Vittoz Low-Power Crystal and MEMS Oscillators

The Experience of Watch Developments
2010
ISBN: 978-90-481-9395-0
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 206 Seiten

Reihe: Integrated Circuits and Systems

Electronic oscillators using an electromechanical device as a frequency reference are irreplaceable components of systems-on-chip for time-keeping, carrier frequency generation and digital clock generation. With their excellent frequency stability and very large quality factor Q, quartz crystal resonators have been the dominant solution for more than 70 years. But new possibilities are now offered by micro-electro-mechanical (MEM) resonators, that have a qualitatively identical equivalent electrical circuit. Low-Power Crystal and MEMS Oscillators concentrates on the analysis and design of the most important schemes of integrated oscillator circuits. It explains how these circuits can be optimized by best exploiting the very high Q of the resonator to achieve the minimum power consumption compatible with the requirements on frequency stability and phase noise. The author has 40 years of experience in designing very low-power, high-performance quartz oscillators for watches and other battery operated systems and has accumulated most of the material during this period. Some additional original material related to phase noise has been added. The explanations are mainly supported by analytical developments, whereas computer simulation is limited to numerical examples. The main part is dedicated to the most important Pierce circuit, with a full design procedure illustrated by examples. Symmetrical circuits that became popular for modern telecommunication systems are analyzed in a last chapter.

Eric A. VITTOZ received the M.S. and Ph.D. degrees in electrical engineering from the Swiss Federal Institute of Technology in Lausanne ( EPFL) in 1961 and 1969 respectively. He joined the Centre Electronique Horloger S.A. (CEH), Neuchâtel, in 1962, where he participated in the development of the first prototypes of electronic watches. In 1971, he was appointed Vice-Director of CEH, supervising advanced developments in electronic watches and other micropower systems. In 1984, he took the responsibility of the Circuits and Systems Research Division of the Swiss Center for Electronics and Microtechnology (CSEM) in Neucâtel, where he was appointed Executive Vice-President, Integrated Circuits and Systems, in 1991. He is also directly responsible for the Advanced Research section of CSEM. His field of personal research interest and activity is the design of low-power analog CMOS circuits, with emphasis on their application to advanced perceptive processing. Since 1975, he has been lecturing and supervising undergraduate and graduate student projects in analog circuit design at EPFL, where he became Professor in 1982. Dr. Vittoz is an IEEE Fellow, has published more than 100 papers and holds 25 patents.

Autoren/Hrsg.

