Tensorial Analysis of Networks (TAN) Modelling for PCB Signal Integrity and EMC Analysis (Materials, Circuits and Devices)

Cover
Contents
About the editors
Foreword
	References
1 General introduction
	Abstract
	1.1 Preliminary introduction
	1.2 Chapter 2: Basic knowledge to practice TAN for PCB SI/PI/EMC investigation
	1.3 Chapter 3: PCB primitive components analysis with TAN
	1.4 Chapter 4: Analytical calculation of PCB trace
	1.5 Chapter 5: Fast
	1.6 Chapter 6: Time domain TAN modelling of PCB lumped system with Kron's method
	1.7 Chapter 7: Direct time-domain analysis with TAN method for distributed PCB modelling
	1.8 Chapter 8: Coupling between EM field and multilayer PCB with MKME
	1.9 Chapter 9: Conducted emissions (CEs) EMCTAN modelling
	1.10 Chapter 10: PCB-conducted susceptibility (CS) EMCTAN modelling
	1.11 Chapter 11: PCB-radiated susceptibility (RS) EMCTAN modelling
	1.12 Chapter 12: TAN model of loop probe coupling onto shielded coaxial short cable
	1.13 Chapter 13: Nonlinear behaviour conducted EMC model of an ADC-based mixed PCB under radiofrequency interference (RFI)
	1.14 Chapter 14: Far-field prediction combining simulations with near-field measurements for EMI assessment of PCBs
	1.15 Chapter 15: Element of information for numerical modelling on PCB
	1.16 Chapter 16: General conclusion
2 Basic knowledge to practice TAN for PCB SI/PI/EMC investigation
	Abstract
	2.1 TAN principles
	2.2 Electronic world and electronic scaling
		2.2.1 Propagation
		2.2.2 Lines and microstrips modelling
		2.2.3 Some particular applications
		2.2.4 Lossy propagation model
		2.2.5 Asymptotic behaviour without propagation
		2.2.6 Field coupling modelling
			2.2.6.1 Capacitive coupling
			2.2.6.2 Common ground couplings
			2.2.6.3 Mutual inductance coupling
			2.2.6.4 Crosstalk coupling
		2.2.7 Components modelling
			2.2.7.1 Model for nonlinear behaviour in general
			2.2.7.2 ICEM model
			2.2.7.3 IBIS model
	Annexe 2. A
	Annexe 2. B
	References
3 PCB primitive components analysis with TAN
	Abstract
	3.1 TAN operators for electrical application
		3.1.1 Covariant parameters: voltage tensors
		3.1.2 Contravariant parameters: current tensors
		3.1.3 Twice covariant parameters: impedance tensors
		3.1.4 Electrical problem metric elaboration
		3.1.5 Branch space to mesh space conversion
	3.2 TAN modelling methodology
	3.3 PCB elements modelling
		3.3.1 Interconnects
			3.3.1.1 Telegrapher's model
			3.3.1.2 PCB trace modelling
			3.3.1.3 Kron–Branin model
		3.3.2 Vias
		3.3.3 Power-ground plane
		3.3.4 SMA connectors
	References
4 Analytical calculation of PCB trace Z/Y/T/S matrices with TAN approach
	Abstract
	4.1 Introduction
	4.2 General description of P-port system
		4.2.1 Diagram representation
		4.2.2 Analytical variables constituting PCB electrical interconnections
			4.2.2.1 Z-matrix definition
			4.2.2.2 Y-matrix definition
			4.2.2.3 T-matrix definition
			4.2.2.4 S-matrix definition
		4.2.3 TAN modelling methodology
			4.2.3.1 Algorithmic methodological representation
			4.2.3.2 Topological parameters
			4.2.3.3 Branch space variables
			4.2.3.4 Mesh space variables
			4.2.3.5 Branch and mesh current identity
			4.2.3.6 Calculation of S-matrix
	4.3 Application study of the TAN method to Y-tree shape PCB trace modelling
		4.3.1 Y-tree PCB problem description
		4.3.2 TAN modelling of RLC Y-tree
			4.3.2.1 TAN graph topology
			4.3.2.2 Topological index parameters
			4.3.2.3 Branch space analysis
			4.3.2.4 Mesh space analysis
			4.3.2.5 Z-matrix calculation
			4.3.2.6 Y-matrix calculation
			4.3.2.7 S-matrix extraction
		4.3.3 Validation result with SPICE simulations
			4.3.3.1 POC description
			4.3.3.2 Discussion on computed results
			4.3.3.3 Partial conclusion
	4.4 Application study to Ψ-shape microstrip interconnect
	4.4.1 Analytical investigation on the TAN modelling of Ψ-tree PCB
		4.4.1.1 Problem formulation of Ψ-tree PCB trace
		4.4.1.2 Topological index parameters
		4.4.1.3 TAN graph topology
		4.4.1.4 Branch space analysis
