An electromagnetic topology based simulation for wave propagation through shielded and semi-shielded systems following aperture interactions

Transcription

1 Computational Methods and Experimental Measurements XII 6 An electromagnetic topology based simulation for wave propagation through shielded and semi-shielded systems following aperture interactions F. J. Agee, P. Kirawanich 2, J. Yakura 3, G. Tzeremes 4, C. Christodoulou 4 & N. E. Islam 2 Air Force Office of Scientific Research, USA 2 University of Missouri-Columbia, USA 3 Air Force Research Laboratory, USA 4 University of New Mexico, USA Abstract Electromagnetic topology based simulations have been performed for external field penetration and propagation through cables in adjacent semi-shielded and shielded systems. Following penetration through an aperture, the external pulse interacts with cables as distributed source elements. The interaction transfer function for the topological network was generated by assuming a short-circuited radiating dipole at the aperture. The simulation and analysis were performed using an electromagnetic topology domain computer code that analyzes multi-conductor transmission lines. Results show that the effects on cables depend on the nature of the external pulse and also on the amplitude and frequency component of the interacting pulse. In all cases of studies involving cross-talk geometry considerations the cables were terminated with 5 Ω. Other terminations are expected to produce different results. Keywords: electromagnetic topology, transmission line theory, system interaction, CRIPTE network simulation. Introduction Electromagnetic compatibility (EMC) and interference (EMI) analysis of electrical systems has been analyzed for some time through an alternate

2 62 Computational Methods and Experimental Measurements XII simulation technique known as electromagnetic topology (EMT) or volume decomposition of the electrical system s geometry [-4]. This simulation technique is most suited for very large electrical systems where the number of grid-points generated through conventional codes becomes unmanageable, specifically when the thinnest wires in the system need to be accounted for. For external pulse interactions through apertures it is also necessary to generate transfer functions for interactions when topological methods are used for analysis. The transfer functions can be generated through experiments and used as input to the code [5]. The transfer function can also be generated through a combination of measured and computed data or alternately computed through generated functions [4,6]. In this paper we present a topological scheme to analyze the interactions of an external electromagnetic pulse with cables inside a semi-shielded system and propagating onto a shielded system. Thus the interactions decomposed in the topological scheme include electromagnetic pulse penetration through an aperture (semi-shielded system), followed by interactions through cables that proceed to a shielded system through cables. In section 2 we begin with a brief introduction to the topological method and our topological simulation scheme. Section 3 briefly describes the transfer function method employed and the simulation results. We conclude in section 4. 2 Electromagnetic topology The Air Force Research Laboratory (AFRL), NM, has been working in developing concepts for electromagnetic topology since the early 98s for the EMC analysis of large systems [-3]. Experiments on large electrical system was carried out and verified through a topological based code in the early 99 s [7]. In our simulation studies we have used the same code for analysis (CRIPTE, Calcul sur Reseaux des Interactions Perturbatrices en Topologie Electromagnetique) [8]. In the EMT simulation method a volume can be defined as a region of space where the fields and currents are created by the same source of interference. Consider Fig. (a), with shielding structures SS and SS 2 protecting electrical systems E and E 2, respectively. E and E 2 are connected to each other by a cable running through an opening O 2. Structure SS also has an aperture O and hence is a semi-shielded system, allowing wave penetration. EMT volume decomposition of Fig. (a) is shown in Fig. (b). Volume V is the proper volume covering the entire system. Volumes V, and V,2 are the elementary volumes representing structures SS and SS 2 respectively. The volumes V 2, - V 2,4 are the elementary volumes for electrical systems and the connecting cables. The first shielding level S ; (structure outer surface) and the second shielding level S ;2 (surfaces of cable outer layer and electrical system housings) separate the volume V and V,n, and V,n and V 2,n, respectively. Each volume has different shielding levels and the interactions between the volumes are only possible through cables linking the two volumes or through openings and apertures between them. The interaction sequence diagram corresponding to the system

3 Computational Methods and Experimental Measurements XII 63 shown in Fig. is shown in Fig. 2(a) where the volume nodes and surface nodes represent physical volumes and surfaces. The volume breakdown is made under the assumption of the good shielding approximation (GSA) theory assuming that external volumes can generate interferences inside inner volumes, but the counter-interactions can be neglected [3]. Incident pulse V O V, (SS ) V,2 (SS 2 ) SS SS 2 E O 2 V 2, (E ) V 2,2 V 2,3 V 2,4 (E 2 ) E 2 (a) (b) Figure : Diagrams of (a) the shielded rooms with aperture and (b) the volume decomposition. The branch between two volume nodes shows the penetration path from one volume to the other through surface openings or cables (solid-arrow lines) within the same shielding level, and through ambient space (dashed-arrow lines) between two different shielding levels. The surface nodes are associated with the penetration points through apertures. This concept makes EMT a feasible way to treat the internal EMI problems separately from the outer volume. Fig. 2(b) shows the tube and junction-like topological network associated with the topological diagram shown in Fig. 2(a). It is also assumed that SS 2 (V,2 ) is perfectly shielded. The interactions through the cables are represented by the solid-line tubes while the dashed-line tubes show the outside-to-inside transfer function. The topological code (CRIPTE) solves the network representation shown in Fig. 2(b), through solution of tubes and junctions that are incorporated through the BLT (Baum Liu and Tesche [9]) equation given by ([ I ] [ S][ Γ]).[ W ()] = [ S].[ Ws], () where [I], [S], and [Γ] are the identity, network scattering, and propagation supermatrices, respectively. The terms [W()] and [Ws] are the outgoing and source wave supervectors, respectively. The solution of the BLT equations has been incorporated in the CRIPTE code using the well-known LU method []. The interactions caused by the penetration through the ambient space (dashedline tube) have been investigated by the power balance concept [] and the extended BLT equation [2].

4 64 Computational Methods and Experimental Measurements XII O V Surface node Volume node S; V V, O2 V,2 TF O2 S;2 E O2 E2 V2, V2,2 V2,3 V2,4 (a) (b) Figure 2: Schematics of (a) interaction diagrams and (b) topological network associated with the system in Fig.. 3 System interaction technique based on transmission line theory The aperture equivalent sources can be represented by equivalent electric and magnetic dipole moments as discussed earlier [3-5]. The system coupling using the short imaginary radiating dipole method is shown in Fig. 3 as represented by network I. Network II in Fig. 3 represents components and connections of the system interior. It consists of two main tubes (T and T 2 ) for eight-conductor cables and two junctions (E and E 2 ) for the terminating impedances of both electrical modules and one junction (O 2 ) for the straightthrough connection type between cables T and T 2. The dotted-line junction between E and O 2 represents the coupling on tube T of the distributed equivalent generator V s originally generated by the topological network I. The equivalent voltage generators, which represent distributed source couplings on the cable over the ground plane, are derived from the incident electric field on the cable and from the reflected electric field from the ground plane in the absence of wiring so as to avoid wave reflection. The coupling methods of the incident fields on the cable incorporated in the code can be implemented through the Agrawal s formulation [6], as given by inc ref Vs ( z) = Ez ( h, z) + Ez ( h, z). (2) By incorporating the voltage in eqn (2), the source waves in eqn () can be written as [ Ws( z)] = z γ ( z ) [ e [ V ( z )] + [ Z ][ I ( z )]] dz z s C s, (3)

5 Computational Methods and Experimental Measurements XII 65 where [γ] is a propagation matrix and I s (z) = for the distributed source coupling. Then the voltage and current along the transmission line in the z direction can be determined through the definition of waves by [ W ( z)] = [ V ( z)] + [ Z ][ I( z)]. (4) C _ + Z H SC E SC Z Junction O2 (direct connection) Network I Z L Junctions E and E2 Network II E T O2 T2 Vs Vs Vs E x z Cable cross section for T and T2 Figure 3: Detailed configuration of topological networks and their components used in the EMT calculations. We make the following assumptions in our analysis: (a) the dimension of the radiating transmission line, the height of the transmission line from the ground, and the aperture length are assumed to be electrically small compared to the wavelength λ at the frequency of interest (λ = v /f, where v is the speed of light in free apace = 3 8 m/s); (b) the internal cable is located over the perfectly conducting ground plane in order to eliminate the antenna mode currents. Therefore, in the CRIPTE transmission line model it is possible to consider only the transmission line mode current; (c) the radiation losses due to the medium inside the inner volume are neglected; (d) since the aperture is assumed to be a one-dimensional gap, for convenience, the aperture polarizabilities are not taken into account; and (e) the coupling voltage generator in eqn (2) on the multiconductor cable T account only for the incident and ground-reflected E-fields, neglecting the wall-reflected E-field. 4 Simulation results In both the FDTD and EMT simulation approaches, we consider the case when the dimension of the aperture is electrically small relative to the wavelength. The

