1	QUARTZ CRYSTAL RESONATORS AND OSCILLATORS
2	Disclaimer
3	Table of Contents
4	Preface Why This Tutorial?
5	Notes and References
6	CHAPTER 1 Applications and Requirements
7	Electronics Applications of Quartz Crystals
8	Frequency Control Device Market
9	Navigation
10	Commercial Two-way Radio
11	Digital Processing of Analog Signals
12	Digital Network Synchronization
13	Phase Noise in PLL and PSK Systems
14	Utility Fault Location
15	Space Exploration
16	Military Requirements
17	Impacts of Oscillator Technology Improvements
18	Spread Spectrum Systems
19	Clock for Very Fast Frequency Hopping Radio
20	Clocks and Frequency Hopping C³Systems
21	Identification-Friend-Or-Foe (IFF)
22	Effect of Noise in Doppler Radar System
23	Bistatic Radar
24	Doppler Shifts
25	CHAPTER 2 Quartz Crystal Oscillators
26	Crystal Oscillator
27	Oscillation
28	Oscillation and Stability
29	Tunability and Stability
30	Oscillator Acronyms
31	Crystal Oscillator Categories
32	Crystal Oscillator Categories
33	Hierarchy of Oscillators
34	Oscillator Circuit Types
35	OCXO Block Diagram
36	Oscillator Instabilities - General Expression
37	Instabilities due to Sustaining Circuit
38	Oscillator Instabilities - Tuned Circuits
39	Oscillator Instabilities - Circuit Noise
40	Oscillator Instabilities - External Load
41	Oscillator Outputs
42	Resonator Self-Temperature Sensing
43	Thermometric Beat Frequency Generation
44	Microcomputer Compensated Crystal Oscillator (MCXO)
45	MCXO Frequency Summing Method
46	MCXO - Pulse Deletion Method
47	MCXO - TCXO Resonator Comparison
48	Opto-Electronic Oscillator (OEO)
49	CHAPTER 3 Quartz Crystal Resonators
50	Why Quartz?
51	The Piezoelectric Effect
52	The Piezoelectric Effect in Quartz
53	Modes of Motion
54	Motion Of A Thickness Shear Crystal
55	Resonator Vibration Amplitude Distribution
56	Resonant Vibrations of a Quartz Plate
57	Overtone Response of a Quartz Crystal
58	Unwanted Modes vs. Temperature
59	Mathematical Description of a Quartz Resonator
60	Mathematical Description - Continued
61	Infinite Plate Thickness Shear Resonator
62	Quartz is Highly Anisotropic
63	Zero Temperature Coefficient Quartz Cuts
64	Comparison of SC and AT-cuts
65	Mode Spectrograph of an SC-cut
66	SC- cut f vs. T for b-mode and c-mode
67	B and C Modes Of A Thickness Shear Crystal
68	Singly Rotated and Doubly Rotated Cuts’ Vibrational Displacements
69	Resistance vs. Electrode Thickness
70	Resonator Packaging
71	Equivalent Circuits
72	Equivalent Circuit of a Resonator
73	Crystal Oscillator f vs. T Compensation
74	Resonator Reactance vs. Frequency
75	Equivalent Circuit Parameter Relationships
76	What is Q and Why is it Important?
77	Decay Time, Linewidth, and Q
78	Factors that Determine Resonator Q
79	Resonator Fabrication Steps
80	X-ray Orientation of Crystal Plates
81	Contamination Control
82	Crystal Enclosure Contamination
83	What is an “f-squared”?
84	Milestones in Quartz Technology
85	Quartz Resonators for Wristwatches
86	Why 32,768 Hz?
87	Quartz Tuning Fork
88	Watch Crystal
89	Lateral Field Resonator
90	Electrodeless (BVA) Resonator
91	CHAPTER 4 Oscillator Stability
92	The Units of Stability in Perspective
93	Accuracy, Precision, and Stability
94	Influences on Oscillator Frequency
95	Idealized Frequency-Time-Influence Behavior
96	Aging and Short-Term Stability
97	Aging Mechanisms
98	Typical Aging Behaviors
99	Stresses on a Quartz Resonator Plate
100	Thermal Expansion Coefficients of Quartz
101	Force-Frequency Coefficient
102	Strains Due To Mounting Clips
103	Strains Due To Bonding Cements
104	Mounting Force Induced Frequency Change
