Resolution Is Limited by Sensor Noise When Tracking Motion
One issue with sensors is that their many characteristics aren't usually shown in a way that makes direct comparisons possible. This makes it difficult to confirm that the best sensor for the money was generated throughout the selection process. Resolution is one of the most commonly misinterpreted and inadequately specified parameters. Measurements from a sensor with inadequate resolution could not be accurate. However, a sensor that provides unnecessary resolution can be expensive. The system bandwidth, the application, the measuring technique, and the output noise unit of measurement are the only factors that affect resolution. Seldom does a data sheet's basic resolution specification provide enough details to enable a well-informed sensor selection. Engineers must be aware of the elements influencing this standard in order to make confident decisions.
Resolution, to put it simply, is the smallest measurement that a sensor can consistently distinguish. It's not accurate. In certain situations, a low resolution sensor may be highly accurate, and an inaccurate sensor may have a high resolution. Furthermore, resolution is neither the least important bit in a conversion between the digital and analog worlds nor the least important number on a display. Although the resolution of digital devices is dependent on the least significant digit or bit, this constraint may only worsen the overall sensor resolution. In the analog world, the fundamental limit of sensor resolution is established, and the drive for higher resolutions is largely a war against electrical noise.
Electrical noise becomes the primary factor limiting the smallest possible measurement in any electronic device that detects minute voltage changes. When seen with an oscilloscope, the tiny, random variations in voltage potentials produced by all electrical components aggregate throughout the circuitry to form a band of noise.
For instance, photographs taken by telescopes using CCD detectors include graininess due to electrical noise. If the objects are the same size as the noise-induced granularity, it is impossible to see small distant things.
Supercooled CCDs are used by some advanced telescopes to increase their signal-to-noise ratios. By virtually completely removing the random movement of charges in the CCD, the extremely low temperature lowers electrical noise to almost nothing. The little items become apparent when there is less noise to obstruct the view.
The noise problem in displacement/position sensor specification indicates that if the sensor has 10 μm of noise in the output, a 1-μm displacement disappears. To forecast the smallest feasible measurement in an application, the resolution specification must take into account additional resolution-influencing variables, such as bandwidth, unit of measure, and other data, in addition to the output noise.
Bandwidth and resolution
The way sensors react at various frequencies is indicated by their bandwidth or frequency response. Motion and vibration at higher frequencies can be detected by sensors with a larger bandwidth. Broadband refers to the large range of frequencies that are present in electrical noise. Although it decreases sensor bandwidth, a low-pass filter aids in reducing noise at high frequencies. Better resolution and reduced noise are the results of low-pass filtering, but useful bandwidth is sacrificed. The system can react to smaller displacements thanks to the low-pass filter's reduced noise level, but it cannot reliably detect displacements at frequencies higher than the filter cutoff, which is usually 100 Hz or greater for physical sensors.
For this reason, a resolution specification that isn't accompanied by a bandwidth specification isn't really helpful. At the measurement frequency, the resolution specification must remain valid. A sensor's resolution may have been set at or below 100 Hz, even though its broad bandwidth may be 1 kHz or more. This discrepancy might not be made evident on the data sheet. Unless otherwise stated, it is best to presume that the resolution specifications and the general bandwidth cannot be realized simultaneously for the majority of sensor data sheets.
Static and dynamic resolution parameters are offered by certain manufacturers. Only when the sensor output is low-pass filtered for low bandwidth—sometimes as low as 10 Hz—does the static standard apply. When the sensor is used in conjunction with an analogous bandwidth filter to measure slow-moving systems, static resolution is helpful. An unfiltered sensor is usually the dynamic specification. This is the anticipated resolution in high-speed dynamic scenarios when the sensor is operating at full bandwidth. Look for a remark that specifies precisely which frequencies are represented by the static and dynamic numbers if the data sheet uses both static and dynamic terminology. It isn't feasible.To eliminate any uncertainty, some manufacturers list resolution at particular bandwidths.
The filter is where?
