Department of Optical Engineering Zhejiang University Department of Optical Engineering Zhejiang University Advanced Sensor Technology Lecture 4 Jun. QIAN

Department of Optical Engineering Zhejiang University A Review of Lecture 3 Background on electrical measurement of sensor outputs Background on electrical measurement of sensor outputs Resistive Resistive Voltage divider Voltage divider Bridge circuit Bridge circuit Capacitive Capacitive Pure resistive load resistor Pure resistive load resistor Inductive Inductive Temperature Effect and Compensation Temperature Effect and Compensation Provide an overview of piezoresistive devices. Some examples are worked out using this sensing technique Provide an overview of piezoresistive devices. Some examples are worked out using this sensing technique

Department of Optical Engineering Zhejiang University A Review of Lecture 3 Strain gauge Strain gauge Strain Strain Poisson’s ratio Poisson’s ratio Gauge factor Gauge factor Mercury tube/metal wire Mercury tube/metal wire Resistance change 1%-0.001% Resistance change 1%-0.001% Various bridge circuits Various bridge circuits Temperature Effect Temperature Effect

Department of Optical Engineering Zhejiang University Lecture 4: Basic Intent Overview of the use of capacitance measurements in sensors Overview of the use of capacitance measurements in sensors Describe the fundamentals of accelerometers. Describe the fundamentals of accelerometers. Capacitance measuring systems, Capacitance measuring systems, Limiting factors of the measurement, and obtainable performance levels. Limiting factors of the measurement, and obtainable performance levels. Fundamentals of accelerometer operation, including Fundamentals of accelerometer operation, including The relationship between the mechanical characteristics of the sensor and its performance, The relationship between the mechanical characteristics of the sensor and its performance, The limitations of the performance of most accelerometers. The limitations of the performance of most accelerometers.

Department of Optical Engineering Zhejiang University Capacitive Sensing The capacitance The capacitance C=Q/V C=Q/V If the capacitance is large, more charge is needed to establish a given voltage difference. If the capacitance is large, more charge is needed to establish a given voltage difference. In practice, capacitance between two objects can be measured experimentally. In practice, capacitance between two objects can be measured experimentally. Predicting the capacitance between a pair of arbitrary objects is very complicated, Predicting the capacitance between a pair of arbitrary objects is very complicated, to know the electric field throughout the space between the objects. to know the electric field throughout the space between the objects. The field distribution is affected by the charge distribution, which is, in turn, affect the field distribution. The field distribution is affected by the charge distribution, which is, in turn, affect the field distribution. Iterative analytical techniques are generally required, and accurate calculations are very costly. Iterative analytical techniques are generally required, and accurate calculations are very costly.

Department of Optical Engineering Zhejiang University One application: proximity sensing

Department of Optical Engineering Zhejiang University Capacitors with Simple Geometry Parallel plates Parallel plates Electrodes Electrodes with area 10mm x 10mm, with area 10mm x 10mm, separation 1  m. separation 1  m. C~ 1000 pF, C~ 1000 pF, which isn't very big but still about the biggest you would ever expect to find in a real sensor ! More generally, capacitive sensors have capacitance closer to 100 pF or less. More generally, capacitive sensors have capacitance closer to 100 pF or less.

Department of Optical Engineering Zhejiang University Change in Capacitance due to the Lateral Movement The capacitance signal changes linearly with displacement. The capacitance signal changes linearly with displacement. To implement such a sensor, it is necessary to guarantee that the lateral motion does not also affect the separation between the electrodes, d. To implement such a sensor, it is necessary to guarantee that the lateral motion does not also affect the separation between the electrodes, d. Difficult to use for measurement of very small lateral displacements, Difficult to use for measurement of very small lateral displacements, A 1um lateral displacement would cause only 100 PPM change in the capacitance of the capacitor geometry worked out earlier. A 1um lateral displacement would cause only 100 PPM change in the capacitance of the capacitor geometry worked out earlier.

