Chi-Wah Kok, Canaan Microelectronics Corporation Limited, ChinaChi-Wah Kok obtained his degree from the University of Wisconsin Madison. Since 1992, he has been working with various semi-conductor companies, research institutions and universities, which include AT&T Labs Research, Holmdel, SONY U.S. Research Labs, Stanford University, Hong Kong University of Science and Technology, Hong Kong Polytechnic University, City University of Hong Kong, and Lattice Semiconductor. In 2006, he founded Canaan Microelectronics Corp Ltd., a fabless IC company with products in mixed signal IC for consumer electronics. He has extensively applied signal processing techniques to improve the circuit topologies, designs, and fabrication technologies within Canaan. This includes the application of semidefinite programming to circuit design optimization, abstract algebra in switched capacitor circuit topologies improvement, and nonlinear optimization methods to optimize high voltage MOSFET layout and fabrication.Wing-Shan Tam, Canaan Microelectronics Corp Limited, ChinaWing-Shan Tam received her BEng degree in electronic engineering from The Chinese University of Hong Kong, and MSc degree in electronic and information engineering from The Hong Kong Polytechnic University, and PhD degree in electronic engineering from the City University of Hong Kong in 2004, 2007, and 2010, respectively. Currently, she is the Engineering Manager of Canaan Microelectronics Corp Ltd., and she has been working with CMOS circuit design since 2004. Her research interests include mixed-signal integrated circuit design for data conversion and power-management.

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• About the Authors ixPreface xiAcknowledgements xiiiNomenclature xv1 Warm Up 11.1 Bipolar Junction Transistors 21.1.1 Differential VBE 51.2 Metal-Oxide Semiconductor Field-Effect Transistor 71.2.1 Cutoff Region 111.2.2 Subthreshold Conduction 111.2.3 Triode Region 141.2.4 Saturation Region 161.2.5 Thermal Properties 191.2.6 Channel Length Modulation Effect 231.3 Diode 231.4 Resistor 251.4.1 Dummy Element 271.4.2 Guard Ring 271.4.3 Sheet Resistance 271.5 Device Matching 281.5.1 Application of Statistics to Circuit Design 281.5.2 Systematic Variation 301.6 Simulation Models for Circuit Design 311.6.1 Process Variation and Typical Design 321.6.2 Process Corners 341.7 Noise 361.7.1 Types of Noises 361.7.2 Sums and Multiplications of Noises 381.8 Fabrication Technology 391.9 Book Organization 401.10 Exercises 42References 462 Voltage Reference 492.1 Performance Measures 492.1.1 Line Regulation 512.1.2 Temperature Coefficient 542.1.3 Power Supply Rejection Ratio 562.1.4 Quiescent Current 592.1.5 Output Noise 602.2 Other Design Considerations 622.3 Summary 632.4 Exercises 65References 703 Bandgap Voltage Reference 713.1 Widlar Bandgap Voltage Reference Circuit 713.2 Drain Voltage Equalization Current Mirror 743.2.1 Opamp Basedβ-Multiplier Bandgap Voltage Reference Circuit 763.2.2 Bandgap Voltage Reference Circuit 773.3 Major Circuit Elements 813.3.1 Operational Amplifier 813.3.2 Current Mirror 863.3.3 Startup Circuit 883.3.4 Resistor Network 933.3.5 Bipolar Transistor 943.4 Complete Layout 953.5 Summary 953.6 Exercises 96References 1014 Error Sources in Bandgap Voltage Reference Circuit 1034.1 Non-Ideal Opamp 1034.1.1 Input Offset Voltage 1044.1.2 Limited Gain and Power Supply Rejection Ratio 1124.1.3 Noise 1134.2 Current Mirror Mismatch 1144.2.1 Channel Length Modulation Effect Compensation 1164.2.2 Cascode Current Mirror 1174.3 Bipolar Transistor 1224.3.1 Size Variation 1224.3.2 Series Base Resistance 1224.3.3 β Variation 1254.4 Resistor Variation 1264.5 Power Supply Variation 1274.5.1 Pre-Regulation 1324.6 Output Loading 1354.7 Output Noise 1384.8 Voltage Reference Circuit Trimming 1404.8.1 Linked Fuse Resistor Trimming 1414.8.2 Resistor Trimming Circuit Analysis 1424.8.3 Modulated Trimming 1464.8.4 Voltage Domain Trimming 1484.8.5 Current Domain