This paper discusses switching schemes for gradient error compensation in unary (thermometer-decoded) arrays of digital-to-analog converters (DAC's). The absolute lower bound of integral nonlinearity (INL) by optimizing switching sequences is established and optimal switching sequences that meet the lower bound of INL are presented for linear error compensation in one-dimensional arrays. A rapidly converging algorithm is developed to obtain INL bounded switching sequences for any given type of gradient error compensation. Simulation results show that the new switching sequences substantially reduce the nonlinearity of DAC's due to gradient errors.
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