Mathematical model of multi-channel analog-digital converter with optimum code selection procedure

Multichannel converters are usually built based on the traditional multiplexer-analog digital converter (ADC) scheme, and the increase in speed is ensured by the improvement of the element base, the use of improved circuit design solutions. Based on the application of the principle of logical deployment, a structure of a multichannel analog-to-digital converter is proposed, a distinctive feature of which is the use of an optimal code selection procedure that takes into account the dynamic parameters of the digital-to-analog converter (DAC) and the probabilistic characteristics of the input signals. The process of functioning of a multi-channel ADC is represented as the execution of a certain set of strategies for searching for a set of codes corresponding to the input signals. Each strategy consists of a sequence of tests, characterized by execution time, and the probability of its positive or negative outcome. The execution time of each test depends on the number of the previous one. The probability of a particular outcome of the test depends on the distribution function of the input signals. The derivation of the formula for calculating the average execution time of search strategies is given. he method of solving the construction of optimal strategies based on the branch and bound method, with the calculation of  lower bounds by solving the problem of the least coverage, is indicated. The estimation of the increase in the ADC speed is given taking into account the probability characteristics of the input signal, taking into account the dynamic parameters of the DAC. It is shown that the application of the proposed transformation scheme allows to increase the conversion speed several times.