Gradient error cancellation and quadratic error reduction in unary and binary D/A converters

A novel geometrical arrangement of unit cells in a digital-analog converter (D/A) converter, along with a new switching sequence results in full cancellation of gradient errors. This is achieved without using quad, quad-quad, or triple-quad techniques which increase the number of units by a factor of 4 or 16. In an M-b D/A, by proper arrangement of (2^M-1) units in a matrix having odd number of rows and odd number of columns, a central unit is established allowing complete cancellation of gradient errors. The decoding logic has the same simplicity of a standard row-column decoder with the advantage of being half in size. This technique, called "symmetric-pair switching," avoids large routing between multiple subunits in quad, quad-quad and triple-quad techniques thus improving D/A performance. Another independent technique, "balanced-ring switching," is introduced for reduction of quadratic errors. This technique achieves an order of magnitude reduction in quadratic errors compared to the "Q² Random Walk" technique.