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=Parameters of D/A converters=

These short articles are written for the purpose of summarizing knowledge gained during work on different projects.


This article is a brief overview of DAC parameters. The first picture is a simple illustration of how Digital to Analog converter works.

The analog output as we can see is in direct relation to VREF and digital input code.
The next picture illustrates the following DAC parameters: LSB, Gain, FSR, Offset and Gain Errors.
3-bit DAC is used for this example with the maximum output voltage of 0.7v

Resolution - normally given in bits.
Resolution indicates the smallest increment of its output corresponding to a 1 LSB input code change. For example for 10 bit DAC, 2^10 = 1024 codes, so the resolution is 1/1024 of the output range.

Full scale range (FSR) - maximum output signal for the DAC, specified as current or voltage (ma or V).
Can be negative ,positive or both.

Offset error   - difference between the ideal and actual DAC output when zero digital code applied to the input.

Gain error  -  the difference between the ideal and actual output when full scale digital code applied to the input.
Strongly depends on VREF stability. The next two important parameters, DNL and INL, are usually measured whith the input code representing a ramp applied to the input of a DAC.
Now it is a good time to discuss the reference line for our measurements, because it usually causes confusions and misunderstanding. The drawing below compares the ideal line, best fit line and end-point line which is used most frequently.

Differential Nonlinearity - describes the uniformity of the LSB sizes between DAC codes. DNL represents the error in each step size, expressed in fractions of LSB.
We already know that LSB corresponds to the analog output change between the two adjacent codes applied to the DAC input. We also need to know the average LSB size to compare against for DNL measurements.
We calculate the average LSB size from our gain and offset measurements:
  LSB = FSR/N-1
 where N is maximum bit number.
Differential Nonlinearity represents the error from the average LSB for each step (the worst case is reported).

Integral Nonlinearity - shows how the output differs from the straight line, weather it is an ideal line or best-fit or end-point. As you can see, Offset and Gain are absolute measurements while DNL and INL are referenced to the zero and FSR outputs of the DAC.

Once again we repeat, that to generate the ramp we applied continuously increasing code from 000 to 111 to the DAC input. The output should represent a rising staircase with equal steps. If staircase is smoothed, a perfectly straight line should result.
The INL defines the overall straightness of this line, whereas the DNL describes differences in amplitude between adjacent steps in the staircase waveform.

Which of these two parameters is more important depends on the application.
 In the imaging application, it may be necessary to distinguish between slightly different color densities in adjacent areas of an image. Here DNL is more important .
But in an application in which a widely varying parameter like speed must be continuously monitored INL is usually more important.

DNL must be less than 1lsb to garantee DAC's monotonic behavior .
A Monotonic DAC  has an output that changes in the same direction (or remains constant) for each increase of the input code. The quality of monotonicy is important if DAC is used in feedback loop.
When a non-monotonic device is used in a feedback loop, the loop can get stuck and DAC will toggle forever between 2 input codes.

The next group of parameters are the dynamic parameters. They measure DAC performance with a sine wave signal (in digital form) is applied to the input.

SNR - signal to noise ratio. Fundamental and harmonic components of the sine wave are filtered out. Any remaining signal at the output of the DAC is considered as a noise.
SNR is a ratio of the full scale sine wave output to the noise level.
Some companies specify SINAD parameter. SINAD - is a signal to noise and distortion ratio. It is similar to SNR, but the harmonic signal components are not removed.
Specified in dB.

THD - total harmonic distortion - measured with digital code representing sinewave, applied to the DAC input continuously.
The output is analyzed in the frequency domain to find harmonic components related to the fundamental output signal.
Specified in dB.

SFDR - spurious free dynamic range - the difference between the rms power of the fundamental and the largest spurious signal in the given bandwidth.
IM - intermodulation distortion - non harmonic product terms that appear in the output signal due to nonlinearity of the DAC. Measured with two sine wave signals applied to the input.
The output is tested on harmonic components, appearing due to modulation affect on non linear characteristics within DAC.
   The harmonic components are (F1+F2), (F1-F2) , (2F1+/-F2), (F1+/-2F2) etc


Max conversion rate - it is the maximum input signal frequency the DAC can handle. The worst case is when input signal changes from zero to max, and the output should reach the max level and settle.

Settling time - the time required for the output to reach the final value and remain within +/-1 LSB after overshoot.

PSRR  - power supply rejection ratio. The output signal should remain within limits while power supply voltage changes from Min to Max.


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