INL/DNL Measurements for High-Speed Analog-to-Digital Converters (ADCs) – Tutorial – Maxim.

*Techniques: Measuring INL and DNL — of ADCs.*

**Differential nonlinearity (DNL) :**

DNL error is defined as the difference between an actual step width and the ideal value of 1 LSB. For an ideal ADC, in which the differential nonlinearity coincides with DNL = 0LSB, each analog step equals 1LSB (1LSB = V_{FSR}/2^{N}, where V_{FSR} is the full-scale range and N is the resolution of the ADC) and the transition values are spaced exactly 1LSB apart. A DNL error specification of less than or equal to 1LSB guarantees a monotonic transfer function with no missing codes. An ADC’s monotonicity is guaranteed when its digital output increases (or remains constant) with an increasing input signal, thereby avoiding sign changes in the slope of the transfer curve. DNL is specified after the static gain error has been removed. It is defined as follows:

DNL = | [(V

_{D+1}– V_{D})/V_{LSB-IDEAL}– 1] | , where 0 < D < 2^{N }– 2.

V_{D} is the physical value corresponding to the digital output code D, N is the ADC resolution, and V_{LSB-IDEAL} is the ideal spacing for two adjacent digital codes. By adding noise and spurious components beyond the effects of quantization, higher values of DNL usually limit the ADC’s performance in terms of signal-to-noise ratio (SNR) and spurious-free dynamic range (SFDR).

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** Integral nonlinearity (INL) :**

INL error is described as the deviation, in LSB or percent of full-scale range (FSR), of an actual transfer function from a straight line. The INL-error magnitude then depends directly on the position chosen for this straight line. At least two definitions are common: “best straight-line INL” and “end-point INL” (see Figure 1b):

**Best straight-line INL**provides information about offset (intercept) and gain (slope) error, plus the position of the transfer function (discussed below). It determines, in the form of a straight line, the closest approximation to the ADC’s actual transfer function. The exact position of the line is not clearly defined, but this approach yields the best repeatability, and it serves as a true representation of linearity.**End-point INL**passes the straight line through end points of the converter’s transfer function, thereby defining a precise position for the line. Thus, the straight line for an N-bit ADC is defined by its zero (all zeros) and its full-scale (all ones) outputs.

The best straight-line approach is generally preferred, because it produces better results. The INL specification is measured after both static offset and gain errors have been nullified, and can be described as follows:

INL = | [(V

_{D}– V_{ZERO})/V_{LSB-IDEAL}] – D | , where 0 < D < 2^{N}-1.

V_{D} is the analog value represented by the digital output code D, N is the ADC’s resolution, V_{ZERO} is the minimum analog input corresponding to an all-zero output code, and V_{LSB-IDEAL} is the ideal spacing for two adjacent output codes.

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*Figure 4b. This plot shows typical differential nonlinearity for the MAX108, captured with the analog integrating servo loop.*

*Figure 4a. This plot shows typical integral nonlinearity for the MAX108 ADC, captured with the analog integrating servo loop.*