Digitization Errors due to A/D Conversion

In most circumstances, the signal from the probe is analog and it is digitized either in a digital measuring instrument or with the help of an ADC DAC card, before being acquired by the PC through appropriate interfaces and software. One of the major source of errors during data acquisition is the A D conversion process itself. In this section, a quantitative estimate of the digitization error is provided. Analog to digital conversion proceeds at a finite rate and during this period of conversion changes that take place in the input voltage level are ignored in S H circuit. If is the number of points into which the voltage range is discretized by the A D converter, then the average discretization error in measuring a voltage in this range of . For a -bit converter . The discretization error spread over the period for which data is collected is equivalent to a noise signal. If the analog signal has a variance and the noise signal has a variance it is desirable that the signal-to-noise ratio be as large as possible. Let be the probability density function of the input signal. Let be the total number of points in the digitized signal. We may then estimate and as follows:

The function can be assumed to be a constant in the small integration interval . Hence,

Since can be assumed to be a constant , the value of is nearly . The magnitude of however, will depend on the form of function . Table 1 summarizes the value of for a variety of input signals and bit converters.

		Gaussian	Sine wave	White noise
4	16	9	18	14
8	24	147	311	24

Table 1: Signal-to-Noise Ratio in A D Conversion