		4.4.1.5 Connectivity
		4.4.1.6 Mesh space analysis
	4.4.2 Validation results with SPICE simulations
		4.4.2.1 POC description
		4.4.2.2 Discussion on computed results
		4.4.2.3 Partial conclusion
	4.5 Conclusion
	References
5 Fast S-parameter Kron–Branin's modelling of rectangular wave guide (RWG) structure via mesh impedance reduction
	Abstract
	5.1 Introduction to Chapter 5
	5.2 Problem formulation
		5.2.1 Structural description
		5.2.2 Representation of S-matrix black box
	5.3 KB theorization of RWG matrix
		5.3.1 Recall on RWG and TL theory
			5.3.1.1 RWG characterization
			5.3.1.2 TL equivalent circuit of the RWG structure
			5.3.1.3 TL equivalent circuit of RWG with the first propagative mode
			5.3.1.4 TL equivalent circuit of RWG under the evanescent mode
		5.3.2 KB modelling of RWG
			5.3.2.1 TL equivalent circuit
			5.3.2.2 KB graph topology equivalent to the RWG
			5.3.2.3 S-matrix analytical expression of the RWG
	5.4 Validation results with parametric analyses
		5.4.1 Description of RWG POC
			5.4.1.1 RWG POC description
			5.4.1.2 Equivalent TL parameters
			5.4.1.3 Routine algorithm of the RWG KB modelling
		5.4.2 Discussion on RWG simulation results
			5.4.2.1 S-parameter parametric analyses versus position z
			5.4.2.2 Comparisons between S-parameter KB-computed and ADS-simulated results
	5.5 Conclusion
	References
6 Time-domain TAN modelling of PCB-lumped system with Kron's method
	Abstract
	6.1 Introduction
	6.2 Basic definitions and general methodology of the innovative direct TD TAN modelling of PCBs
		6.2.1 Representation of TAN topology in the TD
			6.2.1.1 Excitation signal description
			6.2.1.2 Block diagram representation
		6.2.2 Key parameters of TD implementation of TAN approach
		6.2.3 TAN TD primitive elements
			6.2.3.1 TD TAN general transfer equation
			6.2.3.2 Dictionary of TD TAN modelling
			6.2.3.3 Inductive element time-difference tensorial expression
			6.2.3.4 Capacitive element time-difference tensorial expression
		6.2.4 Methodology of PCB trace modelling with TAN TD approach
	6.3 Application to two port LC circuits
		6.3.1 TD TAN application with TT LC circuit
			6.3.1.1 Description of the TT-topology circuit
			6.3.1.2 Equivalent of the TT-topology circuit
			6.3.1.3 Branch space analysis
			6.3.1.4 Mesh space analysis
			6.3.1.5 Expression of VTF
			6.3.1.6 Discrete expression of the output
			6.3.1.7 Computed results
			6.3.1.8 Partial conclusion
		6.3.2 TD TAN application with Y-tree LC circuit
			6.3.2.1 Recall on the mesh impedance of based Y-tree network
			6.3.2.2 TAN modelling of RLC-basedY-tree network
			6.3.2.3 VTFs of Y-tree
			6.3.2.4 Time-domain metric
			6.3.2.5 Computed results
			6.3.2.6 Partial conclusion
	6.4 Conclusion
	References
7 Direct time-domain analysis with TAN method for distributed PCB modelling
	Abstract
	7.1 Introduction
		7.1.1 Branin's TD expression
		7.1.2 Via's TD expression
	7.2 Application example of TD TAN modelling
		7.2.1 Graph topology of the 3D multilayer hybrid PCB
		7.2.2 Integration of the innovative direct TD method
			7.2.2.1 Characteristic matrix in mesh space
			7.2.2.2 TD KB modelling principle
		7.2.3 Validation results
			7.2.3.1 Prototype design and fabrication
			7.2.3.2 TD experimental results
	7.3 Conclusion
	Reference
8 Coupling between EM field and multilayer PCB with MKME
	Abstract
	8.1 Introduction to R-EMC analytical modelling
	8.2 Bibliography of MKME formalism on EMC of PCB
	8.3 Recall on MKME mesh space to moment space definition
	8.4 Recall on field coupling with MKME formalism
		8.4.1 Electric coupling
		8.4.2 Magnetic coupling
	8.5 MKME model for 3D multilayer PCB illuminated by EM plane wave
		8.5.1 Formulation of the problem
		8.5.2 MKME model establishment
			8.5.2.1 Graph topology establishment
			8.5.2.2 Graph to tensorial object
		8.5.3 Validation results
			8.5.3.1 Description of the POC
			8.5.3.2 Case 1: frequency-independent field with different angles
			8.5.3.3 Case 2: illuminated field square waveform
