# inldnl

Integral nonlinearity (INL) and differential nonlinearity (DNL) of data converters

## Syntax

``s = inldnl(analog,digital,range,type)``
``s = inldnl(___,Name,Value)``

## Description

example

````s = inldnl(analog,digital,range,type)` calculates the integral nonlinearity (INL) and differential nonlinearity (DNL) errors of ADCs and DACs. The function calculates INL and DNL using the analog and digital input output data and the nominal analog dynamic range of the converter. The function can calculate INL and DNL either using the endpoint method, or the best fit method, or using both methods.The `inldnl` function only analyzes converters with a finite number of bits. That means ADCs must have saturation and quantization. The function ignores any digital value pairs that contain NaN values.```
````s = inldnl(___,Name,Value)` calculates the INL and DNL errors of ADCs and DACs using one or more name-value pair arguments in addition to the input arguments in the previous syntax. Enclose each argument name in quotes. Unspecified arguments take default values. NoteInitial conditions and other anomalous data can cause this function to behave erratically. This function can analyze nonmonotonic converters, but it cannot handle multiple distinct occurrences of the same code in one transfer function. ```

## Examples

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Load the digital input and the analog output of a DAC from MAT-files.

```load 'digital.mat' load 'analog.mat'```

The nominal analog dynamic range of the DAC is `[-1,1]`. Turn on plotting for the output converter threshold. Calculate INL and DNL using both best fit and endpoint methods.

`inldnl(a,d,[-1 1],'DAC','GenPlotData','on','INLMethod','All','DNLMethod','All')`

```ans = struct with fields: Type: 'DAC' NBits: 5 LSB: 0.0625 MissingCodes: [0x1 double] Codes: [-16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 ... ] IdealCodeCenters: [-1 -0.9375 -0.8750 -0.8125 -0.7500 -0.6875 ... ] CodeCenters: [-0.9465 -0.8780 -0.8048 -0.7310 -0.6557 -0.5862 ... ] CodeCenterStD: [0.0282 0.0292 0.0296 0.0287 0.0254 0.0237 0.0207 ... ] EndpointINL: [1.7764e-15 0.0465 0.1679 0.2985 0.4547 0.5169 ... ] BestFitINL: [-0.5244 -0.4713 -0.3432 -0.2060 -0.0432 0.0257 ... ] EndpointDNL: [0.0465 0.1215 0.1305 0.1562 0.0623 0.0654 0.0331 ... ] BestFitDNL: [0.0531 0.1281 0.1371 0.1628 0.0689 0.0720 0.0397 ... ] BestFitPoly: [0.0652 0.1293] OffsetError: 0.8562 GainError: 1.5393 GainErrorUnit: 'LSB' TCNominal: [32x2 double] TCMeasured: [32x2 double] ```

## Input Arguments

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• If the DUT is a DAC, analog output from the DAC, specified as a vector.

Data Types: `double`

• If the device under test (DUT) is an ADC, digital output from the ADC, specified as a vector of integers.

• If the DUT is a DAC, digital input to the DAC, specified as a vector with integer values.

Data Types: `fi` | `single` | `double` | `int8` | `int16` | `int32` | `uint8` | `uint16` | `uint32`

Nominal analog dynamic range of the ADC or DAC, specified as a 2-element vector.

Data Types: `double`

Type of the device under test, specified as `Auto`, `ADC`, or `DAC`. The `type` determines whether to analyze the data as an ADC or DAC.

If The `type` is set to `Auto` and if the transfer function is discrete, the `inldnl` function analyzes the data as a DAC. The transfer function is considered as discrete if the analog data is less than half of the digital code width for each digital code.

If The `type` is set to `Auto` and if the transfer function is continuous, the `inldnl` function analyzes the data as an ADC.

Data Types: `string`

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Example: ```inldnl(a,d,[-1 1],'DAC', 'INLMethod', 'All', 'DNLMethod','All')``` calculates the INL and DNL of a DAC using both endpoint and best fit method.

Unit of reported offset error, specified as LSB (least significant bit), %FS (percentage full scale), FS (full scale), or all.

Data Types: `string`

Unit of reported gain error, specified as LSB (least significant bit), %FS (percentage full scale), FS (full scale), or all.

