Article: “Resolution Resolved,” http://tinyurl.com/c8bbqh
There’s one problem with sensors: The array of specifications that describe them aren’t always presented in a way that allows direct comparison. This makes it tough to be sure the selection process has produced the best sensor for the money.
One of the most-frequently misunderstood and poorly defined specifications is resolution. A sensor with insufficient resolution may not be able to make reliable measurements. But a sensor supplying unneeded resolution can be costly.
Resolution is only meaningful within the context of system bandwidth, the application, the measurement method, and the unit of measure for the output noise. A simple resolution spec in a data sheet rarely gives enough information for a fully informed sensor selection. For confident decision making, engineers need to understand the factors that impact this specification.
Simply stated, resolution is the smallest measurement a sensor can reliably differentiate. It is not accuracy. An inaccurate sensor could have high resolution, and a low resolution sensor may be quite accurate in some applications. Resolution is also not the least-significant digit in a display or the least-significant bit in a conversion between the digital and analog worlds. Digital devices do possess a resolution based on the least significant digit/bit, but that limitation may only further degrade overall sensor resolution. The fundamental limit of sensor resolution is determined in the analog world with the battle for higher resolutions primarily a fight against electrical noise.
In any electronic system that senses tiny voltage changes, electrical noise becomes the dominant factor that limits the 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.
For example, electrical noise creates the graininess in images captured by telescopes that use CCD detectors. It becomes impossible to see small distant objects if the objects are the same size as the noise-induced granularity.
Some high-tech telescopes use super cooled CCDs to improve their signal-to-noise ratios. The extremely low temperature reduces electrical noise to near zero by almost totally eliminating the random movement of charges in the CCD. With little noise to interfere with the image, the small objects become visible.
When specifying a displacement/position sensor, the noise problem means a 1-μm displacement vanishes if the sensor has 10 μm of noise in the output. Aside from the output noise, other factors that influence resolution, such as bandwidth, unit of measure, and other information, must be included in the resolution specification to predict the smallest practical measurement in an application.
Resolution and bandwidth
Bandwidth or 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. A low-pass filter helps cut the noise at high-frequencies, but also reduces sensor bandwidth. Low-pass-filtered signals have less noise and, therefore, better resolution but at the expense of usable bandwidth. The lower noise level offered by the low-pass filter lets the system respond to smaller displacements, but would not accurately detect displacements at frequencies above the filter cutoff, typically 100 Hz or higher for physical sensors.
This is why a resolution specification apart from a bandwidth specification is not entirely useful. The resolution specification must hold at the measurement frequency. While a sensor may have a 1-kHz or higher general bandwidth, sensor resolution may have been specified at or below 100 Hz. The data sheet may not clearly indicate this difference. For most sensor data sheets it’s best to assume that the general bandwidth and the resolution specifications cannot be realized simultaneously, unless otherwise indicated.
Some manufacturers provide two resolution specifications: static and dynamic. The static specification only applies when the sensor output is low-pass filtered for low bandwidth, sometimes as low as 10 Hz. Static resolution is useful when the sensor is teamed with an equivalent bandwidth filter to measure slow moving systems. The dynamic specification is typically an unfiltered sensor. This is the resolution expected when using the sensor at full bandwidth in high-speed dynamic situations. If the data sheet uses static and dynamic terms, search for a note that defines exactly what frequencies are represented by the static and dynamic figures. It’s impossible to know if the sensor is a good choice for an application without actual frequencies. Some manufacturers list resolution at specific bandwidths, removing any guesswork.
Where’s the filter?
The operation of commercial low-pass filter designs also depends on many parameters besides the cutoff frequency. Thus, two different 1-kHz filters may produce different results when used with a specific sensor. When sensor resolution is reported for lower bandwidths, it is critical to know if the filter used in the measurement was integral or external to the sensor. Integral bandwidth filters promote confidence in attaining the specified resolution. However, if the specification was generated with an external filter, you’ll need an identical filter to assure the same results.
A resolution specification may be given in volts, percent- of-full-scale, or dimensional units. Perhaps dimensional units are the most meaningful to the engineer trying to measure position or displacement. A dimensional unit specification, such as nanometers, will clearly indicate the smallest displacement measurement you can reliably expect to 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 multiply the value by the sensor’s sensitivity (displacement/ΔV) to determine the smallest possible measured displacement. Once you know the sensor’s resolution in dimensional units, it’s necessary to determine whether the specification represents an RMS (root-meansquare) or peak-to-peak (P-P) value.
The distinction between RMS and peak-to-peak (sometimes called by the equivalent name peak-to-valley) is critical in understanding absolute sensor performance. Analog methods of measuring these values employ special meters and visual interpretation of oscilloscope displays. In the digital world, these values are calculated by capturing a large number of samples of the output voltage and analyzing the data statistically.
The power in dynamic electrical signals measured in RMS values equates to the same amount of power from a dc source. Analog meters typically measure RMS values. 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 is the difference between the maximum and minimum peaks of noise over a specific period of time. For example, a P-P noise level might measure 2.4 mV over 1 sec. If the signal is captured digitally, the samples can be analyzed to find the maximum and minimum peaks. If the samples create a perfectly normal (Gaussian) distribution, the P-P value can be estimated as six times the standard deviation. In practice, noise signals are rarely so well behaved. They usually contain spurious peaks that create actual P-P values much higher than six times the standard deviation. This means resolution values specified by their P-P range must be at least six times greater than RMS values and are usually considerably higher than that. That 2.4-mV P-P example may translate to 0.29-mV RMS; that makes the P-P value more than eight times higher than the RMS value.
The P-P value is the most appropriate specification when trying to determine the instantaneous position of your target. At any moment in time, the sensor output can vary by an amount equal to the P-P resolution specification; therefore, your position measurement can vary by that same amount.
Reading the data sheets
When reading data sheets to determine sensor resolution, there are four specific parameters that must be identified: the resolution specification(s), bandwidth at which the stated resolution will materialize, whether any bandwidth filters are integral to the sensor, and the unit and type of measure (P-P or RMS) of the resolution specification.
Most sensor data sheets list a resolution specification but may not provide all the information needed to fully understand the actual resolution available to the application. Resolution may be listed as a single specification that applies to all ranges for a particular model, or there may be separate resolution specifications for each probe/ range combination.
The data sheet will likely include a bandwidth specification for the sensor, but it may or may not clearly list the frequency at which the resolution was specified; the resolution bandwidth may be asterisked with footnotes or other small print. If the bandwidth is not listed, verify with the manufacturer that the resolution specification applies to the full bandwidth of the system. If resolution information is available at multiple bandwidths, it may be difficult to determine if the bandwidth filters are integral to the sensor.
For example, if the sensor is listed as being available in multiple bandwidth configurations, the filters are likely to be integral and the resolution specification applies to the sensor. If there’s no mention of the sensor’s capacity to be configured at different bandwidths, ask the manufacturer how the other bandwidths were arrived at when the resolution was specified.
Because RMS resolution specifications are always significantly lower than P-P, most data sheets list resolution as an RMS value. But the measurement of continuous instantaneous position needs the P-P resolution. The data sheet may list both RMS and P-P values, or provide a multiplier for converting RMS values to P-P. If no P-P value or multiplier is listed, then contact the manufacturer for the exact value. In the meantime, it’s safe to assume the P-P value is at least six times higher and often closer to 10 times higher than the RMS value.
There is nothing like the pain of discovering in midprocess that some component of your system doesn’t perform as you expected. By understanding sensor resolution, its relationship to bandwidth, and the different units of measure, you can now make confident decisions about displacement sensors.