Vittoz, Eric

Inhaltsverzeichnis

1;Copyright;4
2;Contents;6
3;Preface;9
4;Symbols;11
5;Chapter 1:Introduction;16
5.1;1.1 Applications of Quartz Crystal Oscillators;16
5.2;1.2 Historical Notes;17
5.3;1.3 The Book Structure;17
5.4;1.4 Basics on Oscillators;19
6;Chapter 2:Quartz and MEM Resonators;21
6.1;2.1 The Quartz Resonator;21
6.2;2.2 Equivalent Circuit;22
6.3;2.3 Figure of Merit;24
6.4;2.4 Mechanical Energy and Power Dissipation;29
6.5;2.5 Various Types of Quartz Resonators;29
6.6;2.6 MEM Resonators;32
6.6.1;2.6.1 Basic Generic Structure;32
6.6.2;2.6.2 Symmetrical Transducers;35
7;Chapter 3:General Theory of High-Q Oscillators;37
7.1;3.1 General Form of the Oscillator;37
7.2;3.2 Stable Oscillation;39
7.3;3.3 Critical Condition for Oscillation and Linear Approximation;41
7.4;3.4 Amplitude Limitation;41
7.5;3.5 Start-up of Oscillation;43
7.6;3.6 Duality;44
7.7;3.7 Basic Considerations on Phase Noise;45
7.7.1;3.7.1 Linear Circuit;45
7.7.2;3.7.2 Nonlinear Time Variant Circuit;47
7.8;3.8 Model of the MOS Transistor;50
8;Chapter 4:Theory of the Pierce Oscillator;55
8.1;4.1 Basic Circuit;55
8.2;4.2 Linear Analysis;56
8.2.1;4.2.1 Linearized Circuit;56
8.2.2;4.2.2 Lossless Circuit;60
8.2.3;4.2.3 Phase Stability;64
8.2.4;4.2.4 Relative Oscillator Voltages;65
8.2.5;4.2.5 Effect of Losses;66
8.2.5.1;4.2.5.1 Numerical Example;66
8.2.5.2;4.2.5.2 Approximative Expression for the Increase of Gm;67
8.2.6;4.2.6 Frequency Adjustment;68
8.3;4.3 Nonlinear Analysis;69
8.3.1;4.3.1 Numerical Example;69
8.3.2;4.3.2 Distortion of the Gate Voltage;71
8.3.3;4.3.3 Amplitude Limitation by the Transistor Transfer Function;72
8.3.3.1;4.3.3.1 Introduction;72
8.3.3.2;4.3.3.2 Transistor inWeak Inversion;74
8.3.3.3;4.3.3.3 Larger Amplitude by Capacitive Attenuator;76
8.3.3.4;4.3.3.4 Transistor in Moderate or Strong Inversion;77
8.3.3.5;4.3.3.5 Transistor Strictly in Strong Inversion;80
8.3.4;4.3.4 Energy and Power of Mechanical Oscillation;82
8.3.5;4.3.5 Frequency Stability;83
8.3.5.1;4.3.5.1 Introduction;83
8.3.5.2;4.3.5.2 Resonator;83
8.3.5.3;4.3.5.3 Nonlinear Effects in the Circuit;83
8.3.5.4;4.3.5.4 Variation of Linear Effects;84
8.3.6;4.3.6 Elimination of Unwanted Modes;85
8.3.6.1;4.3.6.1 Introduction;85
8.3.6.2;4.3.6.2 Wanted Mode More Active Than Unwanted Modes (a > 1);86
8.3.6.3;4.3.6.3 Effect of Losses;89
8.3.6.4;4.3.6.4 Wanted Mode Less Active Than Unwanted Modes (a < 1);89
8.4;4.4 Phase Noise;91
8.4.1;4.4.1 Linear Effects on Phase Noise;91
8.4.1.1;4.4.1.1 General Case;91
8.4.1.2;4.4.1.2 Channel Noise of the Active Transistor;92
8.4.2;4.4.2 Phase Noise in the Nonlinear Time Variant Circuit;92
8.4.2.1;4.4.2.1 Introduction;92
8.4.2.2;4.4.2.2 Effect of theWhite Channel Noise inWeak Inversion;93
8.4.2.3;4.4.2.3 Effect of theWhite Channel Noise in Strong Inversion;94
8.4.2.4;4.4.2.4 Effect of the Flicker Noise in Weak Inversion;95
8.4.2.5;4.4.2.5 Effect of the Flicker Noise in Strong Inversion;96
8.4.2.6;4.4.2.6 Effect of the Noise in the Bias Current;97
8.5;4.5 Design Process;98
8.5.1;4.5.1 Design Steps;98
8.5.1.1;4.5.1.1 Selection of a Quartz Crystal or MEM Resonator;98
8.5.1.2;4.5.1.2 Choice of Circuit Capacitances C1 and C2 and Estimation of C3;99
8.5.1.3;4.5.1.3 Calculation of Pulling and Series Resonant Frequency;100
