Sensing and Sensors: Fundamental Concepts Sensitivity Range Precision Accuracy Resolution Offset Hysteresis Response Time Source: sensorwebs.jpl.nasa.gov
Sensor: a device the receives and responds to a stimulus; a device that detects a changing condition (change in presence or absence of something) Stimulus: something external that elicits activity - anything that may have an impact on a system; an input to the system So, what is NOT a sensor? Sources: Fraden: Handbook of Modern Sensors Press et alt: Numerical Recipes The Art of Scientific Computing Nilson: Electric Circuits Dunne: Hertzian Tales
Sensing natural, human, synthetic Natural systems Sensing mostly reflexive Human beings Sensing intuitive, reflexive and intimately linked to cognition and every aspect related to cognition (philosophy, culture) Synthetic systems Inspired by natural systems, modeled by laws of physics, implemented in mechanical and electronic media, known as sensors and transducers
A sensor is a device that receives a stimulus and responds with an electrical signal. A transducer is a converter from one type of energy into another one. Loudspeaker: electric signal -> variable magnetic field -> acoustic wave / sound Direct sensor: converts a stimulus into an electrical signal by using a physical effect (photo effect, for example) Complex sensor: needs in addition one or more transducers before the sensor can generate an electrical signal
Sensors do not operate in isolation; they are connected to and part of a larger system -
... including: other sensors signal conditioners signal processors memory devices data recorders actuators... and they are dependent on: material properties engineering constraints monetary constraints political issues... fear beliefs (prejudices) Dunne: Hertzian Tales
Classifying sensors passive vs. active passive sensors need no additional power, generate a signal directly in response to an external stimulus >> examples: photodiode, piezoelectric sensor active sensors require external power for their operation (an excitation signal). This signal, in turn, is modified by the sensor to produce an output. Active sensor properties change in response to the external input (they are parametric). >> examples: thermistor (temperature sensitive resistor) contact vs. non-contact contact sensors detect change through direct physical contact with a target object >>examples: limit switches, safety switches non-contact sensors create an energy field or beam and react to disturbances in that field; no physical contact is required >>example: ultrasonic sensors
Camera: Image formation (lens), image capture (CCD) CCD: charge coupled device Reprinted from the January 2001 issue of PHOTONICS SPECTRA
Basic concepts Sensitivity the minimum input (of a physical parameter) that will create a detectable output Range the minimum and maximum values of a given parameter the sensor can measure Precision the ability of the sensor to reproduce the same results in repeated tests of identical conditions Accuracy the maximum difference between the actual value and the value indicated by the sensor Resolution the smallest detectable incremental change of input that can be detected in the output signal Offset the output existing in the absence of an input Hysteresis the effect of direction of the input on the output Response time the time required for a sensor to change from a previous state to a new state
Full scale input and full scale output
Accuracy / Inaccuracy Accuracy is measured as the highest deviation of a value represented by the sensor from the ideal or true values at its input. example: A linear displacement-sensor should generate 1 mv per 1 mm displacement. However, measurement shows that a displacement of s = 10.5 mm produced and output of S = 10.0V. 1/b = 1mm/mV sx = S/b = 10.5mm, s x s = 0.5 (0.5 mm in error) inaccuracy = (0.5mm/10mm)* 100% = 5% ->often the deviation from the ideal transfer function is given as δ (+-δ) in terms of the measured value or as percentage of the full span input or in terms of the output -> often one performs accuracy ratings to find the real performance of a sensor. They include combined effects of variations, hysteresis, dead band, calibration and repeatability errors -> worst case scenario
Repeatability Reliability is the ability to recreate the same result under the same condition at different times. It is often expressed as the maximum difference between output readings from two calibrating cycles: δr = (Δ / FS)*100% (FS: full scale) Dead Band The dead band is an insensitivity of a sensor in a specific range of input signals the sensor's blind spot.