Trimming 1494.9 Summary 1494.10 Exercises 151References 161ADVANCED VOLTAGE REFERENCE CIRCUITS5 Temperature Compensation Techniques 1655.1 VBE − DeltaVBE Compensation 1665.1.1 Brokaw Bandgap Voltage Reference 1685.1.2 β-Multiplier VBE − DeltaVBE Compensation 1705.2 Widlar PTAT Current Source and VBE Compensation 1755.3 VGS Based Temperature Compensation 1775.3.1 VGS Current Source 1785.4 Summary 1825.5 Exercises 183References 1896 Sub-1V Voltage Reference Circuit 1916.1 Sub-1V Output Stage 1936.2 Voltage Headroom in Opamp based β-multiplier Voltage Reference Circuit 1956.2.1 Opamp with NMOS Input Stage 1976.2.2 Local Voltage Boosting 1986.2.3 Low Vth Transistor 1986.2.4 Bulk-Driven Transistors 1996.3 Sub-1V Bandgap Voltage Reference by Resistive Division 1996.3.1 Resistive Divided VBE 2026.3.2 Independent Biased Resistive Divided VBE 2066.4 Peaking Current Source and VBE Compensation 2096.5 Weighted DeltaVGS Compensation 2116.6 Summary 2146.7 Exercises 215References 2227 High Order Curvature Correction 2237.1 Compensation Order 2247.2 Second Order Temperature Compensation 2287.2.1 Second Order Current Source 2297.2.2 Current Subtraction 2327.2.3 Current Addition 2367.3 BJT Current Subtraction 2387.4 Piecewise Linear Compensation 2407.5 Sum and Difference of Sources with Similar Temperature Dependence 2437.5.1 Difference of Voltages with Similar Temperature Dependence 2447.5.2 Sum of Voltages with Inverted Temperature Dependence 2457.5.3 Multi-threshold Voltages Curvature Compensated Voltage Reference 2477.6 Summary 2527.7 Exercises 253References 2578 CMOS Voltage Reference without Resistors 2598.1 Generation of Weighted PTAT Source By Inverse Functions 2608.1.1 Weighted Differential Circuit 2608.1.2 Negative Impedance Converter 2628.2 Resistorless Voltage and Current Sources 2658.2.1 Resistorless Voltage Source 2658.2.2 Resistorless Current Source 2668.3 First Order Compensated Resistorless Bandgap Voltage Reference Circuit 2688.3.1 Voltage Summation Based Resistorless Reference Circuit 2698.3.2 Current Summation Based Resistorless Reference Circuit 2708.4 Resistorless Sub-Bandgap Reference Circuit 2708.4.1 The Voltage Summation Approach 2718.4.2 CTAT Voltage Reduction 2738.5 Summary 2798.6 Exercises 280References 281A SPICE Model File 283B SPICE Netlist of Voltage Reference Circuit 287Index 289

Chi-Wah Kok, Canaan Microelectronics Corporation Limited, ChinaChi-Wah Kok obtained his degree from the University of Wisconsin Madison. Since 1992, he has been working with various semi-conductor companies, research institutions and universities, which include AT&T Labs Research, Holmdel, SONY U.S. Research Labs, Stanford University, Hong Kong University of Science and Technology, Hong Kong Polytechnic University, City University of Hong Kong, and Lattice Semiconductor. In 2006, he founded Canaan Microelectronics Corp Ltd., a fabless IC company with products in mixed signal IC for consumer electronics. He has extensively applied signal processing techniques to improve the circuit topologies, designs, and fabrication technologies within Canaan. This includes the application of semidefinite programming to circuit design optimization, abstract algebra in switched capacitor circuit topologies improvement, and nonlinear optimization methods to optimize high voltage MOSFET layout and fabrication.Wing-Shan Tam, Canaan Microelectronics Corp Limited, ChinaWing-Shan Tam received her BEng degree in electronic engineering from The Chinese University of Hong Kong, and MSc degree in electronic and information engineering from The Hong Kong Polytechnic University, and PhD degree in electronic engineering from the City University of Hong Kong in 2004, 2007, and 2010, respectively. Currently, she is the Engineering Manager of Canaan Microelectronics Corp Ltd., and she has been working with CMOS circuit design since 2004. Her research interests include mixed-signal integrated circuit design for data conversion and power-management.