8.5.1.4;4.5.1.4 Calculation of the Minimum Start-up Time Constant and of the Corresponding Transconductance;100
8.5.1.5;4.5.1.5 Calculation of the Critical Transconductance and Minimum Critical Bias Current;100
8.5.1.6;4.5.1.6 Choice of the Amplitude of Oscillation |V1| at the Gate;101
8.5.1.7;4.5.1.7 Calculation of Power;101
8.5.1.8;4.5.1.8 Choice of the Amount of Overdrive;101
8.5.1.9;4.5.1.9 Calculation of Critical Current, Bias Current and Specific Current of the Transistor;102
8.5.1.10;4.5.1.10 Calculation of the Active Transistor;102
8.5.1.11;4.5.1.11 Calculation of Energy and Phase Noise;102
8.5.1.12;4.5.1.12 Final Complete Design;103
8.5.2;4.5.2 Design Examples;103
9;Chapter 5:Implementations of the Pierce Oscillator;107
9.1;5.1 Grounded-Source Oscillator;107
9.1.1;5.1.1 Basic Circuit;107
9.1.2;5.1.2 Dynamic Behavior of Bias;109
9.1.3;5.1.3 Dynamic Behavior of Oscillation Amplitude;111
9.1.4;5.1.4 Design Examples;114
9.1.5;5.1.5 Implementation of the Drain-to-Gate Resistor;116
9.1.6;5.1.6 Increasing the Maximum Amplitude;120
9.2;5.2 Amplitude Regulation;121
9.2.1;5.2.1 Introduction;121
9.2.2;5.2.2 Basic Regulator;122
9.2.3;5.2.3 Amplitude Regulating Loop;129
9.2.4;5.2.4 Simplified Regulator Using Linear Resistors;132
9.2.5;5.2.5 Elimination of Resistors;134
9.3;5.3 Extraction of the Oscillatory Signal;137
9.4;5.4 CMOS-Inverter Oscillator;138
9.4.1;5.4.1 Direct Implementation;138
9.4.2;5.4.2 Current-controlled CMOS-inverter oscillator;143
9.5;5.5 Grounded-Drain Oscillator;146
9.5.1;5.5.1 Basic Implementation;146
9.5.2;5.5.2 Single-Substrate Implementation;147
10;Chapter 6:Alternative Architectures;150
10.1;6.1 Introduction;150
10.2;6.2 Symmetrical Oscillator for Parallel Resonance;150
10.2.1;6.2.1 Basic Structure;150
10.2.2;6.2.2 Linear Analysis with the Parallel Resonator;152
10.2.3;6.2.3 Linear Analysis with the Series Motional Resonator;153
10.2.4;6.2.4 Effect of Losses;156
10.2.5;6.2.5 Nonlinear Analysis;157
10.2.6;6.2.6 Phase Noise;162
10.2.6.1;6.2.6.1 Noise Current;162
10.2.6.2;6.2.6.2 Phase Noise of the Linear Circuit;163
10.2.6.3;6.2.6.3 Phase Noise due to White Channel Noise in the Nonlinear Time Variant Circuit;164
10.2.6.4;6.2.6.4 Phase Noise Due to 1/f Flicker Noise;167
10.2.7;6.2.7 Practical Implementations;170
10.3;6.3 Symmetrical Oscillator for Series Resonance;177
10.3.1;6.3.1 Basic Structure;177
10.3.2;6.3.2 Linear Analysis;178
10.3.2.1;6.3.2.1 Circuit Impedance in the General Case;178
10.3.2.2;6.3.2.2 Particular Case with CL =CP/n;180
10.3.2.3;6.3.2.3 Relative Oscillation Currents;185
10.3.3;6.3.3 Nonlinear Analysis;185
10.3.4;6.3.4 Phase Noise;190
10.3.4.1;6.3.4.1 Noise Voltage;190
10.3.4.2;6.3.4.2 Phase Noise of the Linear Circuit;191
10.3.4.3;6.3.4.3 Phase Noise due to White Noise in the Nonlinear Time Variant Circuit;192
10.3.4.4;6.3.4.4 Phase Noise due to the Flicker Noise of the Active Transistors;194
10.3.5;6.3.5 Practical Implementation;196
10.4;6.4 Van den Homberg Oscillator;203
10.4.1;6.4.1 Principle and Linear Analysis;203
10.4.2;6.4.2 Practical Implementation and Nonlinear Behavior;206
10.5;6.5 Comparison of Oscillators;207
10.5.1;6.5.1 Pierce Oscillator (1);208
10.5.2;6.5.2 Van den Homberg Oscillator (2);209
10.5.3;6.5.3 Parallel Resonance Oscillator (3);209
10.5.4;6.5.4 Series Resonance Oscillator (4);210
11;Bibliography;214
12;Index;216