In addition to the cutoff frequency, a number of other factors affect how well commercial low-pass filter designs perform. As a result, using two distinct 1-kHz filters with a particular sensor may yield different results. It is crucial to determine whether the filter employed in the measurement was internal or external to the sensor when sensor resolution is given for smaller bandwidths. Integral bandwidth filters increase the likelihood of achieving the desired resolution. To ensure the same outcomes, you will require an equivalent filter if the specification was created using an external filter.
Volts, percent-of-full-scale, or dimensional units can be used to specify a resolution. When an engineer is attempting to measure position or displacement, dimensional units could be the most useful. The smallest displacement measurement you may dependably anticipate using the sensor will be made evident by a dimensional unit definition, such as nanometers. To find the smallest displacement measurement feasible, multiply the specification, if it is expressed as a percentage, by the sensor's range. To find the minimum possible detected displacement, multiply the value by the sensor's sensitivity (displacement/ΔV) if the specification is provided as a voltage. After determining the sensor's resolution in dimensional units, you must ascertain if the specification refers to a peak-to-peak (P-P) or root-mean-square (RMS) value.
Understanding the difference between peak-to-peak and RMS is essential to comprehending absolute sensor performance. Special meters and visual interpretation of oscilloscope displays are used in analog ways of measuring these variables. In the digital realm, these values are determined through statistical analysis of a large number of output voltage samples.
The power from a dc source is equivalent to the power in dynamic electrical signals expressed in RMS values. RMS values are usually measured via analog meters. The RMS value is equivalent to the standard deviation of the recorded samples after being digitalized and statistically examined. When measuring broadband vibration, RMS is the most significant specification.
The difference between the highest and lowest noise peaks over a given time period is known as peak-to-peak. A P-P noise level, for instance, could be 2.4 mV over one second.The highest and minimum peaks can be found by analyzing the samples if the signal is digitally recorded. The P-P value can be calculated as six times the standard deviation if the samples form a perfectly normal (Gaussian) distribution. In reality, noise signals rarely behave this well. Typically, they have erroneous peaks that provide P-P values that are far larger than six times the standard deviation. Accordingly, resolution values indicated by their P-P range are typically much higher than RMS values and must be at least six times greater. The P-P value is more than eight times more than the RMS value in the 2.4-mV P-P example, which may correspond to a 0.29-mV RMS.
The best specification to use when attempting to ascertain your target's current position is the P-P value. Your position measurement may fluctuate by the same amount as the P-P resolution specification at any given time due to variations in the sensor output.
Examining the data sheets
Four specific parameters need to be identified when reading data sheets to determine sensor resolution: the resolution specification(s), the bandwidth at which the stated resolution will materialize, whether the sensor has any built-in bandwidth filters, and the resolution specification's unit and type of measure (P-P or RMS).
The majority of sensor data sheets give a resolution specification, however they might not include all the details required to completely comprehend the potential resolution.There may be distinct resolution specifications for every probe/range combination, or resolution may be given as a single specification that applies to all ranges for a specific model.
The resolution bandwidth may be asterisked with footnotes or other small type; the data sheet will probably include a bandwidth specification for the sensor, but it may or may not explicitly state the frequency at which the resolution was specified. Check with the manufacturer to make sure the resolution specification covers the system's whole bandwidth if it isn't specified. Determining if the bandwidth filters are essential to the sensor may be challenging if resolution information is available at several bandwidths.
For instance, the filters are probably integral and the resolution standard is applicable to the sensor if it is stated that it is available in several bandwidth combinations. Ask the manufacturer how the other bandwidths were determined when the resolution was set if the sensor's ability to be configured at different bandwidths isn't mentioned.
Most data sheets list resolution as an RMS value since RMS resolution specifications are always far lower than P-P. However, P-P resolution is required for continuous instantaneous position measurement. A multiplier for converting RMS numbers to P-P may be included on the data sheet, or it may list both RMS and P-P values. Ask the manufacturer for the precise figure if there is no P-P value or multiplier mentioned. It's reasonable to expect that the P-P value is at least six times larger than the RMS value, and frequently it's closer to ten.
Nothing compares to the agony of realizing midprocess that a system component isn't working as you had anticipated. You may now choose displacement sensors with confidence after learning about sensor resolution, its connection to bandwidth, and the various units of measurement.
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