By Len Staller
Embedded Systems Design
(02/24/05, 05:24:00 PM EST)
(02/24/05, 05:24:00 PM EST)
Non-linearity
Ideally, each code width (LSB) on an ADC's transfer function should be uniform in size. For example, all codes in Figure 2 should represent exactly 1/8th of the ADC's full-scale voltage reference. The difference in code widths from one code to the next is differential nonlinearity (DNL). The code width (or LSB) of an ADC is shown in Equation 1.
LSB = Vref / 2N (Equation 1)
The voltage difference between each code transition should be equal to one LSB, as defined in Equation 1. Deviation of each code from an LSB is measured as DNL. This can be observed as uneven spacing of the code "steps" or transition boundaries on the ADC's transfer-function plot. In Figure 6, a selected digital output code width is shown as larger than the previous code's step size. This difference is DNL error. DNL is calculated as shown in Equation 2.
Figure 6: Differential nonlinearity
DNL = (Vn+1 – Vn) / VLSB (Equation 2)
The integral nonlinearity (INL) is the deviation of an ADC's transfer function from a straight line. This line is often a best-fit line among the points in the plot but can also be a line that connects the highest and lowest data points, or endpoints. INL is determined by measuring the voltage at which all code transitions occur and comparing them to the ideal. The difference between the ideal voltage levels at which code transitions occur and the actual voltage is the INL error, expressed in LSBs. INL error at any given point in an ADC's transfer function is the accumulation of all DNL errors of all previous (or lower) ADC codes, hence it's called integral nonlinearity. This is observed as the deviation from a straight-line transfer function, as shown in Figure 7.
Figure 7: Integral nonlinearity error
Because nonlinearity in measurement will cause distortion, INL will also affect the dynamic performance of an ADC.
Reference:
- http://www.embended.com/
- http://en.wikipedia.org
