3 SUCCESSIVE APPROXIMATIONS

The successive approximations algorithm allows to find quickly a digital value by dichotomic search. By performing a sequence of comparisons, it converges to the desired value. The algorithm is presented here as a means for calibrating circuits. However, it has other well-known applications, in analog-to-digital converters for example ^[7].

Let's consider that the DAC of figure 17 is an ideal binary-radix digital-to-analog converter with n bits of resolution. It has a digital input bus D, consisting in n digital inputs (d ₁, , d _n), where d ₁ corresponds to the least significant bit (LSB) and d _n to the most significant bit (MSB). The analog output value A of the DAC for each bit is b ₁, , b _n. They are binary weighted and perfectly linear, and b ₁ = 1 arbitrarily. Consequently:

The output of the DAC for a digital input word D is:

with d _i = 0 if bit i is cleared, and d _i = 1 if bit i is set.

The input/output characteristics of such an ideal DAC with 4 bits (n = 4) is shown in figure 18. The grey line is the identity function y = x.

Figure 18: Ideal 4-bits DAC input/output characteristics