			8.5.3.4 Comments on the calculated and simulated results
			8.5.3.5 Experimental results
	8.6 Conclusion
	References
9 Conducted emissions (CEs) EMCTAN modelling
	Abstract
	9.1 The ICEM model and the EMC problem
	9.2 Noise source
		9.2.1 Current noise source
		9.2.2 Thermal noise source
	9.3 IC package
		9.3.1 First or second order access network (AN)
		9.3.2 N order AN
		9.3.3 Couplings between AN
			9.3.3.1 Mutual inductance couplings
			9.3.3.2 Capacitive couplings
	9.4 Synthesis of the package impedance operator construction methodology
	9.5 Computing the package model
		9.5.1 Measuring resistances
		9.5.2 Measuring inductances
			9.5.2.1 Low frequency limit determination
			9.5.2.2 High frequency limit determination
			9.5.2.3 measurement
			measurement
		9.5.3 Measuring mutual inductances
		9.5.4 Measuring capacitance
		9.5.5 Measuring mutual capacitance
	9.6 Acquiring the IA and complete component model for conducted emissions
	9.7 Coupling between blocks in the chip
	9.8 Conducted emissions of power electronics
		9.8.1 Power chopper
			9.8.1.1 Direct commutation modelling
			9.8.1.2 Commutation through ccc
		9.8.2 The generic power chopper
	9.9 Other nonlinear noise sources
	9.10 From the component to the PCB connectors
		9.10.1 PP diagram
		9.10.2 Interaction matrix and architecture decision
		9.10.3 Box influence
		9.10.4 Connecting the component to the microstrip network
		9.10.5 Multilayers PCB
			9.10.5.1 Common impedance and transfer impedance coupling
			9.10.5.2 Couplings through PCB borders
		9.10.6 Locating the solution on the PP diagram and conclusion on the EMC risk
	9.11 Some indications on hyperfrequency modelling
	Annexe 9. A
	Annexe 9. B
	Annexe 9. C
	References
10 PCB-conducted susceptibility (CS) EMCTAN modelling
	Abstract
	10.1 Disturbing mechanisms
	10.2 Field-to-line coupling
		10.2.1 Magnetic field coupling
		10.2.2 Electric field coupling
		10.2.3 Conclusion on the field-to-line coupling fundamental processes
	10.3 Coupling to shielded cables
	10.4 An example of a conducted source coming from an external field to harnesses coupling
	10.5 In-band component disturbance risk
		10.5.1 Digital circuits
		10.5.2 Analogue circuits—operational amplifiers
	10.6 Transmission to the component through the PCB
	10.7 The failure risk
	10.8 Out-band component disturbance risk
	10.9 Radioreceptor circuits
		10.9.1 In-band radioreceptor disturbances
		10.9.2 Out-band radioreceptor disturbances
		10.9.3 Sources of disturbances of radio receptor on the PCB
			10.9.3.1 Couplings through layers
			10.9.3.2 Couplings through the equipment cavity
	Annexe 10. A
	References
11 PCB-radiated susceptibility (RS) EMCTAN modelling
	Abstract
	11.1 Far-field coupling
	11.2 MKME for 3D multilayer PCB illuminated by I-microstrip line
		11.2.1 Description of system
		11.2.2 MKME topological analysis
		11.2.3 Validation results
			11.2.3.1 POC description
			11.2.3.2 Discussion on the computed coupling voltages
	11.3 Sensitivity analysis with MKME
		11.3.1 Sensitivity analysis with theoretical expression for Branin's model
			11.3.1.1 Theoretical analysis
			11.3.1.2 Numerical analysis
		11.3.2 Conclusion
	References
12 TAN model of loop probe coupling onto shielded coaxial short cable
	Abstract
	12.1 Introduction
	12.2 Formulation of problem constituted by shielded cable under loop probe radiated field aggression
		12.2.1 Geometrical definition of the problem
		12.2.2 Electrical description of the problem
			12.2.2.1 Circuit model
			12.2.2.2 Impedance description of constituting network elements
		12.2.3 Formulation of shielding effectiveness (SE)
	12.3 Theoretical investigation of SE modelling with TAN approach
		12.3.1 Methodology of the S-parameter modelling of coaxial modelling under probe EM radiation
		12.3.2 Elaboration of equivalent graph
			12.3.2.1 TAN graph index parameters
			12.3.2.2 Branch space analysis
			12.3.2.3 TAN connectivity dedicated to full
			parameter modelling
			12.3.2.4 Mesh space analysis
		12.3.3 Equivalent equation of multi-port black box
