When an analog sensors’ output is converted to a digital output with an analog to digital converter (ADC), conversion resolution, conversion accuracy, conversion speed or bandwidth, inherent system noise levels, and power consumption are all ADC tradeoffs. Errors due to temperature, supply voltage, linearity, quantizing, and other factors may reduce the accuracy of an ADC by several bits.
There are several calculations that can be made to determine the adequacy of the ADC for a specific application.
- The resolution is the least significant bit (LSB) % full scale/100.
- The quantization error (as a % of full-scale range) is ±1/2 • 1/(2n– 1) • 100 which is also ±1/2 LSB.
- The theoretical root mean square (rms) signal-to noise ratio (SNR) for an N-bit ADC is:
SNR = 6.02 • N + 1.76dB
where
N = number of bits.
Sensors with millivolt-level outputs are well below the values required for use in a system, so amplification is necessary. This amplification plays an important role in the converted digital value. An amplified pressure signal supplied to an 8-bit ADC provides an example of the combined capability of the amplifier and the ADC. The A/D conversion is related to the pressure input by:
count = [VFS – VOffset] * 255/[VRH – VRL]
where
VFS – VOffset is the sensor’s full-scale span voltage
255 is the maximum number of counts from the 8-bit converter, and
VRH – VRL is 5V, based on using the same 5V supply as the MCU.
For a sensor with a 0.25 to 4.75V output, the maximum number of counts available at the output register will be:
count (full scale) = 229
Therefore, a full-scale pressure of 15 psi with 5.0V supply results in a system resolution of:
15 psi/229 = 0.066 psi/count
In addition to SNR, ADC suppliers may provide several specifications to quantify the performance of an ADC including: total harmonic distortion (THD) and total harmonic distortion plus noise (THD+N), popular specifications include Signal-to-Noise-and-Distortion (SINAD, or S/(N + D) and the effective number of bits (ENOB).
ENOB = (SINAD – 1.76 dB)/6.02