PCB Trace and Via Current/Temperature Relationships: The Complete Analysis

by Douglas Brooks, Johannes Adam

Overview

A very important part of printed circuit board (PCB) design involves sizing traces and vias to carry the required current. This exciting new book will explore how hot traces and vias should be and what board, circuit, design, and environmental parameters are the most important. PCB materials (copper and dielectrics) and the role they play in the heating and cooling of traces are covered. The IPC curves found in IPC 2152, the equations that fit those curves and computer simulations that fit those curves and equations are detailed.

Sensitivity analyses that show what happens when environments are varied, including adjacent traces and planes, changing trace lengths, and thermal gradients are presented. Via temperatures and what determines them are explored, along with fusing issues and what happens when traces are overloaded. Voltage drops across traces and vias, the thermal effects going around right-angle corners, and frequency effects are covered. Readers learn how to measure the thermal conductivity of dielectrics and how to measure the resistivity of copper traces and why many prior attempts to do so have been doomed to failure. Industrial CT Scanning, and whether or not they might replace microsections for measuring trace parameters are also considered.

Product Details

ISBN-13:	9781630818609
Publisher:	Artech House, Incorporated
Publication date:	02/28/2021
Pages:	246
Product dimensions:	6.20(w) x 9.20(h) x 0.90(d)

About the Author

Douglas Brooks has a BS/EE and an MS/EE from Stanford and a Ph.D. from the University of Washington. For the last 30 years he has owned a small engineering service firm and written numerous technical articles on Printed Circuit Board Design and Signal Integrity issues and has published two books on these topics.

Johannes Adam is the founder of AD-AM Research in Germany. He received his Ph.D. from the University of Heidelberg.

