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, 2016 1
Transmission Line Networks 2
Transmission Line Networks Source: DELTEC electronic GmbH, Dresden, Germany http://www.deltec.de/tl_files/bilder/ \elektronikfertigung/produkte/kabel/kabelbaeume/kabelbaum_001.jpg 2
Introduction Techniques Example Stochastic Electromagnetic Fields 3 Results and Discussion Conclusion
Introduction Techniques Example Results and Discussion Conclusion Stochastic Electromagnetic Fields In electrically large cavities: By Master Sgt. John E. Lasky, U.S. Air Force http://www.defenseimagery.mil; VIRIN: 060906-F-0994L-520, Public Domain, https://commons.wikimedia.org/w/index.php?curid=4583586 3
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 https://commons.wikimedia.org/w/index.php?curid=49858294 4
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
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. 209 217, Aug. 1998, issn: 0018-9375. doi: 10.1109/15.709418 6
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. 209 217, Aug. 1998, issn: 0018-9375. doi: 10.1109/15.709418 6
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. 818 823, isbn: 978-1-4799-6615-8. doi: 10.1109/ISEMC.2015.7256269 7
Not to be Confused With a BLT Sandwich source: http://www.baconunwrapped.com/2008_06_01_archive.html 8
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
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
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. 37 44, isbn: 978-3-8007-3405-4 9
Corresponding Software 10
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
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
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: 210.2 Ω, 221.1 Ω and 234.5 Ω Alignment of line 3: ψ = 30 13
Screenshot of the Simulation Model 14
Simulation Settings 15
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
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 ) 150 100 50 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency, f (in GHz) Figure: Average squared magnitude of the coupled voltage at the terminals of the transmission line network 17
Different Load Resistances 10 3 10Z c,3 2Z c,3 Z c,3 1/2Z c,3 1/10Z c,3 U3 2 (in mv 2 ) 10 2 10 1 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 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
Different Alignments 50 ψ = 0 ψ = 30 ψ = 60 ψ = 90 U3 2 (in mv 2 ) 40 30 20 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 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
Statistic Distribution of the Squared Magnitude Cumulative distribution function 1 0.8 0.6 0.4 0.2 Minimum: Magnitude: Maximum: Simulation Simulation Simulation Theory Exponential dist. Theory 0 10 5 10 4 10 3 10 2 10 1 10 0 10 1 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
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
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
When Cables do Crosstalk... What have you guys been doing all day? We have been networking! 23
When Cables do Crosstalk... What have you guys been doing all day? We have been networking! Thanks for your attention! Are there questions? 23
Download Available Material: CONCEPT-II files MATLAB programs presentation https://www.researchgate.net/profile/mathias_ Magdowski/publications 24
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. 209 217, Aug. 1998, issn: 0018-9375. doi: 10.1109/15.709418 25