4.3AD/DA conversion

For an embedded device to process a sensor's continuous analog signal, it must always pass through a conversion to a digital value (AD conversion). Here the designer must work backward from the frequency content of the signal to be measured and the required precision to decide two numbers: "how many bits should the AD converter have?" and "at what frequency should it sample?" This section builds the judgment needed to decide how to select AD/DA converter specifications in practice, grounded in three pieces of theory: resolution, quantization error, and the sampling theorem.

4.3.1Resolution and quantization error

• Resolution indicates how many discrete digital levels an AD converter can use to represent its input voltage range, and is normally expressed in bits. n-bit resolution means 2^n levels; for example, 10 bits divides the range into 2^10 = 1024 levels, and 12 bits into 2^12 = 4096 levels. As the bit count increases, the voltage width per level becomes finer, allowing a more precise representation of the analog value.
• Quantization error is the error that inevitably arises when a continuous analog value is rounded into a discrete level. If the input voltage range is V and the resolution is n bits, the voltage width per level (one LSB) is V / 2^n, and the theoretical maximum quantization error is half that (±1/2 LSB). There is a tradeoff: raising the resolution reduces quantization error, but increases the bit count, conversion time, and cost required.