First- and Second-Order Gradient Compensation with Only Eight Parts per Element in Unary DACs

Non-idealities in technology process lead to variations of element values in digital-to-analog converters (DACs). As a consequence, ratio of elements changes and contributes to the nonlinearity of the DAC transfer curve, affecting both the integral (INL) and differential (DNL) nonlinearity. These variations have a random component and a systematic component. The systematic component is usually described as a combination of a linear and a quadratic component, with the latter generally having a rotation term. Special placement techniques ("switching schemes") exist that allow for lowering the nonlinearity induced by the systematic error. If an element has only one part in the unary DAC array, only the INL can be decreased. With many parts per element, also the reduction of the DNL becomes possible. The linear component is easily compensated if the common-centroid property is fulfilled, that is with two parts per element. Techniques compensating the quadratic component normally demand 2
^N
parts for an element in an N-bit array, and to compensate the rotation term, the whole array should be additionally mirrored. In this paper, we show that 8 parts per element are just enough for gradient compensation for any resolution N>2. With this option, realization of such DAC arrays (in order to decrease the DNL) becomes more practical.