Optimal resistor ratio in the DAC with low precision resistors $statistical approach

The widely used digital-analog converter is the one with 2R/R ladder circuit. It can be easy realized as an integrated circuit, but accurate input-output characteristic require extremely precise resistors. With the laser trimming technology it is possible to improve converter accuracy, but aging and environmental factors decrease linearity and overall accuracy of a converter, thus reducing the usable life and the converter applicability. We propose a new DAC design based on 2R/sup +//R ladder circuit, where a high precision is obtained due to better coverage of analog range at the transfer characteristic (even for low precision resistors, ex. 1%, 2% and 5% resistor tolerance). Statistical method shows that various allowed tolerances of the circuit resistors are associated with various optimal resistor ratios in an 2R/sup +//R circuit.