Department of Optical Engineering Zhejiang University Lateral displacement capacitive transducers Useful for many applications Useful for many applications Rotary capacitive transducers for positioning Rotary capacitive transducers for positioning High precision monitoring system High precision monitoring system Military application Military application 140 ± 8 mV/degrees of shaft rotation Manufacturer: Bently, USA

Department of Optical Engineering Zhejiang University Lateral displacement capacitive transducers

Department of Optical Engineering Zhejiang University Capacitance Change v.s. Plate Separation change in capacitance isn't obviously linear, change in capacitance isn't obviously linear, but for small changes in separation, but for small changes in separation, If the initial separation ~ a few microns, a 1% change in the capacitance  displacement of a few tens of nanometers, If the initial separation ~ a few microns, a 1% change in the capacitance  displacement of a few tens of nanometers, Such a measurement should be considered well within the capabilities of capacitive sensing. Such a measurement should be considered well within the capabilities of capacitive sensing.

Department of Optical Engineering Zhejiang University Capacitance Change v.s. Plate Separation Nice features associated with such a measurement include Nice features associated with such a measurement include good sensitivity to very small deflections good sensitivity to very small deflections Precision fabrication is required, since it is necessary to produce electrodes which are very close to one another and highly parallel Precision fabrication is required, since it is necessary to produce electrodes which are very close to one another and highly parallel Capacitive sensing is generally used for situations in which a precision measurement is required, and the expense associated with the sensor fabrication is acceptable. Capacitive sensing is generally used for situations in which a precision measurement is required, and the expense associated with the sensor fabrication is acceptable.

Department of Optical Engineering Zhejiang University Differential Capacitor One technique for reducing the effect of the nonlinearity : differential capacitor One technique for reducing the effect of the nonlinearity : differential capacitor The circuit is set up to measure the difference between the two capacitances, The circuit is set up to measure the difference between the two capacitances, the nonlinearity associated with the term  2 /d 2 is subtracted away, and the first nonlinearity appears as a cubic term  3 /d 3, substantially smaller than the squared term. the nonlinearity associated with the term  2 /d 2 is subtracted away, and the first nonlinearity appears as a cubic term  3 /d 3, substantially smaller than the squared term.

Department of Optical Engineering Zhejiang University Linearity Why do we care so much about linearity in capacitive sensors? Why do we care so much about linearity in capacitive sensors? Generally, capacitive measuring techniques are only applied in cases where precision measurement is necessary Generally, capacitive measuring techniques are only applied in cases where precision measurement is necessary Otherwise, a strain gauge based measurement would suffice. Otherwise, a strain gauge based measurement would suffice. One example of such a measurement is the measurement of acceleration for inertial navigation applications. A common problem in navigation situations is due to vibrations of the vehicle. One example of such a measurement is the measurement of acceleration for inertial navigation applications. A common problem in navigation situations is due to vibrations of the vehicle.

Department of Optical Engineering Zhejiang University What is navigation? In geomatics engineering sense, navigation is understood as (quasi-) continuous positioning of a moving object In geomatics engineering sense, navigation is understood as (quasi-) continuous positioning of a moving object Modern navigation makes use of the so-called hybrid (integrated) navigation systems, Modern navigation makes use of the so-called hybrid (integrated) navigation systems, two or more electronic sensing devices (sensors) are used together to collect the information necessary to find the position of the object. two or more electronic sensing devices (sensors) are used together to collect the information necessary to find the position of the object. These systems can then be installed on-board vehicles, ships, aircraft, or missiles. These systems can then be installed on-board vehicles, ships, aircraft, or missiles. Some of the sensors that are being part of such systems are: Some of the sensors that are being part of such systems are: Inertial Navigation Systems (INS), Inertial Navigation Systems (INS), radio-navigation aids (LORAN, GPS, etc.), radio-navigation aids (LORAN, GPS, etc.), Doppler Velocity Sensors (DVS), Doppler Velocity Sensors (DVS), laser-ranging devices, barometric altitude-meters, etc laser-ranging devices, barometric altitude-meters, etc

