By Len Staller
Embedded Systems Design
(02/24/05, 05:24:00 PM EST)
The ideal transfer functionEmbedded Systems Design
(02/24/05, 05:24:00 PM EST)
The transfer function of an ADC is a plot of the voltage input to the ADC versus the code's output by the ADC. Such a plot is not continuous but is a plot of 2N codes, where N is the ADC's resolution in bits. If you were to connect the codes by lines (usually at code-transition boundaries), the ideal transfer function would plot a straight line. A line drawn through the points at each code boundary would begin at the origin of the plot, and the slope of the plot for each supplied ADC would be the same as shown in Figure 1.
Figure 1: Ideal transfer function of a 3-bit ADC
Figure 1 depicts an ideal transfer function for a 3-bit ADC with reference points at code transition boundaries. The output code will be its lowest (000) at less than 1/8 of the full-scale (the size of this ADC's code width). Also, note that the ADC reaches its full-scale output code (111) at 7/8 of full scale, not at the full-scale value. Thus, the transition to the maximum digital output does not occur at full-scale input voltage. The transition occurs at one code width—or least significant bit (LSB)—less than full-scale input voltage (in other words, voltage reference voltage).
Figure 2: 3-bit ADC transfer function with - 1/2 LSB offset
The transfer function can be implemented with an offset of - 1/2 LSB, as shown in Figure 2. This shift of the transfer function to the left shifts the quantization error from a range of (- 1 to 0 LSB) to (- 1/2 to +1/2 LSB). Although this offset is intentional, it's often included in a data sheet as part of offset error (see section on offset error). Limitations in the materials used in fabrication mean that real-world ADCs won't have this perfect transfer function. It's these deviations from the perfect transfer function that define the DC accuracy and are characterized by the specifications in a data sheet. The DC performance specifications described have accompanying figures that depict two transfer function segments: the ideal transfer function (solid, blue lines) and a transfer function that deviates from the ideal with the applicable error described (dashed, yellow line). This is done to better illustrate the meaning of the performance specifications.
Reference:
- http://www.embended.com/
- http://en.wikipedia.org
