Resolution of Force Sensors
Resolution describes the value at which two adjacent measurements can be distinguished. It therefore defines the smallest possible difference that can be clearly identified.
Resolution
In the context of visual displays, the dictionary of metrology defines resolution as the “smallest difference that can be meaningfully distinguished”.
The concept of resolution is closely related to the concept of response threshold: The response threshold is the highest possible value that does not cause a detectable change in the display.
Resolution is not the same as accuracy .
The achievable resolution depends primarily on the choice of measuring amplifier. Typically, a resolution of 1/10,000 to 1/100,000 of the measuring range can be achieved.
For a 2N sensor, this means a resolution of 0.2mN is possible with the BX8 measuring amplifier.
Resolution Measurement
A “meaningful distinction” between two measured values
Resolution = 1x Noise Amplitude (According to Peak Value Definition)
Interface defines resolution as the difference between the maximum and minimum values
This is a strict definition of resolution. Alternatively, one could use the rectified mean value (RMS value) of the last 3 seconds, or the last 30 measurements.
Applied to a graphics screen, one could say: For the resolution to be sufficient, a difference of 1x line width must be visible and clearly perceptible.
Parts = Measuring Range / Resolution
Since the absolute resolution is usually very small compared to the measuring range (e.g. 1/10,000 to 1/100,000 of the measuring range), and since it depends on the measuring range of the sensor, we calculate a relative numerical value for the resolution: We relate the resolution to the measuring range and calculate (for better “readability”) its reciprocal.
Since the resolution is largely determined by the measuring amplifier used, the resolution is referenced to the standard measuring range of 2.0 mV/V or 3.5 mV/V of the measuring amplifier.
The resolution is thus described by a numerical value. This numerical value describes how many times the measuring range can be divided into line widths. The higher the number of divisions, the better (“higher”) the resolution.
The BlueDAQ software allows the resolution to be displayed using various definitions: resolution as a numerical value in “parts”, resolution as a dimensionless, absolute quantity “peak values
Factors influencing the resolution
The relative resolution (within the measurement range) is essentially a quality characteristic of the measuring amplifier: The inherent noise of the first amplification stage is decisive for the resolution. The resolution of the analog-to-digital converter (the digitization noise) is generally better (finer) than the noise amplitude in 16- or 24-bit technology.
This fact is also responsible for the fact that an exact adjustment of the gain to the measurement range of the analog/digital converter does not lead to a significant improvement in resolution: Doubling the gain also results in a doubling of the noise amplitude.
Bandwidth
The bandwidth of the measurements essentially determines the noise amplitude. If the bandwidth is restricted by filters to, for example, 0-10 Hz, the noise amplitude is significantly lower than with a bandwidth of 0-100 Hz or even 0-1 kHz.
With noise that is uniformly distributed across all frequency components (white noise), a 10-fold bandwidth results in a noise amplitude that is √10 ≈ 3 times greater.
Shielding, Grounding, Mass Concept
Besides the inherent noise of the measuring amplifier, external factors determine the achievable resolution. In particular, the shielding of the sensor leads is an essential prerequisite for high resolution.
Other influences include, for example,
- Non-star-shaped ground wires (ground loops),
- Conducted interference via USB ports,
- Power supplies,
- Capacitive interference (especially in 1/4 bridges) due to lack of grounding.
Environmental Influences
Vibration, drafts, or the introduction of heat reduce the resolution.
Influence of the Bridge Supply Voltage
A higher supply voltage is often considered as a measure to reduce noise, since increasing the supply voltage – and thus the bridge output signal – is associated with a decrease in gain and therefore a reduction in intrinsic noise.
The uneven heating of the strain gauges within a sensor, both temporally and spatially, leads to thermal noise that reduces the resolution. Supply voltages of 2.5V to 5V have proven optimal. High strain gage resistance results in increased resistance noise and more interference due to the higher input impedance of the measurement chain.
Reducing the bridge supply voltage can lead to better stability of the bridge circuit.
Influence of Strain Gages
A higher k-factor of the strain gage does not necessarily lead to higher resolution. High resolution requires good self-compensation and, above all, consistent temporal behavior with respect to drift and creep.
The following figures illustrate the requirements:
- Typical maximum strain of a sensor: 1000 µm/m
- Achievable resolution “10000 parts”: 0.1 µm/m
- Underlying resistance change at 0.1 µm/m: 0.05 10E-6 * 350 Ohm = 17.5E-6 Ohm.
- Thermal expansion of aluminum: 23 µm/m /K
- Required thermal symmetry for 0.1 µm/m: 1/230 K = 0.004 K
- Absolute length change at a 3mm measuring grid length: 0.1 µm/1000mm * 3mm = 0.0003 µm = 0.3 nm
- Distance between two atoms: approx. 0.1 nm
In fact, the maximum strain of most sensors is only 500µm/m, the resolution of the BX8 measuring amplifier is approximately 100,000 parts, and the measuring grid length is often only 1.6mm!
BX/BSC Series Resolution Comparison
The BX/BSC measuring amplifier offers the highest achievable resolution currently available.
Resolution 3A40-2N
Bandwidth 10 Hz: Over a period of 10 seconds, the measurement signal remains stable within 0.1 mN. According to this definition, the resolution is 0.1 mN.
Resolution 3A40-2N
Higher bandwidth increases the noise amplitude.