Department of Optical Engineering Zhejiang University Inertia Navigation System (INS) Three main forces that an INS has to take into account are: Three main forces that an INS has to take into account are: (a) Gravitational acting down; (a) Gravitational acting down; (b) Centrifugal due to Earth’s rotation and sensed by gyros – a radial force acting outward from the object, unlike centripetal that acts toward the object; and (b) Centrifugal due to Earth’s rotation and sensed by gyros – a radial force acting outward from the object, unlike centripetal that acts toward the object; and (c) Coriolis force in the direction of the movement, coming from compound acceleration of coriolis (in navigation: Coriolis correction of the sensed acceleration) : (c) Coriolis force in the direction of the movement, coming from compound acceleration of coriolis (in navigation: Coriolis correction of the sensed acceleration) : a c = 2  v’, a c = 2  v’,

Department of Optical Engineering Zhejiang University Nonlinearity Problem In inertial navigation, offset errors in the output of the accelerometer accumulate as errors in position as t 2 : In inertial navigation, offset errors in the output of the accelerometer accumulate as errors in position as t 2 : If an accelerometer with a small nonlinearity in the form of a term  2 : If an accelerometer with a small nonlinearity in the form of a term  2 : in a situation which includes a vibration, there will be a displacement of the form  sin(  t). There will be a term in the output of the sensor of the form in a situation which includes a vibration, there will be a displacement of the form  sin(  t). There will be a term in the output of the sensor of the form

Department of Optical Engineering Zhejiang University Vibration Rectification This expression includes This expression includes an oscillating term an oscillating term a static term. a static term. Generally, this phenomenon is referred to as vibration rectification - the process of generating a dc offset signal from a vibration signal. Generally, this phenomenon is referred to as vibration rectification - the process of generating a dc offset signal from a vibration signal. As described above, inertial navigation is one application which is particularly concerned about such phenomena, and so cancellation of nonlinearities in capacitive sensing is very important for such applications. As described above, inertial navigation is one application which is particularly concerned about such phenomena, and so cancellation of nonlinearities in capacitive sensing is very important for such applications.

Department of Optical Engineering Zhejiang University Capacitance Measurement: bridge circuit

Department of Optical Engineering Zhejiang University Sensors using cap measurement Pressure sensors, accelerometers, position detectors, level sensors, … Pressure sensors, accelerometers, position detectors, level sensors, … A good way to measure displacement. If implemented carefully, very small displacements may be measured. A good way to measure displacement. If implemented carefully, very small displacements may be measured. Best suited to applications which require better performance than can be obtained from a strain gauge, and where the added cost of the capacitance detection is allowed. Best suited to applications which require better performance than can be obtained from a strain gauge, and where the added cost of the capacitance detection is allowed. However, the output of a capacitive transducer is not immediately linear. If linearity is important, differential capacitance schemes are advisable. However, the output of a capacitive transducer is not immediately linear. If linearity is important, differential capacitance schemes are advisable.

Department of Optical Engineering Zhejiang University Accelerometer overview Accelerometers: devices that produce voltage signals in proportion to the acceleration experienced. Accelerometers: devices that produce voltage signals in proportion to the acceleration experienced. Techniques for converting an acceleration to an electrical Techniques for converting an acceleration to an electrical Spring-mass+cap measurement Spring-mass+cap measurement Potentiometric Potentiometric Variable Reluctance Variable Reluctance Piezoelectric Piezoelectric

Department of Optical Engineering Zhejiang University General Accelerometer The most general way: suspend a mass on a linear spring from a frame which surrounds the mass, The most general way: suspend a mass on a linear spring from a frame which surrounds the mass, When the frame is shaken, it begins to move, pulling the mass along with it. When the frame is shaken, it begins to move, pulling the mass along with it. If the mass is to undergo the same acceleration as the frame, there needs to be a force exerted on the mass, which will lead to an elongation of the spring. If the mass is to undergo the same acceleration as the frame, there needs to be a force exerted on the mass, which will lead to an elongation of the spring. We can use any of a number of displacement transducers (such as a capacitive transducer) to measure this deflection. We can use any of a number of displacement transducers (such as a capacitive transducer) to measure this deflection. A

