Efficient Full-Wave Simulation of the Stochastic Electromagnetic Field Coupling to Transmission Line Networks using the Method of Moments

Transcription

1 Efficient Full-Wave Simulation of the Stochastic Electromagnetic Field Coupling to Transmission Line Networks using the Method of Moments Mathias Magdowski and Ralf Vick Chair for Electromagnetic Compatibility Institute for Medical Engineering Otto von Guericke University, Magdeburg, Germany July 11,

2 Transmission Line Networks 2

3 Transmission Line Networks Source: DELTEC electronic GmbH, Dresden, Germany \elektronikfertigung/produkte/kabel/kabelbaeume/kabelbaum_001.jpg 2

4 Introduction Techniques Example Stochastic Electromagnetic Fields 3 Results and Discussion Conclusion

5 Introduction Techniques Example Results and Discussion Conclusion Stochastic Electromagnetic Fields In electrically large cavities: By Master Sgt. John E. Lasky, U.S. Air Force VIRIN: F-0994L-520, Public Domain, 3

6 Stochastic Electromagnetic Fields In reverberation chambers: Small mode-stirred chamber of the chair for electromagnetic compatibility at the Otto von Guericke university in Magdeburg, Germany Available via Wikimedia Commons 4

7 Overview Introduction Simulation Techniques Simulation Example Results and Discussion Coupled Voltage as a Function of the Frequency Statistic Distribution of the Coupled Voltage Conclusion 5

8 Plane Wave Integral Representation Idea: Source: D. A. Hill, Plane wave integral representation for fields in reverberation chambers, IEEE Transactions on Electromagnetic Compatibility, vol. 40, no. 3, pp , Aug. 1998, issn: doi: /

9 Plane Wave Integral Representation Idea: Source: D. A. Hill, Plane wave integral representation for fields in reverberation chambers, IEEE Transactions on Electromagnetic Compatibility, vol. 40, no. 3, pp , Aug. 1998, issn: doi: /

10 BLT Equation (named after Baum, Liu & Tesche) Terminal voltages: [ ] [UL1 ] [U L ] = = [ [E] + [ρ] ] [[Γ] [ρ] ] 1 [S] [U L2 ] }{{}}{{}}{{} current or transmission source voltage line vector response resonances [E]: identity matrix [ρ]: reflection matrix [Γ]: propagation matrix Source: M. Magdowski and R. Vick, Numerical simulation of the stochastic electromagnetic field coupling to transmission line networks, in Proceedings of the Joint IEEE International Symposium on Electromagnetic Compatibility and EMC Europe, IEEE Catalog Number: CFP15EMC-USB, Dresden, Germany, Aug. 2015, pp , isbn: doi: /ISEMC

11 Not to be Confused With a BLT Sandwich source: 8

12 Full Wave Simulations Using the Method of Moments Problems when simulating the whole cavity: large number of unknowns, high computational effort resonance problems specific to the MoM 9

13 Full Wave Simulations Using the Method of Moments Problems when simulating the whole cavity: large number of unknowns, high computational effort resonance problems specific to the MoM How about using the plane wave approach: + less unknowns, no resonances still long computation time 9

14 Full Wave Simulations Using the Method of Moments Problems when simulating the whole cavity: large number of unknowns, high computational effort resonance problems specific to the MoM How about using the plane wave approach: + less unknowns, no resonances still long computation time Solution: A. Schröder, H.-D. Brüns, and C. Schuster, Beschleunigung schneller Löser in der Momentenmethode bei Einkopplungsproblemen mit Mehrfachanregung, in EMV 2012 Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf, Germany: VDE Verlag, Feb. 2012, pp , isbn:

15 Corresponding Software 10

16 Intermediate Overview Introduction Simulation Techniques Simulation Example Results and Discussion Coupled Voltage as a Function of the Frequency Statistic Distribution of the Coupled Voltage Conclusion 11

17 Schematic of the Transmission Line Network 2 Z L2 = 2Z c,2 1 Z L1 = Z c,1 3 ψ Z L3 = Z c,3 2 12

18 Parameters of the Transmission Line Network Line lengths: 40 cm, 30 cm and 50 cm Line radii: 0.6 mm, 0.5 mm and 0.4 mm Line heights: 1 cm (transmission line theory is applicable up to 4.7 GHz) Characteristic impedances: Ω, Ω and Ω Alignment of line 3: ψ = 30 13

19 Screenshot of the Simulation Model 14

20 Simulation Settings 15

21 Intermediate Overview Introduction Simulation Techniques Simulation Example Results and Discussion Coupled Voltage as a Function of the Frequency Statistic Distribution of the Coupled Voltage Conclusion 16

22 Basic Configuration of the Network 200 BLT Equations: U 1 U 2 U 3 Method of Moments: U 1 U 2 U 3 U 2 (in mv 2 ) Frequency, f (in GHz) Figure: Average squared magnitude of the coupled voltage at the terminals of the transmission line network 17

23 Different Load Resistances Z c,3 2Z c,3 Z c,3 1/2Z c,3 1/10Z c,3 U3 2 (in mv 2 ) Frequency, f (in GHz) Figure: Average squared magnitude of the coupled voltage at the end of transmission line 3 for different load resistances at this line end 18

24 Different Alignments 50 ψ = 0 ψ = 30 ψ = 60 ψ = 90 U3 2 (in mv 2 ) Frequency, f (in GHz) Figure: Average squared magnitude of the coupled voltage at the end of transmission line 3 for different alignments of this line 19

25 Statistic Distribution of the Squared Magnitude Cumulative distribution function Minimum: Magnitude: Maximum: Simulation Simulation Simulation Theory Exponential dist. Theory Normalized squared voltage magnitude, U 3 2 / U 3 2 Figure: Cumulative distribution function of the squared magnitude of the coupled voltage at the end of transmission line 3 normalized to the mean 20

26 Intermediate Overview Introduction Simulation Techniques Simulation Example Results and Discussion Coupled Voltage as a Function of the Frequency Statistic Distribution of the Coupled Voltage Conclusion 21

27 Conclusion Results: coupling of stochastic fields into a simple network of single-wire transmission lines above ground classical transmission line theory vs. optimized MoM code comparable computational effort, but MoM allows more arbitrary transmission line structures (e. g. non-uniform lines) Future works: measurements networks of double-wire or multiconductor lines 22

28 When Cables do Crosstalk... What have you guys been doing all day? We have been networking! 23

29 When Cables do Crosstalk... What have you guys been doing all day? We have been networking! Thanks for your attention! Are there questions? 23

30 Download Available Material: CONCEPT-II files MATLAB programs presentation Magdowski/publications 24

31 Chamber Constant QP E 0 = ωεv Q, V : quality factor and volume of the chamber P : input/dissipated power ω: angular frequency of the excitation ε: permittivity of the medium Source: D. A. Hill, Plane wave integral representation for fields in reverberation chambers, IEEE Transactions on Electromagnetic Compatibility, vol. 40, no. 3, pp , Aug. 1998, issn: doi: /