TABLE OF CONTENTS A high-precision DAC is not necessary to perform successive approximations. With only a slight modification, it is though possible to make the ladder sub-binary and to relax the design constraints.
Figure 39 presents a 4-stages R/xR ladder, which is a generalization of the R/2R ladder.
The resistor in the vertical branches has here a value xR, and the terminator x TR. The case with
corresponds to the R/2R ladder. On the opposite, choosing
makes the converter sub-binary. This special case is analyzed below. A theoretical study of the R/xR structure can be found in [36]. Here, a more circuit-oriented analysis is done.
In each stage of the network, the incoming current i i+1 is divided into 2 currents b i and i i:
with
and
More interesting is the ratio ? i between these two currents:
In fact, this ratio can be used to derive the condition which allows the ladder to be used for successive approximations. Let's make two small modifications in the ladder: Using the terminator current as a bit in the converter instead of dumping it, and numbering the bits by taking care to exchange the last two currents to have:
and
Figure 40 shows the resulting circuit.
In each stage of the ladder in figure 40, the remaining current i i is equal to the sum of the less significant bits:
