Resolution represents one of the most frequently misunderstood and poorly defined descriptions of performance. Resolution is an important specification because without sufficient resolution you may not be able to reliably make the required measurement, and an over-performing sensor will burden your budget.
Resolution is only meaningful within the context of the system bandwidth, the application, and the measurement method and unit of measure used by the sensor manufacturer.
Basics of Sensor Resolution
Essentially, a resolution is the smallest measurement a sensor can reliably indicate. Before discussing this in any detail, it is important to understand what resolution is not; it is not accurate.
A very inaccurate sensor can have a very high resolution, and a low-resolution sensor may be very accurate in some applications. Resolution is not the least significant digit in a display or the least significant bit in a conversation between the digital and analog worlds.
The electrical noise in a sensor’s output is the primary factor limiting its smallest possible measurement. All electronic components produce small random changes in voltage potentials that combine throughout the circuitry and appear as a band of noise when viewed with an oscilloscope as shown in Figure 1.
Figure 1. Electrical noise in the sensor output voltage.
Electrical noise is a factor in any electronic system trying to sense very small changes in voltage. For example, electrical noise causes image graininess in telescopes using CCD detectors. Users cannot see small distant objects if the objects are the same size as the noise-induced grains.
Bandwidth, unit of measure and other information must be included in the resolution specification in order to predict the smallest measurement possible in a specific application.
Bandwidth (frequency response) indicates how sensors respond at different frequencies. Higher bandwidth sensors can measure higher frequency motion and vibration. Electrical noise is generally broadband, which means it contains a wide spectrum of frequencies.
Low-pass filtered signals have less noise and therefore better resolution but at the expense of usable bandwidth. Figure 2 shows the noise of a sensor with a 15kHz bandwidth, and Figure 3 shows the same sensor output with a 100Hz low-pass filter.
Figure 2. The noise of a sensor with 15kHz bandwidth.
Figure 3. The noise of a sensor with 100Hz bandwidth.
Due to the low noise level, it is possible to see smaller displacements with the low-pass filtering, but you will not be able to accurately detect displacements occurring at frequencies at 100Hz or higher. This is why a resolution specification apart from a bandwidth specification is not entirely useful.
Certain manufacturers offer two resolution specifications: Static and Dynamic. The Static specification only applies when the sensor output is low-pass filtered for very low bandwidth, sometimes as low as 10Hz. This is useful if you will be using the sensor with an equivalent bandwidth filter to measure slow-moving systems.
The Dynamic specification is usually for an unfiltered sensor; this is the resolution you can expect when using the sensor at full bandwidth in high-speed dynamic applications. If the datasheet uses Static and Dynamic terms, search for a note that defines exactly what frequencies are represented by Static and Dynamic.
Where is the Filter for Low Bandwidth Resolution?
Commercially-available low-pass filter designs are dependent on many parameters in addition to the cut-off frequency. As a result, two different 1kHz filters may produce different results when used with your sensor. When sensor resolution is reported for lower bandwidths, it is critical that you know if the filter used in the resolution measurement is integral to the sensor.
Sensor Resolution Units of Measure
A resolution specification may be given in volts, percent of full scale, or dimensional units. Perhaps the most meaningful to the engineer trying to measure position/displacement is dimensional units.
A dimensional unit specification, such as nanometers, will clearly indicate the smallest displacement measurement you can reliably make with the sensor. If the specification is given as a percent, that value must be multiplied by the sensor’s range to determine the smallest possible displacement measurement. If the specification is given as a voltage, then the value will have to be multiplied by the sensor’s sensitivity (displacement units/voltage change) to determine the smallest possible displacement measurement.
The distinction between RMS (root mean square) and Peak-to-Peak (sometimes called by the equivalent name Peak-to-Valley) is critically important to understanding the absolute sensor performance.
RMS measurements of dynamic electrical signals indicate the equivalent power from a DC source. It is similar to, but not the same as, an average value. RMS values may be determined by analog meters that measure the signal power and equating it to a DC voltage that would produce the same power. When digitized and analyzed statistically, the RMS value is equal to the standard deviation of the captured samples. RMS is the most relevant specification when measuring broadband vibration.
Peak-to-Peak (P-P) is the difference between the maximum and minimum peaks of the noise over some period of time. Figure 3 shows a P-P noise level of 2.4mV over one second. If the signal is captured digitally, the samples can be analyzed to find the maximum and minimum peaks. The 2.4mV P-P value in Figure 3 translates to 0.29mV RMS; the P-P value is more than eight times higher than the RMS value in this case.
The P-P value is the most appropriate specification if you are trying to continuously determine the instantaneous position of your target.
To fully understand the resolution of the sensor you are considering, you must conclusively identify these parameters in the specification:
- A resolution specification(s)
- Bandwidth at which the stated resolution is obtained
- If any bandwidth filters are integral to the sensor
- Unit and type (P-P or RMS) of measure of the resolution specification.
Most sensor datasheets list a resolution specification, but they may not provide all of the information required to fully understand the actual resolution you will have in your application.
The datasheet is likely to include a bandwidth specification for the sensor, but it may or may not clearly list the bandwidth at which the resolution was specified; the resolution bandwidth may have to be searched for in footnotes or other small print. In case the bandwidth is not listed, you will need to verify with the manufacturer that the resolution specification applies at the full bandwidth of the system.
Because RMS resolution specifications are always significantly lower than P-P, most datasheets will list resolution as an RMS value. If you are measuring a continuous instantaneous position, you will need to know the P-P resolution.
The datasheet may list both RMS and P-P values, or a multiplier for converting the RMS value to P-P. If no P-P value or multiplier is listed, you will have to contact the manufacturer; in the meantime, you can assume that the P-P value is at least six times higher and usually closer to ten times higher.
This information has been sourced, reviewed, and adapted from materials provided by Lion Precision.
For more information on this source, please visit Lion Precision.