What is Differential Non-Linearity in ADC?

Maxim said:

Differential Nonlinearity: A specification that appears in data-converter datasheets. In an ideal D/A converter, incrementing the digital code by 1 changes the output voltage by an amount that does not vary across the device's permitted range. Similarly, in an A/D, the digital value ramps smoothly as the input is linearly swept across its entire range. DNL measures the deviation from the ideal. An ideal converter has the code exactly the same size, and a DNL of 0 (zero).

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National Instruments said:

As the input voltage to the ADC increases, the digital codes output by the ADC also increases (See Figure 2). In the case of an ideal ADC, this "voltage vs. code" transfer function looks like a staircase in which no step is taller or wider than any other step. You can calculate this step size, referred to as code width, as

Code Width = (input Voltage Range)/(2^n)
Where "n" represents the resolution of the ADC in bits.

For example, a 16-bit computer-based instrument with an input range of 0 to 10 V has a code width calculated at (10 V)/ 2^16 codes = 153 uV per code. In this example, 153 uV is equivalent to one least significant bit (LSB) for this instrument. This means that the width of each step is 153 uV. In this example, the computer-based instrument ideally can digitize input signals that change by a minimum of 153 uV. Signal changes smaller than 153 uV may go unnoticed by the ADC.

The code width of a computer-based instrument does not have any maximum upper bounds. However, it can never be less than 0 LSB. A code width of 0, or near 0, LSB represents a missing code. See Figure 3 for an example of what a missing code can do to the linearity of the instrument's transfer function.

From Figure 3, you can see that code 00..0101 is missing. In other words, there exists no input voltage which will cause the ADC to output this particular digital value. This means that the instrument would see no difference between an input of 100 uV or an input of 140 uV -- even though the 40 uV difference is much greater than the LSB value of 24 uV. Each missing code is one less step in the transfer function. This means that a 16-bit instrument that can digitize voltages across 65536 steps technically no longer operates at 16 bits if there are missing codes.

The term differential nonlinearity (DNL) is used to quantify how code width affects measurement accuracy. DNL is a measure in LSB of the worst-case deviation of the code width from the ideal value of 1 LSB. A perfect computer-based instrument has DNL of 0 LSB. However, you can expect realistic computer-based instruments to have a DNL of +/-0.5 LSB. In some cases DNL is specified by stating that the instrument has no missing codes. This statement means that the DNL has a lower bound of < -1 LSB, and does not conclude anything about the DNL upper bounds.

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