  Digital correlated double sampling (DCDS), a readout technique for
charge-coupled devices (CCD), is gaining popularity in astronomical
applications. By using an oversampling ADC and a digital filter, a DCDS system
can achieve a better performance than traditional analogue readout techniques
at the expense of a more complex system analysis. Several attempts to analyse
and optimize a DCDS system have been reported, but most of the work presented
in the literature has been experimental. Some approximate analytical tools have
been presented for independent parameters of the system, but the overall
performance and trade-offs have not been yet modelled. Furthermore, there is
disagreement among experimental results that cannot be explained by the
analytical tools available. In this work, a theoretical analysis of a generic
DCDS readout system is presented, including key aspects such as the signal
conditioning stage, the ADC resolution, the sampling frequency and the digital
filter implementation. By using a time-domain noise model, the effect of the
digital filter is properly modelled as a discrete-time process, thus avoiding
the imprecision of continuous-time approximations that have been used so far.
As a result, an accurate, closed-form expression for the signal-to-noise ratio
at the output of the readout system is reached. This expression can be easily
optimized in order to meet a set of specifications for a given CCD, thus
providing a systematic design methodology for an optimal readout system.
Simulated results are presented to validate the theory, obtained with both
time- and frequency-domain noise generation models for completeness.
