create such an electromagnetic field distributions. 
For this, the E.M. fields created by a wire on a conductive plane can be 
calculated. According to the notations of figure 8, we have: 
d - +  Z 
zc d2 t y2 
--+ v o  E = - - -  
sc ex (11) 
and 
+ I d +  
H = - -  e (12) 
R 2  Y sc d t y2 
where 
medium. 
Zcis the characteristic impedance of the wire, Zo the impedance of the 
72-7 
Volume I I "  
1 
Figure 8: Coupling of a plane wave and 
a wire located under an aperture. 
At each extremity (see figure 91, two orthogonal references can be created: Frcrq at port 1, GrCtq at port 2. The short circuit fields 
and Hsc can be expressed according to these new directions and become 
respectively EsCll HsC2 . 
If I is introduced, an index dealing with volume I including indices 1 and 2, 
the topological wave for the fictive wire is defined by: 
_$ + 
Es C 
__++ 
+ w; = VI? ZCIII 
Figure 
on 
9: Electromagnetic field 
created by a wire 
a conductive plane. 
/ 
where t or - indicates incoming and outgoing waves. 
From (11) and (121, defining an equivalent length legby: 
2 dZ+ y2 
1 = -  
e q  Z d 
(141 
72-8 
+ (y = y at the center of the aperture), and a topological field wave WscIby: 
0 + W- S C I  = E S C I +  ZoHscI (15) 
a new scattering equation involving the observables at each port of the 
junction is derived: 
If [SI is the scattering matrix dealing with the coupling of the fictive wire 
and the wire in volume 11, defined in 4 blocks as in (8) , it can be seen that 
[S'] in relation (16) is equal to: 
(17) 1 -'I , I  1 /le q *1 L I I  
As the scattering parameter definition needs to have a ratio V/I equal to Zc, 
it is seen that the ratio E(y)/H(y) remains equal to Zo. So, by adjusting the 
value of the medium impedance, it is possible to simulate any direction of 
the incident plane wave. 
In fact, a single wire can be shown as an approximate tool to simulate a 
plane wave but as a convenient system for testing a structure. One could also 
think of measuring the scattering parameters when the wire in volume I is 
replaced by a conductive plane, thereby defining a stripline. 
4. APPLICATION OF THE TOPOLOGICAL CONCEPTS ON A SCALE MODEL 
CHARACTERIZATION OF THE INJECTION 
The previous results are applied on a scale model (l/lOth 1 of the C160 
Transall aircraft. Figure 10 shows the experimental set-up. Several wires (in 
dotted lines) run inside the structure and the external coupling paths are 
essentially constituted by two apertures 1 and 2. 
An external wire excitation is chosen as in 11.1, 11.2 and 11.3, but to 
maintain a constant characteristic impedance, the wire is replaced by a 
coaxial cable unshielded at the level of the apertures. This convenient means 
of excitation allows to easily choose the aperture to be irradiated. The 
frequency range can reach up to 100 MHz with less than a 3 dB variation and 
Z remains equal to 50 Ci except at the aperture level [7]. 
Figure 10: External and internal 
wire location on the scale model. 
TERNAL WIRE 
HIGH FREQUENCY MODELING OF INTERNAL COUPLINGS 
If interference precalculations are to be made, it is necessary to make 
circuit modelings of the couplings. This can be done using powerful personal 
computer codes such as "Touchstone". Such a code provides the opportunity to 
perform curve optimizations: specific goals are introduced and the adjustment 
of pertinent parameters is made automatically. 
The electrical characterization of the scale model is made in a topological 
sense which means that each part is studied independently. As an example, 
figure 11 represents the different ports where measurements are performed on 
the wing. Considering this configuration as a four port system the So 
parameters have been obtained and simultaneously, a modeling of the 
electrical circuit has been done. To take resonances in the aperture into 
account, several generator cells have been provided as reported in figure 12. 
Finally, a comparison between measured and modeled transfer functions can be 
performed using the B.L.T. equation. Figure 13 gives an example of the good 
agreement between both results at port 4, Consequently, we are now able to 
foresee the consequences of any modification on this geometry, by fitting the 
value of the pertinent circuit elements. 
Figure 11: Different ports 
of measurement on a wing. 
L 
Port 4 Unshielded cable Port 3 
Wire 1 
Figure 12: Electrical modeling of 
the coupling through the aperture 
taking resonances into account. 
Wire 2 
Figure 13: Comparison between measured 
and modeled transfer functions on port 
4 of the- wing. 
2+07 EM8 E+W 
frequencies 
72-1 
5. CONCLUSION 
The electromagnetic topology must lead to the definition of an 
electromagnetic design tool. Nowadays, several methods must be developed at 
the same time: the fundamental concepts, elaborated by C.E. Baum; a 
quantitative way dealing with the use of graph concepts. Another interesting 
method, combining the two previous ones, is to generalize the multiconductor 
transmission line network theory in the aim of integrating well known 
electromagnetic couplings in the formalism. 
The treatment of an aperture as a four-port junction is an aspect of this 
development, and has proved itself to be a convenient means to test internal 
electromagnetics. In the future, other aspects such as antenna couplings and 
current diffusion will be treated. 
In conclusion, the B.L.T. equation coupled with the multiconductor 
transmission line network formalism could become, in the future, the basis of 
an electromagnetic design tool. 
REFERENCES 
[l] C.E. Baum, 
Theory of electromagnetic interference control. Interaction Notes, Note 
478, 28 December 1989. 
[2] C.E. Baum, T.K. Liu, F.M. Tesche, 
On the analysis of general multiconductor transmission line networks. 
Interaction Notes, No 350, November 1978. 
[SI F.C. Yang, C.E. Baum, 
Electromagnetic Topology: measurements and norms of scattering parameters 
of subshields. Electromagnetics 6, 47-59, 1986. 
[4] K.S.H. Lee, 
Principles, techniques and reference data (a complete concatenation of 
technology from EMP interaction notes). EMP Interaction Motes, 2.1, 1980. 
[5] J.P. Parmantier, G .  Labaune, J.C. Alliot, P. Degauque, 
Electromagnetic coupling on complex systems: Topological approach. La 
Recherche Aerospatiale, n"1990-5. 
[6] J.P. Parmantier, G. Labaune, J.C. Alliot, P. Degauque, 
Electromagnetic Topology: Junction characterization methods. La Recherche 
Akrospatiale, n"1990-5. 
[7] J.P. Parmantier, J.P. Aparicio, 
Electromagnetic Topology: coupling of two wires through an aperture. 
Proceedings, Zurich, 1991. 


Electromagnetic topology: Characterization of internal electromagnetic coupling

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