105	Bonding Strains Induced Frequency Changes
106	Bending Force vs. Frequency Change
107	Short Term Instability (Noise)
108	Instantaneous Output Voltage of an Oscillator
109	Impacts of Oscillator Noise
110	Time Domain - Frequency Domain
111	Causes of Short Term Instabilities
112	Short-Term Stability Measures
113	Allan Deviation
114	Why s_y(t)?
115	Frequency Noise and s_y(t)
116	Time Domain Stability
117	Power Law Dependence of s_y(t)
118	Pictures of Noise
119	Spectral Densities
120	Mixer Functions
121	Phase Detector
122	Phase Noise Measurement
123	Frequency - Phase - Time Relationships
124	S_f(f) to SSB Power Ratio Relationship
125	S_f(f), S_v(f) and L (f)
126	Types of Phase Noise
127	Noise in Crystal Oscillators
128	Low-Noise SAW and BAW Multiplied to 10 GHz (in a nonvibrating environment)
129	Low-Noise SAW and BAW Multiplied to 10 GHz (in a vibrating environment)
130	Effects of Frequency Multiplication
131	TCXO Noise
132	Quartz Wristwatch Accuracy vs. Temperature
133	Frequency vs. Temperature Characteristics
134	Resonator f vs. T Determining Factors
135	Frequency-Temperature vs. Angle-of-Cut, AT-cut
136	Desired f vs. T of SC-cut Resonator for OCXO Applications
137	OCXO Oven’s Effect on Stability
138	Oven Stability Limits
139	Warmup of AT- and SC-cut Resonators
140	TCXO Thermal Hysteresis
141	Apparent Hysteresis
142	OCXO Retrace
143	TCXO Trim Effect
144	Why the Trim Effect?
145	Effects of Load Capacitance on f vs. T
146	Effects of Harmonics on f vs. T
147	Amplitude - Frequency Effect
148	Frequency vs. Drive Level
149	Drive Level vs. Resistance
150	Second Level of Drive Effect
151	Activity Dips
152	Frequency Jumps
153	Acceleration vs. Frequency Change
154	2-g Tipover Test (Df vs. attitude about three axes)
155	Sinusoidal Vibration Modulated Frequency
156	Acceleration Levels and Effects
157	Acceleration Sensitivity Vector
158	Vibration-Induced Allan Deviation Degradation
159	Vibration-Induced Phase Excursion
160	Vibration-Induced Sidebands
161	Vibration-Induced Sidebands After Frequency Multiplication
162	Sine Vibration-Induced Phase Noise
163	Random Vibration-Induced Phase Noise
164	Random-Vibration-Induced Phase Noise
165	Acceleration Sensitivity vs. Vibration Frequency
166	Acceleration Sensitivity of Quartz Resonators
167	Phase Noise Degradation Due to Vibration
168	Coherent Radar Probability of Detection
169	Vibration Isolation
170	Vibration Compensation
171	Vibration Sensitivity Measurement System
172	Shock
173	Radiation-Induced Frequency Shifts
174	Effects of Repeated Radiations
175	Radiation Induced Df vs. Dose and Quartz Type
176	Annealing of Radiation Induced f Changes
177	Transient Df After a Pulse of g Radiation
178	Effects of Flash X-rays on R_S
179	Frequency Change due to Neutrons
180	Neutron Damage
181	Summary - Steady-State Radiation Results
182	Summary - Pulse Irradiation Results
183	Summary - Neutron Irradiation Results
184	Other Effects on Stability
185	Interactions Among Influences
186	CHAPTER 5 Quartz Material Properties
187	Hydrothermal Growth of Quartz
188	Deeply Dissolved Quartz Sphere
189	Etching & Chemical Polishing
190	Left-Handed and Right-Handed Quartz
191	The Quartz Lattice
192	Quartz Properties’ Effects on Device Properties
193	Ions in Quartz - Simplified Model
194	Aluminum Associated Defects
195	Sweeping
196	Quartz Quality Indicators
197	Infrared Absorption of Quartz
198	Infrared Absorption Coefficient
199	Quartz Twinning
200	Twinning - Axial Relationships
201	Quartz Lattice and Twinning
202	Quartz Inversion
203	Phase Diagram of Silica (SiO₂)
