DACs' offset and gain error interpretation

Hello Florin,

Thank you for posting the question to the forum from our previous exchange of messages. As I said, I think others may have similar questions so I prefer to answer it here.

Florin Ciortea47 said:

I saw that many datasheets indiacate the gain error as +/-x% and I am wondering if the actual value could go above FSR, in case the DAC is supplied from a higher voltage than FSR, or this means that as the slope is steeper than the ideal one it will touch the FSR value sooner and will saturate at that value for the next upcomming codes.

The exact source of gain error can vary from one DAC to the next as a function of the architecture of the device, but in all cases the gain error is a signal chain parameter as opposed to a power-domain parameter. For example, if we were to consider a simplified string DAC with buffer amplifier on the output stage as an example - a great majority of the gain error is a function of the ratiometric matching of the resistors in the feedback network. This directly contributes a gain error which is purely a function of the input from the DAC, and the output range of the DAC is directly a function of the reference input which in most cases has set the full-scale range (except for cases where some gain is offered - but still then the ideal range is defined by the reference input).

In terms of the absolute value of the DAC output, it is conceivable that the output could be greater than the full-scale range, assuming sufficient head-room in the supply. This would basically be positive gain error leading to some output value greater than the ideal full-scale range. Some similar artifact could be possible for a device which had no gain error, but a positive offset error due to the Vos of the output buffer as well.

To the other end of your comment for devices without extra headroom, yes it is possible that the output would begin to go non-linear early as a result of operating too close to the positive supply rail. This would have to be a case that violates the top-line characteristics of a datasheet, though.

Florin Ciortea47 said:

Also for the offset error I observed +/-1LSB and I am wondering if -1LSB means that if I apply 1 to the input I get 0 on the output (and also if I apply 0 to the input the output is still 0) and +1LSB means that if I apply 0 I get 1 on the output (following the same approach a -1 will generate a 0 to the output, in case of sw calibration)?

Offset error is applied to the linear region of the DAC output, so nothing near either positive or negative supply rails where things are non-linear. Typically offset is specified in voltage, usually millivolts or microvolts. It's fine to use an LSB-based example, though. If you had -1 LSB offset error measured in the linear region, essentially yes that means that codes are approximately 1 LSB lower than they should be. I say approximately because we'd also see some effects of INL and DNL in there - but the transfer function as a whole is -1 LSB "off". Generally speaking calibration only addresses offset and gain errors - so in a majority of situations your comment would be accurate and applicable for the purposes of calibration.

Thanks for your question and I hope this answers everything. If not, please feel free to post another follow-up question.

We're going to refresh our video learning material soon, we'll try to pull some of this information in there as well for future viewers. Thanks.