Department of Optical Engineering Zhejiang University General Accelerometer: Oscillatory force impose an acceleration by forcing X to take the form: impose an acceleration by forcing X to take the form: If we assume all the time varying quantities also oscillate, If we assume all the time varying quantities also oscillate,

Department of Optical Engineering Zhejiang University General Accelerometer: Amplitude Response of Vibration-measuring Instruments If b = 0 (no damping), If b = 0 (no damping), signal at the resonance can lead to infinitely large signals, generally impose finite damping on the system. If  < <  0, this expression simplifies to If  < <  0, this expression simplifies to the displacement of the mass the displacement of the mass is proportional to the acceleration is proportional to the acceleration of the frame. This is the response of the frame. This is the response we would hope for from an accelerometer. we would hope for from an accelerometer. If  > >  0, then If  > >  0, then For high frequency signals, during which the mass remains stationary, and the accelerometer frame shakes around it. The displacement is the same size as the motion of the frame. This mode of operation is generally referred to as `seismometer mode'. Seismometers are instruments which attempt to measure ground motion, rather than ground acceleration. For high frequency signals, during which the mass remains stationary, and the accelerometer frame shakes around it. The displacement is the same size as the motion of the frame. This mode of operation is generally referred to as `seismometer mode'. Seismometers are instruments which attempt to measure ground motion, rather than ground acceleration.

Department of Optical Engineering Zhejiang University An Example EXAMPLE EXAMPLE An accelerometer has a seismic mass of 0.05 kg and a spring constant of 3.0 X 10 3 N/m Maximum mass displacement is ±0.02 m (before the mass hits the stops). Calculate (a) the maximum measurable acceleration in g, and (b) the natural frequency. Solution We find the maximum acceleration when the maximum displacement occurs An accelerometer has a seismic mass of 0.05 kg and a spring constant of 3.0 X 10 3 N/m Maximum mass displacement is ±0.02 m (before the mass hits the stops). Calculate (a) the maximum measurable acceleration in g, and (b) the natural frequency. Solution We find the maximum acceleration when the maximum displacement occursa. b. The natural frequency

Department of Optical Engineering Zhejiang University Accelerometer Selection based on Applications Applications Applications Steady-State Acceleration Steady-State Acceleration Vibration Vibration Shock Shock

Department of Optical Engineering Zhejiang University Steady-state Acceleration Steady-State Steady-State a measure of acceleration that may vary in time but that is nonperiodic. a measure of acceleration that may vary in time but that is nonperiodic. the stop-go motion of an automobile is an example of a steady-state acceleration. the stop-go motion of an automobile is an example of a steady-state acceleration. we select a sensor having we select a sensor having (1) adequate range to cover expected acceleration magnitudes (2) a natural frequency sufficiently high that its period is shorter than the characteristic time span over which the measured acceleration changes. (3) By using electronic integrators, the basic accelerometer can provide both velocity (first integration) and position (second integration) information.

Department of Optical Engineering Zhejiang University Steady-state Acceleration: an example An accelerometer outputs 14 mV per g. Design a signal-conditioning system that provides a velocity signal scaled at 0.25 volt for every m/s, and determine the gain of the system and the feedback resistance ratio. An accelerometer outputs 14 mV per g. Design a signal-conditioning system that provides a velocity signal scaled at 0.25 volt for every m/s, and determine the gain of the system and the feedback resistance ratio. Solution Solution We chose T = RC = 1 so that the integrator output is scaled at We pick R = 1 M  and C = 1uF and make R2 = 175 k  R1 = 1 k 

Department of Optical Engineering Zhejiang University Vibration The application of accelerometers for vibration The application of accelerometers for vibration first requires that the applied frequency is less than the natural frequency of the accelerometer. first requires that the applied frequency is less than the natural frequency of the accelerometer. Second, one must be sure the stated range of acceleration measured will never exceed that of the specification for the device. Second, one must be sure the stated range of acceleration measured will never exceed that of the specification for the device. This assurance must come from a consideration of the following equation under circumstances of maximum frequency and vibration displacement. This assurance must come from a consideration of the following equation under circumstances of maximum frequency and vibration displacement.