Table of Contents

Preface xiii

Technical Note: TRM xvii

Acknowledgments xix

1 Introduction and Historical Background 1

1.1 Bottom Line 1

1.2 Historical Background 1

1.3 A Note about Consistency 5

End Notes 6

2 Materials Used in PCBs 7

2.1 Bottom Line 7

2.2 Background 7

2.3 Copper Used in PCBs 8

2.3.1 Copper-clad laminates 8

2.3.2 Copper Plating Manufacturing Step 10

2.3.3 Copper Resistivity 12

2.3.4 Summary 12

2.4 Dielectrics Used in PCBs 13

2.4.1 Thermal Conductivity (Tcon or k) 13

2.4.2 Glass Transition Temperature (Tg) 13

2.4.3 Decomposition Temperature (Td) 14

2.4.4 Time to Delamination (T260/T288) 14

2.4.5 Summary 15

End Notes 15

3 Resistivity and Resistance 17

3.1 Bottom Line 17

3.2 Resistivity 17

3.3 Resistance 20

3.4 Thermal Coefficient of Resistivity (a) 21

3.5 Measuring Resistivity 22

3.5.1 Resistivity Investigation 25

3.5.2 Nondestructive Measurements 25

End Notes 25

4 Trace Heating and Cooling 27

4.1 Bottom Line 27

4.2 Overview 27

4.3 Trace Heating 28

4.3.1 Power and Energy 28

4.3.2 Trace Heating 29

4.4 Trace Cooling 29

4.4.1 Conductive Cooling 30

4.5 Mathematical Model of Trace Heating and Cooling 32

4.6 Role of Current Density 32

4.7 Measuring Trace Temperature 33

4.7.1 IPC Procedure 33

4.7.2 Infrared Measurement 34

4.7.3 Thermocouple Measurement 35

4.7.4 Point versus Average Measurements 36

4.8 Trace Temperature Curves 36

4.8.1 Typical Curve 37

4.8.2 Heavy Overload 37

4.8.3 Marginal Overload 37

End Notes 39

5 IPC Curves 41

5.1 Bottom Line 41

5.2 IPC-2152 41

5.3 Measuring the Temperature 41

5.4 IPC Curves 44

5.4.1 External Results 44

5.4.2 External IPC Data Equations 45

5.4.3 Internal IPC Data Equations 47

5.4.4 IPC Vacuum Data 48

End Notes 50

6 Thermal Simulations 51

6.1 Bottom Line 51

6.2 Background 51

6.3 Modeling Traces 51

6.4 The Modeling Process 54

End Notes 62

7 Thermal Simulations 63

7.1 Bottom Line 63

7.2 Sensitivities: Layout Parameters 63

7.2.1 Small Trace Widths 64

7.2.2 Transient Response 66

7.2.3 Thermal Gradients 66

7.2.4 Changing Trace Length 67

7.2.5 Dimensional Uncertainties 68

7.2.6 Presence of Planes 69

7.2.7 Adjacent Trace 69

7.2.8 Adjacent Trace with Underlying Plane 71

7.2.9 Parallel Power Traces 71

7.2.10 Stacked Power Traces 72

7.2.11 Air Flow 73

7.2.12 Summary 73

7.3 Sensitivities: Material Parameters 75

7.3.1 Board Thickness and Planes 75

7.3.2 Effect of Resistivity 77

7.3.3 Effect of Heat Transfer Coefficient 78

7.3.4 Effects of Thermal Conductivity Coefficient 79

7.3.5 Effect of Trace Thickness 80

7.3.6 Summary 80

7.4 Sensitivities: Trace Depth 82

7.5 Conclusions 86

7.5.1 Call to Action 87

End Notes 87

8 Via Temperatures 89

8.1 Bottom Line 89

8.2 Background Information 89

8.3 Thermal Simulation 91

8.3.1 Simulation Strategy 91

8.3.2 Board Model 92

8.3.3 First Simulation 92

8.3.4 Additional Simulations 93

8.3.5 Two Vias 96

8.3.6 Conclusion 98

8.4 Experimental Verification 98

8.4.1 Simulation 98

8.4.2 Simulation Results 99

8.5 Experimental Results 100

8.5.1 Measured Results 100

8.5.2 Conclusion 101

8.6 Voltage Drop Across Trace and Via 102

8.6.1 Summary 103

8.7 Thermal Vias 104

8.7.1 Special Via 107

8.7.2 Conclusion 107

End Notes 107

9 Current Densities in Vias 109

9.1 Bottom Line 109

9.2 Background 109

9.3 Single Via 110

9.4 Multiple Vias 113

9.5 Multiple Vias and Turn 114

9.6 Conclusions 115

End Notes 116

10 Thinking Outside the Box 117

10.1 Bottom Line 117

10.2 Start Thinking Outside Our Boxes 117

10.3 Test Board 118

10.4 Copper Under the Trace 118

10.4.1 Discussion 119

10.5 Adding Additional Copper to Traces 120

10.5.1 Discussion 121

10.6 Dealing with Connecting Links 121

10.6.1 Discussion 123

10.7 Conclusions 124

End Notes 124

11 Fusing Currents: Background 125

11.1 Bottom Line 125

11.2 Background 125

11.3 W. H. Preece 126

11.4 I. M. Onderdonk 127

11.4.1 Cautions 129

End Notes 130

12 Fusing Currents: Analyses 133

12.1 Bottom Line 133

12.2 Background 133

12.3 Fusing Time and Temperature 134

12.4 Assumptions and Cautions 134

12.5 Simulation Models 135

12.5.1 Simulation Results, TRM Fuse 136

12.5.2 Simulation Results, TRM Trace 137

12.5.3 Short-time Effects 138

12.5.4 Final Conclusions 142

12.6 Experimental Results: 142

12.6.1 Heating Uncertainties 143

12.6.2 Cooling Uncertainties 143

12.7 The Fusing Process 144

12.7.1 Strong Overbad 145

12.7.2 Slight Overload 145

12.8 Experimental Results 145

12.8.1 Case A: Fast Fusing 146

12.8.2 Case B: Slow Fusing 147

12.83 Other Cases 149

12.9 Summary 149

End Notes 151

13 Do Traces Heat Uniformly? 153

13.1 Bottom Line 153

13.2 Background 153

13.3 Thermal Gradients on Traces 154

13.3.1 Thermal Gradients on Narrow Traces 156

13.3.2 Does Trace Thickness Matter? 156

13.3.3 Is Trace Thickness Uniform? 156

13.3.4 What Causes Thermal Nonuniformity? 157

13.3.5 Conclusion 158

13.4 Thermal Gradients Around Corners 158

13.4.1 Software Simulation 159

13.4.2 Experimental Verification 162

13.4.3 Conclusions 163

End Notes 164

14 Stop Thinking about Current Density 165

14.1 Bottom Line 165

14.2 Background 165

14.3 Current Density Is Not an Independent Variable 166

14.4 IPC Curves 166

14.5 Copper Type 166

14.6 Dielectric Type 167

14.7 Right-Angle Corners 167

14.8 Trace Form Factor 168

14.9 Via Current Densities 168

14.10 Conclusion 170

15 AC Currents 171

15.1 Bottom Line 171

15.2 Digital Simulation Models 171

15.2.1 Preliminary Results 176

15.3 Experimental Verification 177

15.3.1 Conclusions 179

15.4 Analog AC Currents 181

15.4.1 Test Circuit 181

15.4.2 RMS Signal Levels 182

15.4.3 Nonlinearities 183

15.4.4 Results 184

15.4.5 Conclusion 185

End Notes 185

16 Industrial CT (X-Ray) Scanning 187

16.1 Bottom Line 187

16.2 Background 187

16.3 The Promise 188

16.4 The Microsectioning Process 189

16.5 Industrial CT Scanning 190

16.5.1 Results 193

16.6 Comparison of the Processes 195

16.7 Conclusion 196

End Notes 196

Appendix A Measuring Thermal Conductivity 199

A.1 Measurement 199

End Notes 201

Appendix B Measuring Resistivity 203

B.1 Resistance versus Resistivity 203

B.2 How to Measure PCB Trace Resistivity 204

B.3 Problem with Ohmmeter Measurement 206

B.4 Sources of Measurement Error 207

B.4.1 Trace Width 207

B.4.2 Trace Length 208

B.4.3 Trace Thickness 208

B.4.4 Roughness 208

B.5 An Experimental Study 209

B.3.1 What Is Expected Resistivity? 211

B.6 Summary 211

End Notes 211

Appendix C IPC Internal and Vacuum Curves Fitted with Equations 213

Appendix D Detailed Bet of Equations for the Curves 219

Appendix E Current/Temperature Curves, 0.25 to 5.0 oz 221

Appendix F Current Density in Vias 231

F.1 Interpretations 231

F.1.1 Caution 232

F.1.2 Symmetry 233

F.2 Single Via Model 233

F.3 Single Via Model with Core 1 Broken into Three Cores, the First Two with 15-μm Thicknesses 233

F.4 Simulation of Four Vias, Proceeding Straight Ahead 237

F.5 Simulation of Four Vias, Traces at Right Angles 237

Appendix G Derivation of Onderdonk's Equation 243

G.1 Onderdonk's Equation 243

G.2 Background 243

G.2.1 Basic Equation 244

G.2.2 Solving the Equation 245

G.3 Proof that α_T2 *ρ_T2 =ρ_T1 *α_T1 249

End Notes 251

Appendix H Results of All Six Fusing Configuration Simulations 253

Appendix I Nonuniform Heating Patterns 257

About the Authors 261

Index 263