Digital radix converters for high accuracy data conversion

Abstract

A sub-binary radix Digital to Analog converter(DAC) which achieves high effective resolution is demonstrated. The converter does not have any built-in-self calibration mechanisms, but achieves high resolution and accuracy through the sub-binary radix representation. An intentional sub- binary radix creates a redundant number system with radix less than two but with normal binary coefficients. The sub-binary radix scheme is used to design a DAC with twelve bits of effective resolution in small VLSI area in a 2,um CMOS technology. To achieve these advantages generally requires a few extra control bits, and the DAC output is a non-linear and non-monotonic function of the normal binary radix interpretation of the control bits. A simple iterative algorithm to control the DAC is derived which only requires a high/low output test. Numerical Analysis on the conversion algorithm is performed and the boundary conditions for the radix values, to achieve high accuracy, are derived. Two's complement number representation is used for all arithmetic operations, performed using parallel carry lookahead adders.