Department of Optical Engineering Zhejiang University Shock The primary elements of importance in shock measurements are that the device The primary elements of importance in shock measurements are that the device have a natural frequency that is greater than 1 kHz and have a natural frequency that is greater than 1 kHz and a range typically greater than 500 g. a range typically greater than 500 g. The primary accelerometer that can satisfy these requirements is the piezoelectric type The primary accelerometer that can satisfy these requirements is the piezoelectric type

Department of Optical Engineering Zhejiang University COLD ATOMS : Atomic Interferometer The atom as a measuring device Atoms also have mass, which enables them to interact with the gravitational field, just as any other body with mass. Atoms also have mass, which enables them to interact with the gravitational field, just as any other body with mass. Their high thermal agitation speed (several hundreds of metres or even kilometres per second) generally means that this interaction cannot be perceived. Their high thermal agitation speed (several hundreds of metres or even kilometres per second) generally means that this interaction cannot be perceived. Now know how to slow atoms down with laser beams to speeds of a few mm.s-1,  interaction with the gravity field can now be observed. Now know how to slow atoms down with laser beams to speeds of a few mm.s-1,  interaction with the gravity field can now be observed. The atoms' mass also makes them sensitive to inertial fields (Coriolis force, centrifugal force) which occur in non-Galilean reference frames. The atoms' mass also makes them sensitive to inertial fields (Coriolis force, centrifugal force) which occur in non-Galilean reference frames. λ=h/P=h/mv

Department of Optical Engineering Zhejiang University COLD ATOMS : Atomic Interferometer For about twenty years, the development of laser techniques for manipulating atoms has made it possible to determine more easily the wave nature of atoms and has yielded a whole range of applicable tools for these atomic waves. For about twenty years, the development of laser techniques for manipulating atoms has made it possible to determine more easily the wave nature of atoms and has yielded a whole range of applicable tools for these atomic waves. know how to make mirrors, beam splitters, diffraction arrays, lenses and all sorts of other tools for developing operational instruments for atomic optics. know how to make mirrors, beam splitters, diffraction arrays, lenses and all sorts of other tools for developing operational instruments for atomic optics. Given these many possible interactions, the atom thus appears to be an ideal tool for probing the external environment. Given these many possible interactions, the atom thus appears to be an ideal tool for probing the external environment. Steven Chu

Department of Optical Engineering Zhejiang University Atomic gravimeters and gradiometers The phase induced by the gravity field on an atomic wave varies rapidly with the value of this field. This phase may be very precisely measured using an atomic interferometer of the temporal Mach-Zehnder type for instance. The phase induced by the gravity field on an atomic wave varies rapidly with the value of this field. This phase may be very precisely measured using an atomic interferometer of the temporal Mach-Zehnder type for instance. possible to measure gravity (terrestrial potential or any other gravitational potential) very precisely. possible to measure gravity (terrestrial potential or any other gravitational potential) very precisely. The latest experiments conducted have revealed high sensitivity which corresponds typically to a variation of about one centimeter of the gravity field on the ground. (resolution: g) The latest experiments conducted have revealed high sensitivity which corresponds typically to a variation of about one centimeter of the gravity field on the ground. (resolution: g)

Department of Optical Engineering Zhejiang University

Department of Optical Engineering Zhejiang University Summary Capacitive measurement Capacitive measurement Features: Features: High precision/resolution: nanometer High precision/resolution: nanometer Suit for displacement sensing Suit for displacement sensing Switched cap circuit for measurement Switched cap circuit for measurement Cost more than strainresistive type Cost more than strainresistive type Accelerometer overview Accelerometer overview General accelerometer principle General accelerometer principle Applicability Applicability Examples Examples Atomic gravitational sensing Atomic gravitational sensing