Advanced Sensor Technology Lecture 4 Jun QIAN Department

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

A Review of Lecture 3 n Background on electrical measurement of sensor outputs n Resistive n n n Capacitive n n Voltage divider Bridge circuit Pure resistive load resistor Inductive Temperature Effect and Compensation 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 n Strain gauge Strain n Poisson’s ratio n Gauge factor n Mercury tube/metal wire n Resistance change 1%-0. 001% n Various bridge circuits n Temperature Effect n Department of Optical Engineering Zhejiang University

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

Capacitive Sensing The capacitance C=Q/V n n 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. Predicting the capacitance between a pair of arbitrary objects is very complicated, n n n 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. 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 n n Parallel plates Electrodes with area 10 mm x 10 mm, n separation 1 m. n C~ 1000 p. F, which isn't very big but still about the biggest you would ever expect to find in a real sensor ! n n More generally, capacitive sensors have capacitance closer to 100 p. F or less. Department of Optical Engineering Zhejiang University

Change in Capacitance due to the Lateral Movement n n 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. Difficult to use for measurement of very small lateral displacements, A 1 um 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 n Useful for many applications n n n Rotary capacitive transducers for positioning High precision monitoring system Military application 140 ± 8 m. V/degrees of shaft rotation Manufacturer: Bently, USA Department of Optical Engineering Zhejiang University

Lateral displacement capacitive transducers Department of Optical Engineering Zhejiang University

n n Capacitance Change v. s. Plate Separation change in capacitance isn't obviously linear, 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, 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 n Nice features associated with such a measurement include n n n 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 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 n n n 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 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 n 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 n Otherwise, a strain gauge based measurement would suffice. n 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. n Department of Optical Engineering Zhejiang University

What is navigation? n n 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, n n n 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. Some of the sensors that are being part of such systems are: n n Inertial Navigation Systems (INS), radio-navigation aids (LORAN, GPS, etc. ), Doppler Velocity Sensors (DVS), laser-ranging devices, barometric altitude-meters, etc Department of Optical Engineering Zhejiang University

Inertia Navigation System (INS) n Three main forces that an INS has to take into account are: n n (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 (c) Coriolis force in the direction of the movement, coming from compound acceleration of coriolis (in navigation: Coriolis correction of the sensed acceleration) : ac = 2 v’, Department of Optical Engineering Zhejiang University

Nonlinearity Problem n In inertial navigation, offset errors in the output of the accelerometer accumulate as errors in position as t 2: n If an accelerometer with a small nonlinearity in the form of a term 2: n 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 n This expression includes n n an oscillating 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. 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 Department of Optical Engineering for such applications. Zhejiang University

Capacitance Measurement: bridge circuit Department of Optical Engineering Zhejiang University

Sensors using cap measurement n n Pressure sensors, accelerometers, position detectors, level sensors, … 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. 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. n Techniques for converting an acceleration to an electrical n Spring-mass+cap measurement n Potentiometric n Variable Reluctance n Piezoelectric n Department of Optical Engineering Zhejiang University

General Accelerometer n The most general way: suspend a mass on a linear spring from a frame which surrounds the mass, n n n 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. 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 n n impose an acceleration by forcing X to take the form: 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), signal at the resonance can lead to infinitely large signals, generally impose finite damping on the system. n If < < 0, this expression simplifies to n the displacement of the mass is proportional to the acceleration of the frame. This is the response we would hope for from an accelerometer. n 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 Department of Optical Engineering ground motion, rather than ground acceleration. Zhejiang University

An Example EXAMPLE An accelerometer has a seismic mass of 0. 05 kg and a spring constant of 3. 0 X 103 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. n Solution We find the maximum acceleration when the maximum displacement occurs a. b. The natural frequency Department of Optical Engineering Zhejiang University

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

Steady-state Acceleration n Steady-State n a measure of acceleration that may vary in time but that is nonperiodic. n the stop-go motion of an automobile is an example of a steady-state acceleration. n 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 n An accelerometer outputs 14 m. V 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. n Solution We chose T = RC = 1 so that the integrator output is scaled at We pick R = 1 M and C = 1 u. F and make R 2 = 175 k R 1 = 1 k Department of Optical Engineering Zhejiang University

Vibration n The application of accelerometers for vibration n n 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. n 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 n The primary elements of importance in shock measurements are that the device n n n have a natural frequency that is greater than 1 k. Hz and a range typically greater than 500 g. 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 λ=h/P=h/mv n Atoms also have mass, which enables them to interact with the gravitational field, just as any other body with mass. n n n 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. The atoms' mass also makes them sensitive to inertial fields (Coriolis force, centrifugal force) which occur in non-Galilean reference frames. Department of Optical Engineering Zhejiang University

COLD ATOMS : Atomic Interferometer n 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. Steven Chu n 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. Department of Optical Engineering Zhejiang University

Atomic gravimeters and gradiometers n 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. n n 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: 10 -9 g) Department of Optical Engineering Zhejiang University

Department of Optical Engineering Zhejiang University

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