Understanding “True Analog” Resolution

Many distance measurement sensors – regardless of the front-end sensing technology employed – deliver an analog output such as 0-10V or 4-20mA.   A key parameter to understand for any distance measurement sensor is the output resolution.   In a position measurement system, resolution is defined as:     

The smallest increment of position change which can be detected and indicated by the output.      

To understand the ultimate resolution of a given sensor, it is necessary to understand how the device functions to generate the analog output.  In a true analog sensor, the output is developed by purely analog circuitry, without the use of a digital-to-analog converter (a.k.a. DAC: we’ll cover digitally-derived analog outputs in a future post).  In a true analog sensor, the output change is continuous and infinitely variable.  In theory the resolution is infinite, but in practice it is not…read on to find out why.     

Factors Affecting True Analog Resolution

 In sensors delivering a true analog output, practical resolution is determined primarily by:     

• The noise on the output and/or signal lines
• The input resolution of the device to which the sensor is connected

 Noise – This is the main limiting factor in most measurement systems.  Even if the resolution of the sensor is theoretically infinite, it’s only possible to resolve signal changes that are larger than the amount of noise on the output signal lines.  Output changes smaller than the noise level are “lost” in the noise.      

Measurement Length:  60 mm (2.36″)     

Output Range:  0-10 Vdc     

System Noise Level:   10 mV     

In this example, the infinitely variable output signal of the sensor is limited by the fact that there is 10 mV of noise present on the signal lines.   Since 10 mV is 1/1000^th of the entire 0-10V range, the smallest position change that can be detected is 1/1000^th of the working stroke range of 2.36”:      2.36 / 1000 = 0.00236” 

So a good, practical estimate of the resolution is 0.0024”.  Assuming a lower noise level would result in a better estimated resolution, e.g., 5 mV = 0.0012”    

Understanding Controller Input Resolution     

Analog inputs on industrial controls must “digitize” an analog signal in order to utilize the information.   This is accomplished using an Analog-to-Digital Converter (ADC).  An ADC accepts the analog signal and assigns a discrete, digital value to a defined signal value.     

For example, a 12-bit ADC can represent a 0-10V signal as any one of 4,096 “numbers” (2¹² = 4,096).   Using the above example:  2.36” / 4,096 = 0.00058”     

Important – Note that, in the above example, the limitation as a result of noise is still the determining factor.  Even though the input resolution can be as good as 0.00058”, the 10 mV noise level would still limit practical resolution to 0.00236”.