204	Internal Friction (i.e., the Q) of Quartz
205	Langasite and Its Isomorphs
206	CHAPTER 6 Atomic Frequency Standards*
207	Precision Frequency Standards
208	Atomic Frequency Standard Basic Concepts
209	Hydrogen-Like Atoms
210	Atomic Frequency Standard* Block Diagram
211	Generalized Microwave Atomic Resonator
212	Atomic Resonator Concepts
213	Rubidium Cell Frequency Standard
214	Rubidium Cell Frequency Standard
215	Cs Hyperfine Energy Levels
216	Cesium-Beam Frequency Standard
217	Cesium-Beam Frequency Standard
218	Atomic Hydrogen Energy Levels
219	Passive H-Maser Schematic Diagram
220	Atomic Resonator Instabilities
221	Noise in Atomic Frequency Standards
222	Short-Term Stability of a Cs Standard
223	Short-Term Stability of a Rb Standard
224	Acceleration Sensitivity of Atomic Standards
225	Atomic Standard Acceleration Effects
226	Magnetic Field Sensitivities of Atomic Clocks
227	Crystal’s Influences on Atomic Standard
228	Optically Pumped Cs Standard
229	Laser Cooling of Atoms
230	Rubidium - Crystal Oscillator (RbXO)
231	RbXO Principle of Operation
232	Rubidium Crystal Oscillator
233	CHAPTER 7 Oscillator Comparisons and Specifications
234	Oscillator Comparison
235	Clock Accuracy vs. Power Requirement*
236	Clock Accuracy vs. Power Requirement*
237	Battery Life vs. Oscillator Power
238	Short Term Stability Ranges of Various Frequency Standards
239	Phase Instabilities of Various Frequency Standards
240	Weaknesses and Wearout Mechanisms
241	Why Do Crystal Oscillators Fail?
242	Oscillator Selection Considerations
243	Crystal Oscillator Specification: MIL-PRF-55310
244	CHAPTER 8 Time and Timekeeping
245	What Is Time?
246	Dictionary Definition of “Time”
247	The Second
248	Frequency and Time
249	Typical Clock System
250	Evolution of Clock Technologies
251	Progress in Timekeeping
252	Clock Errors
253	Frequency Error vs. Time Error
254	Clock Error vs. Resynchronization Interval
255	Time Error vs. Elapsed Time
256	On Using Time for Clock Rate Calibration
257	Calibration With a 1 pps Reference
258	Time Transfer Methods
259	Global Positioning System (GPS)
260	GPS
261	Oscillator’s Impact on GPS
262	Time Scales
263	Clock Ensembles and Time Scales
264	Relativistic Time
265	Relativistic Time Effects
266	Relativistic Time Corrections
267	Some Useful Relationships
268	One Pulse-Per-Second Timing Signal (MIL-STD-188-115)
269	BCD Time Code (MIL-STD-188-115)
270	Time and Frequency Subsystem
271	The MIFTTI Subsystem MIFTTI = Modular Intelligent Frequency, Time and Time Interval
272	"Time" Quotations
273	Units of Measurement Having Special Names in the International System of Units (SI)
274	Units of Measurement Having Special Names in the SI Units, NOT Needing Standard Uncertainty in SI Average Frequency
275	CHAPTER 9 Related Devices and Application
276	Discrete-Resonator Crystal Filter A Typical Six-pole Narrow-band Filter
277	Monolithic Crystal Filters
278	Surface Acoustic Wave (SAW) Devices
279	Quartz Bulk-Wave Resonator Sensors
280	Tuning Fork Resonator Sensors
281	Dual Mode SC-cut Sensors
282	Separation of Mass and Temperature Effects
283	Dual-Mode Pressure Sensor
284	CHAPTER 10 Proceedings Ordering Information, Standards, Website, and Index
285	IEEE International Frequency Control Symposium PROCEEDINGS ORDERING INFORMATION
286	Specifications And Standards Relating To Frequency Control - 1
287	Specifications And Standards Relating To Frequency Control - 2
288	Specifications And Standards Relating To Frequency Control - 3
289	Specifications And Standards Relating To Frequency Control - 4
290	Frequency Control Website