ADC and DAC Conversion Errors

S.Sai Kishore Kumar154567

ContentsADCTypes of errors in ADCDACTypes of errors in DAC

ADC

What is an ADC?

An analog-to-digital converter is a device that converts a continuous physical quantity (usually voltage) to a digital number that represents the quantity's amplitude.

The conversion involves quantization of the input, so it necessarily introduces a small amount of error.

 Instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input.

The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal.

What is Quantization?

Quantization is the process of converting a continuous range of values into a

finite range of discreet values.

Errors in ADC

Offset errorGain errorNon-linearity error

Differential

Integral

Offset Error

This is defined as the deviation between the first actual transition and the first ideal transition.

The first transition is when the digital output of ADC changes from 0 to 1.

Total system offset error includes offset error from preamplifiers or signal transducers.

Offset error can be removed by measuring a reference point and subtracting that value from future samples.

Gain Error

Defines as the difference of the slope of the actual output values and the ideal output values.

If the transfer function of the actual ADC occurs above the ideal straight line, then it produces positive gain error and vice versa

Gain error is usually expressed in LSB or as a percent of full-scale range.

Gain error is the full-scale error minus the offset error.

Full Scale Error

Full scale error is the deviation of the last transitions of the actual ADC from the last transition of the perfect ADC, measured in LSB or volts.

Full scale error is due to both gain and offset errors.

Non-Linearity

When offset and gain errors are compensated for, the actual transfer function will not be equal to the transfer function of perfect ADC.

There may be the non-linearity in the ADC which may cause the actual curve to deviate slightly from the perfect curve.

There are two major types of non-linearity that degrade the performance of ADC.

i) Differential Non-Linearity (DNL)

ii) Integral Non-Linearity (INL).

Differential Non-Linearity Differential non-linearity (DNL) is defined as the maximum and

minimum difference in the step width between actual transfer function and the perfect transfer function. DNL is defined as

Non-linearity produces quantization steps with varying widths, some narrower and some wider.

DNL is the most critical of the measures of an ADC’s performance for many control applications.

It represents the ADC’s ability to relate a small change in input voltage to the correct change in code conversion. DNL is defined as

Code DNL = CCW – ICW

DNL = Max (Code DNL)

Related to DNL are two critical figures of merit used in defining ADC operation.These are:i) Missing Codesii)Monotonicity

Missing codes

An ADC has missing codes if an infinitesimally small change in voltage causes a change in result of two codes, with the intermediate code never being set. A DNL of –1.0 LSB indicates the

ADC has missing codes (DNL measured by this definition cannot be less than –1.0 LSB).

Monotonicity

An ADC is monotonic if it continually increases conversion result with an increasing voltage (and vice versa).

A non-monotonic ADC may give a lower conversion result for a higher input voltage, which may also mean that the same conversion may result from two separate voltage ranges.

DNL of greater than 1.0 LSB may indicate non-monotonicity.

Integral Non-Linearity

Integral non-linearity (INL) is defined as the maximum vertical difference between the actual and the ideal curve.

It indicates the amount of deviation of the actual curve from the ideal transfer curve.

DAC

What is an DAC?

A digital-to-analog converter (DAC or D-to-A) is a device that converts a digital (usually binary) code to an analog signal (current, voltage, or electric charge).

Errors in DAC

Gain Error Offset Error Full Scale Error Non- Linearity Non-Monotonic Output Error

Gain Error

Slope deviation from ideal gain to the actual gain.

Low Gain Error: Step Amplitude is less than ideal

High Gain Error: Step Amplitude is higher than ideal

Offset Error

A constant voltage difference between the ideal DAC output and the actual.

Full Scale Error

Combination of gain error and offset error

Non-Linearity

The largest difference between the actual and theoretical output as a percentage of full-scale output voltage

Non-monotonic Output Error

A form of non-linearity due to errors in individual bits of the input

THANK YOU