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• About the Authors ixPreface xiAcknowledgements xiiiNomenclature xv1 Warm Up 11.1 Bipolar Junction Transistors 21.1.1 Differential VBE 51.2 Metal-Oxide Semiconductor Field-Effect Transistor 71.2.1 Cutoff Region 111.2.2 Subthreshold Conduction 111.2.3 Triode Region 141.2.4 Saturation Region 161.2.5 Thermal Properties 191.2.6 Channel Length Modulation Effect 231.3 Diode 231.4 Resistor 251.4.1 Dummy Element 271.4.2 Guard Ring 271.4.3 Sheet Resistance 271.5 Device Matching 281.5.1 Application of Statistics to Circuit Design 281.5.2 Systematic Variation 301.6 Simulation Models for Circuit Design 311.6.1 Process Variation and Typical Design 321.6.2 Process Corners 341.7 Noise 361.7.1 Types of Noises 361.7.2 Sums and Multiplications of Noises 381.8 Fabrication Technology 391.9 Book Organization 401.10 Exercises 42References 462 Voltage Reference 492.1 Performance Measures 492.1.1 Line Regulation 512.1.2 Temperature Coefficient 542.1.3 Power Supply Rejection Ratio 562.1.4 Quiescent Current 592.1.5 Output Noise 602.2 Other Design Considerations 622.3 Summary 632.4 Exercises 65References 703 Bandgap Voltage Reference 713.1 Widlar Bandgap Voltage Reference Circuit 713.2 Drain Voltage Equalization Current Mirror 743.2.1 Opamp Basedβ-Multiplier Bandgap Voltage Reference Circuit 763.2.2 Bandgap Voltage Reference Circuit 773.3 Major Circuit Elements 813.3.1 Operational Amplifier 813.3.2 Current Mirror 863.3.3 Startup Circuit 883.3.4 Resistor Network 933.3.5 Bipolar Transistor 943.4 Complete Layout 953.5 Summary 953.6 Exercises 96References 1014 Error Sources in Bandgap Voltage Reference Circuit 1034.1 Non-Ideal Opamp 1034.1.1 Input Offset Voltage 1044.1.2 Limited Gain and Power Supply Rejection Ratio 1124.1.3 Noise 1134.2 Current Mirror Mismatch 1144.2.1 Channel Length Modulation Effect Compensation 1164.2.2 Cascode Current Mirror 1174.3 Bipolar Transistor 1224.3.1 Size Variation 1224.3.2 Series Base Resistance 1224.3.3 β Variation 1254.4 Resistor Variation 1264.5 Power Supply Variation 1274.5.1 Pre-Regulation 1324.6 Output Loading 1354.7 Output Noise 1384.8 Voltage Reference Circuit Trimming 1404.8.1 Linked Fuse Resistor Trimming 1414.8.2 Resistor Trimming Circuit Analysis 1424.8.3 Modulated Trimming 1464.8.4 Voltage Domain Trimming 1484.8.5 Current Domain Trimming 1494.9 Summary 1494.10 Exercises 151References 161ADVANCED VOLTAGE REFERENCE CIRCUITS5 Temperature Compensation Techniques 1655.1 VBE − DeltaVBE Compensation 1665.1.1 Brokaw Bandgap Voltage Reference 1685.1.2 β-Multiplier VBE − DeltaVBE Compensation 1705.2 Widlar PTAT Current Source and VBE Compensation 1755.3 VGS Based Temperature Compensation 1775.3.1 VGS Current Source 1785.4 Summary 1825.5 Exercises 183References 1896 Sub-1V Voltage Reference Circuit 1916.1 Sub-1V Output Stage 1936.2 Voltage Headroom in Opamp based β-multiplier Voltage Reference Circuit 1956.2.1 Opamp with NMOS Input Stage 1976.2.2 Local Voltage Boosting 1986.2.3 Low Vth Transistor 1986.2.4 Bulk-Driven Transistors 1996.3 Sub-1V Bandgap Voltage Reference by Resistive Division 1996.3.1 Resistive Divided VBE 2026.3.2 Independent Biased Resistive Divided VBE 2066.4 Peaking Current Source and VBE Compensation 2096.5 Weighted DeltaVGS Compensation 2116.6 Summary 2146.7 Exercises 215References 2227 High Order Curvature Correction 2237.1 Compensation Order 2247.2 Second Order Temperature Compensation 2287.2.1 Second Order Current Source 2297.2.2 Current Subtraction 2327.2.3 Current Addition 2367.3 BJT Current Subtraction 2387.4 Piecewise Linear Compensation 2407.5 Sum and Difference of Sources with Similar Temperature Dependence 