SENSOR TRANSDUCER DETECTOR: SENSOR CHARACTERISTICS (3)

Sensor Examples:

7. Hysteresis

A hysteresis error is a deviation of the sensor’s output at a specified point of the input signal when it is approached from the opposite directions (Fig. 4). For example,a displacement sensor when the object moves from left to right at a certain point produces a voltage which differs by 20 mV from that when the object moves from right to left. If the sensitivity of the sensor is 10 mV/mm, the hysteresis error in terms of displacement units is 2 mm. Typical causes for hysteresis are friction and structural changes in the materials.

8. Nonlinearity

Nonlinearity error is specified for sensors whose transfer function may be approximated by a straight line [Eq. (1)]. A nonlinearity is a maximum deviation (L) of a real transfer function from the approximation straight line. The term “linearity” actually means “nonlinearity.” When more than one calibration run is made, the worst linearity seen during any one calibration cycle should be stated.

Usually, it is specified either in percent of span or in terms of measured value (e.g, in kPa or °C). “Linearity,” when not accompanied by a statement explaining what sort of straight line it is referring to, is meaningless. There are several ways to specify a nonlinearity, depending how the line is superimposed on the transfer function. One way is to use terminal points (Fig.5A); that is, to determine output values at the smallest and highest stimulus values and to draw a straight line through these two points (line 1). Here, near the terminal points, the nonlinearity error is the smallest and it is higher somewhere in between.

Another way to define the approximation line is to use a method of least squares (line 2 in Fig. 5A). This can be done in the following manner. Measure several (n) output values S at input values s over a substantially broad range, preferably over an entire full scale. Use the following formulas for linear regression to determine intercept a and slope b of the best-fit straight line:

a = (ΣSΣs² - ΣsΣsS) / (nΣs² - (Σs)² , b = (nsS-ΣsΣS)/(nΣs² - (Σs)² (16)
where Σ is the summation of n numbers.

In some applications, a higher accuracy may be desirable in a particular narrower section of the input range. For instance, a medical thermometer should have the best accuracy in a fever definition region which is between 37°C and 38°C. It may have a somewhat lower accuracy beyond these limits.

Usually, such a sensor is calibrated in the region where the highest accuracy is desirable. Then, the approximation line may be drawn through the calibration point c (line 3 in Fig. 2.5A). As a result, nonlinearity has the smallest value near the calibration point and it increases toward the ends of the span. In this method, the line is often determined as tangent to the transfer function in point c. If the actual transfer function is known, the slope of the line can be found from Eq. (5).

Independent linearity is referred to as the so-called “best straight line” (Fig. 5B), which is a line midway between two parallel straight lines closest together and enveloping all output values on a real transfer function. Depending on the specification method, approximation lines may have different intercepts and slopes. Therefore, nonlinearity measures may differ quite substantially from one another.Auser should be aware that manufacturers often publish the smallest possible number to specify nonlinearity, without defining what method was used.

9. Saturation

Every sensor has its operating limits. Even if it is considered linear, at some levels of the input stimuli, its output signal no longer will be responsive. A further increase in stimulus does not produce a desirable output. It is said that the sensor exhibits a span-end nonlinearity or saturation (Fig. 6).

10. Repeatability

A repeatability ( reproducibility) error is caused by the inability of a sensor to represent the same value under identical conditions. It is expressed as the maximum difference between output readings as determined by two calibrating cycles (Fig. 2.7A), unless otherwise specified. It is usually represented as % of FS:

δr = Δ / FS × 100% (17)

Possible sources of the repeatability error may be thermal noise, buildup charge, material plasticity, and so forth.

11. Dead Band

The dead band is the insensitivity of a sensor in a specific range of input signals (Fig. 7B). In that range, the output may remain near a certain value (often zero) over an entire dead-band zone.

12. Band Resolution

Resolution describes the smallest increments of stimulus which can be sensed. When a stimulus continuously varies over the range, the output signals of some sensors will not be perfectly smooth, even under the no-noise conditions. The output may change in small steps. This is typical for potentiometric transducers, occupancy infrared detectors with grid masks, and other sensors where the output signal change is enabled only upon a certain degree of stimulus variation. In addition, any signal converted into a digital format is broken into small steps, where a number is assigned to each step.

The magnitude of the input variation which results in the output smallest step is specified as resolution under specified conditions (if any). For instance, for the occupancy detector, the resolution may be specified as follows: “resolution—minimum equidistant displacement of the object for 20 cm at 5 m distance.” For wire-wound potentiometric angular sensors, resolution may be specified as “a minimum angle of 0.5°.” Sometimes, it may be specified as percent of full scale (FS). For instance, for the angular sensor having 270° FS, the 0.5° resolution may be specified as 0.181% of FS. It should be noted that the step size may vary over the range, hence, the resolution may be specified as typical, average, or “worst.” The resolution of digital output format sensors is given by the number of bits in the data word. For instance, the resolution may be specified as “8-bit resolution.” To make sense, this statement must be accomplished with either the FS value or the value of LSB (least significant bit). When there are no measurable steps in the output signal, it is said that the sensor has continuous or infinitesimal resolution (sometimes erroneously referred to as “infinite resolution”).

13. Special Properties

Special input properties may be needed to specify for some sensors. For instance, light detectors are sensitive within a limited optical bandwidth. Therefore, it is appropriate to specify a spectral response for them.

14. Output Impedance

The output impedance Zout is important to know to better interface a sensor with the electronic circuit. This impedance is connected either in parallel with the input impedance Zin of the circuit (voltage connection) or in series (current connection).

Figure 8 shows these two connections. The output and input impedances generally should be represented in a complex form, as they may include active and reactive components. To minimize the output signal distortions, a current generating sensor (B) should have an output impedance as high as possible and the circuit’s input impedance should be low.

For the voltage connection (A), a sensor is preferable with lower Zout and the circuit should have Zin as high as practical.

15. Excitation

Excitation is the electrical signal needed for the active sensor operation. Excitation is specified as a range of voltage and/or current. For some sensors, the frequency of the excitation signal and its stability must also be specified. Variations in the excitation may alter the sensor transfer function and cause output errors.

An example of excitation signal specification is as follows:
Maximum current through a thermistor in still air 50 µA in water 200 µA