Dimensionless frequency offset values can be converted to units of frequency (Hz) if the nominal frequency is known. To illustrate this, consider an oscillator with a nominal frequency of 5 MHz and a frequency offset of + 1.16 × 10 - 11 . To find the frequency offset in hertz, multiply the nominal frequency by the offset: (5 × 10 6 ) ( + 1.16 × 10 - 11 ) = 5.80 × 10 -5 = +0.0000580 Hz Then, add the offset to the nominal frequency to get the actual frequency: 5,000,000 Hz + 0.0000580 Hz = 5,000,000.0000580 Hz Stability Stability indicates how well an oscillator can produce the same time or frequency offset over a given time interval. It doesn’t indicate whether the time or frequency is “right” or “wrong,” but only whether it stays the same. In contrast, accuracy indicates how well an oscillator has been set on time or on frequency. To understand this difference, consider that a stable oscillator that needs adjustment might produce a frequency with a large offset. Or, an unstable oscillator that was just adjusted might temporarily produce a frequency near its nominal value. Figure 17.7 shows the relationship between accuracy and stability. Stability is defined as the statistical estimate of the frequency or time fluctuations of a signal over a given time interval. These fluctuations are measured with respect to a mean frequency or time offset. Short-term stability usually refers to fluctuations over intervals less than 100 s. Long-term stability can refer to measurement intervals greater than 100 s, but usually refers to periods longer than 1 day. Stability estimates can be made in either the frequency domain or time domain, and can be calculated from a set of either frequency offset or time interval measurements. In some fields of measurement, stability is estimated by taking the standard deviation of the data set. However, standard deviation only FIGURE 17.6 A sample phase plot. FIGURE 17.7 The relationship between accuracy and stability. ©2002 CRC Press LLC Dimensionless frequency offset values can be converted to units of frequency (Hz) if the nominal frequency is known. To illustrate this, consider an oscillator with a nominal frequency of 5 MHz and a frequency offset of + 1.16 × 10 - 11 . To find the frequency offset in hertz, multiply the nominal frequency by the offset: (5 × 10 6 ) ( + 1.16 × 10 - 11 ) = 5.80 × 10 -5 = +0.0000580 Hz Then, add the offset to the nominal frequency to get the actual frequency: 5,000,000 Hz + 0.0000580 Hz = 5,000,000.0000580 Hz Stability Stability indicates how well an oscillator can produce the same time or frequency offset over a given time interval. It doesn’t indicate whether the time or frequency is “right” or “wrong,” but only whether it stays the same. In contrast, accuracy indicates how well an oscillator has been set on time or on frequency. To understand this difference, consider that a stable oscillator that needs adjustment might produce a frequency with a large offset. Or, an unstable oscillator that was just adjusted might temporarily produce a frequency near its nominal value. Figure 17.7 shows the relationship between accuracy and stability. Stability is defined as the statistical estimate of the frequency or time fluctuations of a signal over a given time interval. These fluctuations are measured with respect to a mean frequency or time offset. Short-term stability usually refers to fluctuations over intervals less than 100 s. Long-term stability can refer to measurement intervals greater than 100 s, but usually refers to periods longer than 1 day. Stability estimates can be made in either the frequency domain or time domain, and can be calculated from a set of either frequency offset or time interval measurements. In some fields of measurement, stability is estimated by taking the standard deviation of the data set. However, standard deviation only FIGURE 17.6 A sample phase plot. FIGURE 17.7 The relationship between accuracy and stability. ©2002 CRC Press LLC 18 Sensor and Actuator Characteristics 18.1 Range 18.2 Resolution 18.3 Sensitivity 18.4 Error 18.5 Repeatability 18.6 Linearity and Accuracy 18.7 Impedance 18.8 Nonlinearities 18.9 Static and Coulomb Friction 18.10 Eccentricity 18.11 Backlash 18.12 Saturation 18.13 Deadband 18.14 System Response 18.15 First-Order System Response 18.16 Underdamped Second-Order