Data Types: `string`

Send the output data vectors of the `inldnl` function to the output data structure `s`, specified as `off` or `on`. If `GenPlotData` is set to `on`, the output data structure contains the output data vectors. The output data vectors can then be picked up by the DAC DC measurement, DAC Testbench, ADC DC Measurement, or ADC Testbench blocks to plot the DC analysis results.

Data Types: `string`

Method to calculate INL, specified as `Endpoint`, `BestFit`, or all.

• If `INLMethod` is set to `Enpoint`, the `inldnl` function compares each threshold's position to the threshold position of an ideal converter, as determined by a line from the first code transition to the last code transition.

• If `INLMethod` is set to `BestFit`, the `inldnl` function first takes the best linear fit of the ADC or DAC transfer curve. Then the function proceeds to calculate the INL using the same steps as the `Enpoint` method.

Data Types: `string`

Method to calculate DNL, specified as `Endpoint`, `BestFit`, or all.

• If `DNLMethod` is set to `Enpoint`, the `inldnl` function compares each threshold's position to the threshold position of an ideal converter, as determined by a line from the first code transition to the last code transition to find the INL. The DNL is calculated from the difference between the elements of the INL vector.

• If `DNLMethod` is set to `BestFit`, the `inldnl` function first takes the best linear fit of the ADC or DAC transfer curve. Then the function proceeds to calculate the DNL using the same steps as the `Enpoint` method.

Data Types: `string`

Return absolute error and full scale DNL for testing, specified as `on` or `off`. Absolute error is the total uncompensated error including offset error, gain error, and nonlinearities. In simulation, to specifically test that the measurements match the impairments, absolute error can be used instead of INL. This is because absolute error describes the entire transfer curve in a single vector.

Data Types: `string`

## Output Arguments

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Output information of the `inldnl` function, returned as a structure. The output contains information about the device under test in these fields:

NameValuesDescriptionData Types
Type`ADC` or `DAC`Type of the device under test (DUT)string
Nbitspositive real integerResolution of the ADC or DAC DUTdouble
LSBpositive real scalarLeast significant bit value of the DUT. LSB is the smallest level the ADC can convert or the smallest increment of the DAC output.double
MissingCodesvectorMissing codes in DUT.double
Codescolumn vectorDigital codedouble
IdealCodeCenterscolumn vectorIdeal code center of the digital codedouble
CodeCenterscolumn vectorCalculated code center of the digital codedouble
CodeCenterStDcolumn vectorStandard deviation of the code center from the ideal valuedouble
EndpointINLcolumn vectorINL using `Endpoint` methoddouble
BestFitINLcolumn vectorINL using `BestFit` methoddouble
EndPointDNLcolumn vectorDNL using `Endpoint` methoddouble
BestFitDNLcolumn vectorDNL using `BestFit` methoddouble
BestFitPolyvectorPolynomial describing the best fit using standard curve-fitting technique.double
OffsetErrorreal scalarOffset error of DUTdouble
GainErrorreal scalarGain error of DUTdouble
OffsetErrorUnit`LSB`, `%FS`, or `FS`Unit of reported offset errorstring
GainErrorUnit`LSB`, `%FS`, or `FS`Unit of reported gain errorstring
TCNominalvectorNominal transfer curve of the DUTdouble
TCMeasuredvectorMeasured transfer curve of the DUTdouble

If you do not assign an output variable, the `inldnl` function also plots the transfer function of the device under test in the active figure.

Data Types: `struct`

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### Offset Error

Offset error represents the offset of the data converter transfer function curve from it ideal value at a single point. For more information, see Measuring Offset and Gain Errors in ADC.

### Gain Error

Gain error represents the deviation of the slope of the data converter transfer function curve from its ideal value. For more information, see Measuring Offset and Gain Errors in ADC.

### INL Error

Integral nonlinearity (INL) error, also termed as relative accuracy, is the maximum deviation of the measured transfer function from a straight line. The straight line can either be a best fit using standard curve-fitting technique, or be drawn between the endpoints of the actual transfer function after gain adjustment.

The best fit method gives a better prediction of distortion in AC applications, and a lower value of linearity error. The endpoint method is mostly used in the measurement applications of data converters, since the error budget depends on actual deviation from the ideal transfer function.

### DNL Error

Differential nonlinearity (DNL) is the deviation from the ideal difference (1 LSB) between analog input levels that trigger any two successive digital output levels. The DNL error is the maximum value of DNL found at any transition.

## Version History

Introduced in R2020a