2437.5.1 Difference of Voltages with Similar Temperature Dependence 2447.5.2 Sum of Voltages with Inverted Temperature Dependence 2457.5.3 Multi-threshold Voltages Curvature Compensated Voltage Reference 2477.6 Summary 2527.7 Exercises 253References 2578 CMOS Voltage Reference without Resistors 2598.1 Generation of Weighted PTAT Source By Inverse Functions 2608.1.1 Weighted Differential Circuit 2608.1.2 Negative Impedance Converter 2628.2 Resistorless Voltage and Current Sources 2658.2.1 Resistorless Voltage Source 2658.2.2 Resistorless Current Source 2668.3 First Order Compensated Resistorless Bandgap Voltage Reference Circuit 2688.3.1 Voltage Summation Based Resistorless Reference Circuit 2698.3.2 Current Summation Based Resistorless Reference Circuit 2708.4 Resistorless Sub-Bandgap Reference Circuit 2708.4.1 The Voltage Summation Approach 2718.4.2 CTAT Voltage Reduction 2738.5 Summary 2798.6 Exercises 280References 281A SPICE Model File 283B SPICE Netlist of Voltage Reference Circuit 287Index 289

Chi-Wah Kok, Canaan Microelectronics Corporation Limited, ChinaChi-Wah Kok obtained his degree from the University of Wisconsin Madison. Since 1992, he has been working with various semi-conductor companies, research institutions and universities, which include AT&T Labs Research, Holmdel, SONY U.S. Research Labs, Stanford University, Hong Kong University of Science and Technology, Hong Kong Polytechnic University, City University of Hong Kong, and Lattice Semiconductor. In 2006, he founded Canaan Microelectronics Corp Ltd., a fabless IC company with products in mixed signal IC for consumer electronics. He has extensively applied signal processing techniques to improve the circuit topologies, designs, and fabrication technologies within Canaan. This includes the application of semidefinite programming to circuit design optimization, abstract algebra in switched capacitor circuit topologies improvement, and nonlinear optimization methods to optimize high voltage MOSFET layout and fabrication.Wing-Shan Tam, Canaan Microelectronics Corp Limited, ChinaWing-Shan Tam received her BEng degree in electronic engineering from The Chinese University of Hong Kong, and MSc degree in electronic and information engineering from The Hong Kong Polytechnic University, and PhD degree in electronic engineering from the City University of Hong Kong in 2004, 2007, and 2010, respectively. Currently, she is the Engineering Manager of Canaan Microelectronics Corp Ltd., and she has been working with CMOS circuit design since 2004. Her research interests include mixed-signal integrated circuit design for data conversion and power-management.

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• About the Authors ixPreface xiAcknowledgements xiiiNomenclature xv1 Warm Up 11.1 Bipolar Junction Transistors 21.1.1 Differential VBE 51.2 Metal-Oxide Semiconductor Field-Effect Transistor 71.2.1 Cutoff Region 111.2.2 Subthreshold Conduction 111.2.3 Triode Region 141.2.4 Saturation Region 161.2.5 Thermal Properties 191.2.6 Channel Length Modulation Effect 231.3 Diode 231.4 Resistor 251.4.1 Dummy Element 271.4.2 Guard Ring 271.4.3 Sheet Resistance 271.5 Device Matching 281.5.1 Application of Statistics to Circuit Design 281.5.2 Systematic Variation 301.6 Simulation Models for Circuit Design 311.6.1 Process Variation and Typical Design 321.6.2 Process Corners 341.7 Noise 361.7.1 Types of Noises 361.7.2 Sums and Multiplications of Noises 381.8 Fabrication Technology 391.9 Book Organization 401.10 Exercises 42References 462 Voltage Reference 492.1 Performance Measures 492.1.1 Line Regulation 512.1.2 Temperature Coefficient 542.1.3 Power Supply