Output Impedance A: interface for sensor with voltage output B: interface for sensor with current output To minimize output distortions sensors need to be matched with their connecting circuitry. For voltage generating sensors, a lower impedance (Zout) is preferable and the circuit should have a high input impedance (Zin) A current generating sensor should have an output impedance as high as possible and the circuit's impedance should be as low as possible.
Example of a first order sensor A temperature sensor for which the energy storage is thermal capacity (stays hot for n sec) Often such sensors are described by a frequency response: how fast they can respond to a changed input Example of a second order sensor An accelerometer that incorporates a mass and a spring. A second order response is typical for a sensor that responds with a periodic signal. This is the system s resonant frequency. Typically, the operating range of a sensor is selected below or above the resonant frequency. For some special sensors, however, the resonant frequency IS the operating point (that is where they will have the strongest response). Damping Damping is the suppression of oscillation in a sensor of order > 1. When a sensor's response is maximally fast without overshoot, the response is called critically damped. If an overshoot occurs, the sensor is said to react in underdamped response. If a sensor reacts slower than its max response, it is said to react in overdamped response.
Reliability Reliability is the ability of a sensor to perform a required function under stated conditions for a stated period of time. It is often expressed in statistical terms as a probability that the device will function without failure for a number of uses. Because of this, reliability of a class or batch of devices is evaluated by observing the behavior of a large number of devices. Devices that have been fabricated with the same technology, same materials, and same processes are then assumed to behave in the same way ( > assumed reliability).
A sensor can have more that one dimension if the sensor's output is influenced by more than one input stimulus example: infrared sensor V = G*( T b 4 T s4 ) 4 th order parabola where Ts = temp of sensor surface, Tb = temp of an object of measurement and G a constant
Hysterisis Hysteresis refers to systems which have memory ; that is, the effects of the current input to the system are not felt at the same instant. Such a system may exhibit path dependence. In a deterministic system with no hysteresis, it is possible to predict the system's output at an instant in time, given only its input at that instant in time. In a system with hysteresis, this is not possible; there is no way to predict the output without knowing the system's current state. Hysteresis phenomena occur in magnetic and ferro-magnetic materials, in which a lag occurs between the application and the removal of a force or field and its subsequent effect.
Saturation Everything has a limit. A sensor is no exception. Where the response no longer matches the transfer function, the sensor output can no longer correspond to the input. It then is said to be operating in saturated mode.
Resolution Resolution is defined as the smallest increments of stimuli which can be sensed. Resolution is often expressed as a percent of full scale (FS). Example: an angular sensor has a FS of 270 deg, and its 0.5 deg resolution would be specified as 0.181% FS. When there are no measurable steps in the output of a sensor it is said to be continuous. Often the resolution is not constant over the whole input range. In digital sensors, the resolution is specified as the number of bits used to represent the output, as in '8-bit resolution', where the result is represented by 8 bit long data for FS.
Excitation Excitation is the electric signal needed to make a sensor active for operation. Excitation is often listed as a voltage or current range. In some sensors, the frequency of excitation is also important (and must be specified). Dynamic Characteristics Sensors react with a certain delay to inputs. Sensors are, in this regard, said to be time dependent and show a dynamic characteristic. Some sensors need a warm-up period before they can operate reliably. Including time dependency leads to a different kind mathematical description of sensor behavior, one based on differential equations. Zero order sensor Out(t) = a + b * i(t) a: static sensitivity First order sensor Second order sensor b 1 *(dout(t)/dt) + b 0 *Out(t) = i(t) b 2 *(d 2 Out(t)/dt 2 ) + b 1 *(dout(t)/dt) + b 0 *Out(t) = i(t)
FIT Rates (failures in time) The FIT rate is a statistic measure for a component that describes how many failures the component will have per one billion operating hours. The lower the FIT rate for a component, the better the component is. FIT rate is used to calculate the MTBF. MTBF (mean time between failures) If a product contains n unique components, q i is the quantity of the i th component, and r i is its FIT rate, then the calculated MTBF of the product is : Effectively, this is the inverse of the sum of the FITs