System Response 18.17 Frequency Response Mechatronic systems use a variety of sensors and actuators to measure and manipulate mechanical, electrical, and thermal systems. Sensors have many characteristics that affect their measurement capa- bilities and their suitability for each application. Analog sensors have an output that is continuous over a finite region of inputs. Examples of analog sensors include potentiometers, LVDTs (linear variable differential transformers), load cells, and thermistors. Digital sensors have a fixed or countable number of different output values. A common digital sensor often found in mechatronic systems is the incremental encoder. An analog sensor output conditioned by an analog-to-digital converter (ADC) has the same digital output characteristics, as seen in Fig. 18.1. 18.1 Range The range (or span) of a sensor is the difference between the minimum (or most negative) and maximum inputs that will give a valid output. Range is typically specified by the manufacturer of the sensor. For example, a common type K thermocouple has a range of 800 ∞ C (from - 50 ∞ C to 750 ∞ C). A ten-turn potentiometer would have a range of 3600 degrees. Joey Parker University of Alabama ©2002 CRC Press LLC 19 Sensors 19.1 Linear and Rotational Sensors Contact • Infrared • Resistive • Tilt (Gravity) • Capacitive • AC Inductive • DC Magnetic • Ultrasonic • Magnetostrictive Time-of-Flight • Laser Interferometry 19.2 Acceleration Sensors Overview of Accelerometer Types • Dynamics and Characteristics of Accelerometers • Vibrations • Typical Error Sources and Error Modeling • Inertial Accelerometers • Electromechanical Accelerometers • Piezoelectric Accelerometers • Piezoresistive Accelerometers • Strain-Gauge Accelerometers • Electrostatic Accelerometers • Micro- and Nanoaccelerometers • Signal Conditioning and Biasing 19.3 Force Measurement General Considerations • Hooke’s Law • Force Sensors 19.4 Torque and Power Measurement Fundamental Concepts • Arrangements of Apparatus for Torque and Power Measurement • Torque Transducer Technologies • Torque Transducer Construction, Operation, and Application • Apparatus for Power Measurement 19.5 Flow Measurement Introduction • Terminology • Flow Characteristics • Flowmeter Classification • Differential Pressure Flowmeter • The Variable Area Flowmeter • The Positive Displacement Flowmeter • The Turbine Flowmeter • The Vortex Shedding Flowmeter • The Electromagnetic Flowmeter • The Ultrasonic Flowmeter • The Coriolis Flowmeter • Two-Phase Flow • Flowmeter Installation • Flowmeter Selection 19.6 Temperature Measurements Introduction • Thermometers That Rely Upon Differential Expansion Coefficients • Thermometers That Rely Upon Phase Changes • Electrical Temperature Sensors and Transducers • Noncontact Thermometers • Microscale Temperature Measurements • Closing Comments 19.7 Distance Measuring and Proximity Sensors Distance Measuring Sensors • Proximity Sensors 19.8 Light Detection, Image, and Vision Systems Introduction • Basic Radiometry • Light Sources • Light Detectors • Image Formation • Image Sensors • Vision Systems 19.9 Integrated Microsensors Introduction • Examples of Micro- and Nanosensors • Future Development Trends • Conclusions Kevin M. Lynch Northwestern University Michael A. Peshkin Northwestern University Halit Eren Curtin University of Technology M. A. Elbestawi McMaster University Ivan J. Garshelis Magnova, Inc. Richard Thorn University of Derby Pamela M. Norris University of Virginia Bouvard Hosticka University of Virginia Jorge Fernando Figueroa NASA Stennis Space Center H. R. (Bart) Everett Space and Naval Warfare Systems Center Stanley S. Ipson University of Bradford Chang Liu University of Illinois ©2002 CRC Press LLC . estimated by taking the standard deviation of the data set. However, standard deviation only FIGURE 17.6 A sample phase plot. FIGURE 17.7 The relationship between accuracy and stability. 20 02 CRC Press. estimated by taking the standard deviation of the data set. However, standard deviation only FIGURE 17.6 A sample phase plot. FIGURE 17.7 The relationship between accuracy and stability. 20 02 CRC Press. ten-turn potentiometer would have a range of 3600 degrees. Joey Parker University of Alabama 20 02 CRC Press LLC 19 Sensors 19.1 Linear and Rotational Sensors Contact • Infrared • Resistive