Rejection Ratio 562.1.4 Quiescent Current 592.1.5 Output Noise 602.2 Other Design Considerations 622.3 Summary 632.4 Exercises 65References 703 Bandgap Voltage Reference 713.1 Widlar Bandgap Voltage Reference Circuit 713.2 Drain Voltage Equalization Current Mirror 743.2.1 Opamp Basedβ-Multiplier Bandgap Voltage Reference Circuit 763.2.2 Bandgap Voltage Reference Circuit 773.3 Major Circuit Elements 813.3.1 Operational Amplifier 813.3.2 Current Mirror 863.3.3 Startup Circuit 883.3.4 Resistor Network 933.3.5 Bipolar Transistor 943.4 Complete Layout 953.5 Summary 953.6 Exercises 96References 1014 Error Sources in Bandgap Voltage Reference Circuit 1034.1 Non-Ideal Opamp 1034.1.1 Input Offset Voltage 1044.1.2 Limited Gain and Power Supply Rejection Ratio 1124.1.3 Noise 1134.2 Current Mirror Mismatch 1144.2.1 Channel Length Modulation Effect Compensation 1164.2.2 Cascode Current Mirror 1174.3 Bipolar Transistor 1224.3.1 Size Variation 1224.3.2 Series Base Resistance 1224.3.3 β Variation 1254.4 Resistor Variation 1264.5 Power Supply Variation 1274.5.1 Pre-Regulation 1324.6 Output Loading 1354.7 Output Noise 1384.8 Voltage Reference Circuit Trimming 1404.8.1 Linked Fuse Resistor Trimming 1414.8.2 Resistor Trimming Circuit Analysis 1424.8.3 Modulated Trimming 1464.8.4 Voltage Domain Trimming 1484.8.5 Current Domain Trimming 1494.9 Summary 1494.10 Exercises 151References 161ADVANCED VOLTAGE REFERENCE CIRCUITS5 Temperature Compensation Techniques 1655.1 VBE − DeltaVBE Compensation 1665.1.1 Brokaw Bandgap Voltage Reference 1685.1.2 β-Multiplier VBE − DeltaVBE Compensation 1705.2 Widlar PTAT Current Source and VBE Compensation 1755.3 VGS Based Temperature Compensation 1775.3.1 VGS Current Source 1785.4 Summary 1825.5 Exercises 183References 1896 Sub-1V Voltage Reference Circuit 1916.1 Sub-1V Output Stage 1936.2 Voltage Headroom in Opamp based β-multiplier Voltage Reference Circuit 1956.2.1 Opamp with NMOS Input Stage 1976.2.2 Local Voltage Boosting 1986.2.3 Low Vth Transistor 1986.2.4 Bulk-Driven Transistors 1996.3 Sub-1V Bandgap Voltage Reference by Resistive Division 1996.3.1 Resistive Divided VBE 2026.3.2 Independent Biased Resistive Divided VBE 2066.4 Peaking Current Source and VBE Compensation 2096.5 Weighted DeltaVGS Compensation 2116.6 Summary 2146.7 Exercises 215References 2227 High Order Curvature Correction 2237.1 Compensation Order 2247.2 Second Order Temperature Compensation 2287.2.1 Second Order Current Source 2297.2.2 Current Subtraction 2327.2.3 Current Addition 2367.3 BJT Current Subtraction 2387.4 Piecewise Linear Compensation 2407.5 Sum and Difference of Sources with Similar Temperature Dependence 2437.5.1 Difference of Voltages with Similar Temperature Dependence 2447.5.2 Sum of Voltages with Inverted Temperature Dependence 2457.5.3 Multi-threshold Voltages Curvature Compensated Voltage Reference 2477.6 Summary 2527.7 Exercises 253References 2578 CMOS Voltage Reference without Resistors 2598.1 Generation of Weighted PTAT Source By Inverse Functions 2608.1.1 Weighted Differential Circuit 2608.1.2 Negative Impedance Converter 2628.2 Resistorless Voltage and Current Sources 2658.2.1 Resistorless Voltage Source 2658.2.2 Resistorless Current Source 2668.3 First Order Compensated Resistorless Bandgap Voltage Reference Circuit 2688.3.1 Voltage Summation Based Resistorless Reference Circuit 2698.3.2 Current Summation Based Resistorless Reference Circuit 2708.4 Resistorless Sub-Bandgap Reference Circuit 2708.4.1 The Voltage Summation Approach 2718.4.2 CTAT Voltage Reduction 2738.5 Summary 2798.6 Exercises 280References 281A SPICE Model File 283B SPICE Netlist of Voltage Reference Circuit 287Index 289