How the ADC resolution calculator works
An analogue-to-digital converter divides its input range into 2^N steps, where N is its resolution in bits. One step, the least significant bit or LSB, is the input range divided by 2^N. A 16-bit converter with a 2.5 V range has an LSB of 38.1 µV; a 24-bit converter on the same range has an LSB of 0.149 µV.
The LSB alone says little about a measurement. What matters is how many of those steps the sensor’s signal covers. A sensor that delivers 0 to 10 mV uses 262 of the 65 536 codes of that 16-bit converter if it is connected directly. With an amplifier gain of 128 the same signal becomes 1.28 V and uses 33 554 codes. The calculator divides the measuring range by the codes used and gives the result in the sensor’s own unit: 0.003 N per code for a 100 N force sensor in this example.
The steps of the calculation
- LSB = input range / 2^N.
- Amplified sensor span = (output at range end − output at range start) × gain.
- Codes used = amplified span / LSB.
- Resolution = measuring range / codes used.
The share of the input range used shows how well the gain fits. Below about 10 % the converter is mostly idle and the calculator says so; above 100 % the signal clips and the result is marked as out of range.
Noise-free bits
A high-resolution converter does not deliver all its bits as a steady number. Thermal noise makes the last bits flicker, more so at high data rates and high gains. Datasheets state this as noise-free resolution, or as effective resolution, for each data rate and gain setting. Noise-free resolution is the peak-to-peak figure: the number of bits that do not flicker. Effective resolution is based on RMS noise and is about 2.7 bits higher for the same converter.
Enter the noise-free bits for your settings to see the resolution you can read without averaging. For a 24-bit converter this is often between 16 and 20 bits, which changes the answer by a factor of 16 to 256.
Bridges and ratiometric measurement
A strain-gauge bridge or load cell is usually measured ratiometrically: the excitation voltage is also the converter’s reference. The input range is then tied to the excitation, and a change in excitation cancels out. For a 5 V excitation and a bipolar input of ±2.5 V, enter −2.5 and 2.5 as the input range. The strain gauge bridge calculator and the load cell output calculator give the sensor output to enter here.
Current loops
A 4–20 mA signal measured across a 250 Ω resistor is 1 to 5 V. Enter 1000 and 5000 mV as the sensor outputs and the range of the transmitter as the measuring range; the 4–20 mA converter handles the scaling itself.
Resolution is not accuracy
Resolution is the smallest change that produces a different code. Accuracy is how close the code is to the truth, and it is set by the sensor, the reference voltage, the gain and offset errors of the amplifier and the converter’s non-linearity. A 24-bit converter behind a sensor with 0.1 % error still measures to 0.1 %. Use resolution to decide whether a small change will be visible, not to state an uncertainty.
Frequently asked questions
Why 2^N and not 2^N − 1?
An N-bit converter has 2^N codes and its transfer function is defined with an LSB of full-scale range divided by 2^N. Dividing by 2^N − 1 gives the spacing between the first and last code centre; the difference is far below any other error.
Is more gain always better?
Until the amplified signal reaches the input range, yes for quantisation. But amplifier noise is amplified too, and the noise-free resolution of most converters falls as the gain rises. Compare the result with the noise-free bits for the gain you choose.
Can I improve resolution by averaging?
Averaging reduces noise, by a factor of two for every four-fold increase in samples when the noise is random, at the cost of response time. It does not remove offset, drift or non-linearity.