Question 10.2: Design the current sources for a sine-weighted nonlinear DAC...
Design the current sources for a sine-weighted nonlinear DAC with 8-bit phase and 8-bit amplitude resolution.
For 8-bit phase resolution, W = 8. The two MSBs are used to select the quadrants of the sinusoid, and the remaining W − 2 = 6 bits are used to control the DAC current cells, as shown in Figure 10.17. Thus, a = b = 3, and there is a total of 2^{3} × 2^{3} = 8 × 8 = 64 current cells. According to (10.60),
the sine-weighted current O_{k} in each current cell is given by
O_{k}=\begin{pmatrix} 2&4&6&6&6&5&3&0 \\ 0&3&5&6&6&6&4&2\\ 2&4&6&6&6&5&2&1 \\ 1&3&5&6&6&6&3&2\\ 3&4&6&3&6&5&3&2 \\ 1&3&5&6&7&5&4&1\\ 2&4&5&6&6&5&3&1 \\ 0&4&4&6&7&5&5&1 \end{pmatrix} (10.63)
Note that the above weighted current represents the number of unit current sources in each current cell. In the layout, all of the current cells should have the same height. The sum of each row represents the total number of unit current cells in the row. Thus, the sum of each row in (10.63) is designed to be the same in order to achieve the same layout height and length for each row.
The layout compactness of the current sources is important since it reduces the integral nonlinearity of the nonlinear DAC due to symmetry and minimizes gradient errors. To compensate for symmetry and gradient errors caused by variations in the temperature and process mismatch, a special switching scheme based on double centroid and random walking [22, 23] can be implemented. There are 64 × 2 sine weighted current sources to be placed as close as possible in layout to achieve the best possible matching. The current matrix includes 256 × 2 unit current sources, and each provides the minimum current required to achieve the specified speed.