			12.3.3.1
			matrix extraction
			12.3.3.2 Extraction of
			matrix impedance
	12.4 Validation results
		12.4.1 Description of the POC structure
			12.4.1.1 Description of POC HFSS design
			12.4.1.2 Description of POCADS design
		12.4.2 Comparisons of computed and simulated S-parameters
			12.4.2.1 S-parameter-based validation results
			12.4.2.2 SE analyses
			12.4.2.3 Study of influence of x0
			12.4.2.4 Study of influence of z0
		12.4.3 Discussion on the advantages and drawbacks of the TAN model
	12.5 Conclusion
	References
13 Nonlinear behaviour conduced EMC model of an ADC-based mixed PCB under radio-frequency interference (RFI)
	Abstract
	13.1 Introduction
	13.2 Description of the NL model of a mixed circuit under study
		13.2.1 EMC problem formulation
		13.2.2 Analytical definition of RFI
		13.2.3 Output voltage analytical expression
	13.3 Methodology of the EMC NL modelling of a mixed circuit
		13.3.1 Nonlinear model flow design and an input–output equivalent transfer circuit
		13.3.2 Description of monitoring code implemented in MATLAB
			13.3.2.1 Embedded software implemented into the μC
			13.3.2.2 Implementation of automatic program
	13.4 Validation results with parametric analyses
		13.4.1 Experimental set-up configuration
		13.4.2 Empirical characteristics of RFI
		13.4.3 Discussion on simulation and test results
	13.5 Conclusion
	Acknowledgement
	References
14 Far-field prediction combining simulations with near-field measurements for EMI assessment of PCBs
	Abstract
	14.1 Introduction
	14.2 Near-field scanning fundamentals
		14.2.1 Near-and far-field definition
		14.2.2 Radiation pattern
		14.2.3 Near-field scanner system
		14.2.4 Basic probes for near-field scanning
		14.2.5 Near-field scanner NFS3000
	14.3 Theoretical basics of near-to-far-field transformation
		14.3.1 Introduction
		14.3.2 Maxwell's equations
		14.3.3 Material equations
		14.3.4 Electromagnetic boundary conditions
		14.3.5 Formulations for radiation
		14.3.6 Surface equivalence theorem
		14.3.7 Surface equivalence theorem for the NFS environment
	14.4 Near-field-to-far-field transformation using the Huygens' box principle
		14.4.1 Huygens' box measurement
		14.4.2 Validation example and setup
		14.4.3 Near-field results
		14.4.4 Near-field-to-far-field transformation
			14.4.4.1 Without phase relation
			14.4.4.2 With phase relation
	14.5 Extended use of the near-field scan
	14.6 Conclusion
	References
15 Element of information for numerical modelling on PCB: focus on boundary element method
	Abstract
	15.1 Boundary element method
		15.1.1 Integral representation formulas
		15.1.2 Integral equation
		15.1.3 Variational formulation and finite element approximation
		15.1.4 Solution
	15.2 Numerical and practical issues
		15.2.1 Performance issue and fast solvers
		15.2.2 Low-frequency instability
		15.2.3 Meshing
	15.3 Formulation and stability issues
		15.3.1 LAYER formulation
		15.3.2 Validation with an analytic solution
	15.4 A posteriori error estimate and adaptive BEM
		15.4.1 A posteriori error estimate
		15.4.2 Adaptive mesh refinement
		15.4.3 Stopping criterion
	Acknowledgements
	References
16 General conclusion
	Abstract
	16.1 Final words on the developed EMC, SI and PI analyses of PCBs based on the TAN formalism
	16.2 Summary on the fundamental elements to practice Kron's method
	16.3 Summary on PCB interconnect modelling in the frequency domain with TAN approach
	16.4 Summary on the PCB modelling in the time domain
	16.5 Summary on the radiated EMC modelling of PCB with TAN approach
	16.6 Summary on the conducted EMC modelling of PCBs with TAN approach
	16.7 Summary on the TAN modelling of PCB metallic shielding cuboid
	16.8 Summary on TAN modelling of coaxial cable under EM NF radiation from electronic loop probe
	16.9 Summary on the analysis of NL EMC effect for mixed PCBs
	16.10 Summary on the overview of PCB numerical modelling
	16.11 Concluding remark
	References
Index
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