Stacked A/D converter principle

One way to increase the dynamics of a system is to use the companding method. The companding technique compresses the signal such that signal’s maximum amplitude does not exceed system’s limitations. At the output of the system the original signal is obtained by reverse operation of expanding.

Applied to a uniform quantizer, as shown in the following figure, this leads us to the model of a floating-point quantizer.

Historically, the stacked analog-to-digital converter was introduced to increase the effective dynamic range of radar system. The following figure shows the stacked ADC principle.

This is an extension of the previously described companding principle. The compression law is piecewise linear with M segments. The gain increase is {\Delta G}^{i-1} where i \in 1,\cdots,M.

The analog to digital part of the previous scheme is split in M channels each performing an N-bit conversion.

The expansion consists in selecting the best channel (in terms of quantification error) which is not saturated and applying the appropriate gain to this channel.

Example

Here is an illustrative example with: M=4 channels, N=4 bit, \Delta G=2

Note

The function c^{-1} is, in this case, multivalued: the active segment (channel) give the corresponding expansion factor.

The minimum quantization error is such that:

eq_{min} = \frac{eq_{unif}}{{\Delta G}^{M-1}}

where eq_{unif} is the quantization error of the uniform quantizer Q