6 66 Computational Methods and Experimental Measurements XII results were first simulated using the FDTD method based on Yee s algorithm in free space [7]. The cell dimension is much less than the minimum wavelength. The finite difference equations in three dimensions have the same spatial steps as x = y = z = 6 mm. Once the grid size was defined, the next consideration was the stability by choosing the small enough time step t. The appropriate choice is x/2.c which gives ps where c is the speed of wave in free space. An incident Gaussian pulse is applied as the y-polarized excitation of the difference equations given by E inc 2 2 [ ( n t t ) / 2σ ] e = E, (5) where E is the peak amplitude, t is the original location of the peak, and σ is proportional to the pulse width. Fig. 4 shows the FDTD generated H-field (H SC ) and the E-field (E SC ) waveforms at the screen when the aperture is short-circuited when E is unity. The waveforms in Figs. 4(a) and 4(b) are H SC and E SC, respectively, for the 3.6-ns incident Gaussian pulse. Figs. 4(c) and 4(d) are the corresponding H SC and E SC, for the.36-ns incident Gaussian pulse. These waveforms are used in the radiation dipole antenna to generate fields at a distance from the aperture. To examine the effect of the electromagnetic fields on the system interior, the voltage signals propagating between both computers (E and E 2 ) were simulated. The excitation sources are incident Gaussian pulses as the mechanism of the penetration through the aperture was previously discussed. The -m multiconductor cable connecting both terminals is driven by a -V driving voltage source applied at the terminal E on conductor #, as labeled in Fig. 3. The terminating impedance of each port was represented by a 5-Ω resistance. The simulation results show the behavior of the signals before and after being disturbed by external excitations. Figs. 5(a) and 5(b) show the spectral components of the cable voltages at E and E 2, respectively, for each conductor (# through #8) without any influence caused by external perturbations. The strongest signal appears on conductor # as it is driven by the voltage source. The responses on the other conductors are the crosstalk signals induced by the signal on conductor #. The associated voltage responses of the system after being excited by the Gaussian pulses are shown in Figs. 5(c) through 5(f). The results shown in Figs. 5(c) and 5(d) for the cable signals at terminal E and E 2, respectively, show that the 3.6-ns incident pulse at the outer surface can upset the cable signals when the disturbing frequency range is from dc to MHz. For the system under the external excitation caused by the.36-ns incident pulse, the upset zone can be observed at frequencies from approximately MHz to 2 MHz, as shown in Figs. 5(e) and 5(f) for terminals E and E 2, respectively. The reason is that the amplitudes of pulse spectral contents account for the behaviors of the cable responses. The 3.6-ns Gaussian pulse has large-amplitude frequency components at low frequencies while those of the.36-ns Gaussian pulse exist at high frequencies.

7 Computational Methods and Experimental Measurements XII 67 Severity of the effects at high frequencies is of concern since the faster rise time of external perturbations induced the voltage to increase in amplitude. In addition, the cable resonances due to the mismatched impedances at cable extremities have a tendency to magnify the signal propagating on the cable as the frequency increases. Finally the results also show that even though the sensitive electrical system, i.e. E 2, is securely protected by the shielded wall, the disturbance can still be introduced into the system by the cable interaction through the wall. (a) (b) (c) (d) Figure 4: 5 Conclusion Time-domain plots of (a) H SC and (b) E SC due to a 3.6-ns Gaussian incident pulse, and (c) H SC and (d) E SC due to a.36-ns Gaussian incident pulse. Electromagnetic field perturbation at apertures and propagation along multiple conductors in shielded areas can be studied through topological analysis. The transfer function is generated at the aperture as a short radiating dipole that illuminates the unshielded portion of the cable as distributed sources. The current and voltage wave then propagates through the multi-conductor cables. The external-internal interactions can be initially determined based on the transmission line theory with an FDTD-created driving source. Using the transfer function generated through this technique, it is possible to generate the electric fields coupling on the system interior.

8 68 Computational Methods and Experimental Measurements XII (a) at E (b) at E2.8.8 # # Upset zone (c) at E Upset zone (d) at E (e) at E Upset zone (f) at E2 Upset zone Figure 5: 2 3 Voltage spectral components of individual conductor at both terminals: (a)-(b) without excitation sources, (c)-(d) with a 3.6-ns Gaussian pulse, and (e)-(f) with a.36-ns Gaussian pulse. (E = e3).

9 Computational Methods and Experimental Measurements XII 69 Analysis shows that the responses of a system to external perturbations depend to a large extent on the incident pulse characteristics, conductor geometries and terminating impedances. Results also show that the effects on cables depend on the nature of external pulses and also on the amplitude and frequency components of the interacting pulse. Hardening of even a shielded system is of concern when the communication lines connect to peripherals through its walls. References [] C. E. Baum, Electromagnetic Topology: A formal approach to the analysis and design of complex electronic systems, Interaction Notes, 4, Kirtland, 98; also in Proc. Zurich EMC Symp, pp , 98. [2] J-P. Parmantier, J-C. Alliot, G. Labaune, and P. Degauque, Electromagnetic coupling on complex systems: topological approach, Interaction Notes, 488, 99. [3] C. E. Baum, The theory of electromagnetic interference control, Interaction Notes, 478, 989. [4] P. Kirawanich, R. Gunda, N. Kranthi, J. C. Kroenung, and N. E. Islam, Methodology for interference analysis using electromagnetic topology techniques, Appl. Phys. Lett, 84(5), pp , 24. [5] J-P. Parmantier and J-P. Aparicio, Electromagnetic topology: Coupling of two wires through an aperture, in Proc. Zurich EMC Symp, pp , 99. [6] G. Tzeremes, P. Kirawanich, C. Christodoulou, and N. E. Islam, Transmission lines as radiating antenna in sources aperture interactions in electromagnetic topology simulations, Antennas and Wireless Propagat. Lett, 3(5), pp , 24. [7] J-P. Parmantier, V. Gobin, F. Issac, I. Junqua, Y. Daudy, and J. M. Lagarde, An application of the electromagnetic topology theory on the test-bed aircraft, EMPTAC, Interaction Notes, 56, 993. [8] CRIPTE user s manual: research version. 23. [9] C. E. Baum, T. K. Liu, and F. M. Tesche, On the analysis of general multiconductor transmission-line networks, Interaction Notes, 35, 978. [] J. P. Parmantier, X. Ferrieres, S. Bertuol, and C. E. Baum Various ways to think of the resolution of the BLT equation with an LU technique, Interaction Notes, 535, 998. [] J-P. Parmantier, Numerical coupling models for complex systems and results, IEEE Trans. Electromagn. Compat, 46(3), pp , 24. [2] F. M. Tesche and C. M. Butler, On the addition of EM field propagation and coupling effects in the BLT equation, Interaction Notes, 588, 24. [3] F. M. Tesche, M. Ianoz, and T. Karlsson, EMC: Analysis Methods and Computational Models, Wiley: New York, 997. [4] P. Kirawanich, N. Kranthi, R. Gunda, A. R. Stillwell, and N. E. Islam, A method to characterize the interactions of external pulses and

10 6 Computational Methods and Experimental Measurements XII multiconductor lines in electromenetic topology based simulations, Jour. Appl. Phys., 96(), 24. [5] C. M. Butler, Y. Rahmat-Samii, and R. Mittra, Electromagnetic penetration through apertures in conducting surfaces, IEEE Trans. Electromagn. Compat, EMC-2(), pp , 978. [6] A. K. Agrawal, H. J. Price, and S. H. Gurbaxani, Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field, IEEE Trans. Electromagn. Compat, 22, pp. 9-29, 98. [7] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell s equations in isotropic media, IEEE Trans. Antennas Propagat., AP-4(3), pp , 966.