Lower bounds on the performance of Analog to Digital Converters

This paper deals with the task of finding certified lower bounds for the performance of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. We define the performance of an ADC as the worst-case average intensity of the filtered input matching error. The input matching error is the difference between the input and output of the ADC. This error signal is filtered using a shaping filter, the passband of which determines the frequency region of interest for minimizing the error. The problem of finding a lower bound for the performance of an ADC is formulated as a dynamic game problem in which the input signal to the ADC plays against the output of the ADC. Furthermore, the performance measure must be optimized in the presence of quantized disturbances (output of the ADC) that can exceed the control variable (input of the ADC) in magnitude. We characterize the optimal solution in terms of a Bellman-type inequality. A numerical approach is presented to compute the value function in parallel with the feedback law for generating the worst case input signal. The specific structure of the problem is used to prove certain properties of the value function that allow for iterative computation of a certified solution to the Bellman inequality. The solution provides a certified lower bound on the performance of any ADC with respect to the selected performance criteria.United States. Army Research Office. Efficient Linearized All-Silicon Transmitter IC

Optimality and performance limitations of analog to digital converters

The paper deals with the task of optimal design of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. Its performance is defined as the worst-case average intensity of the filtered input matching error. The design task can be viewed as that of optimal quantized decision making with the objective of optimizing the performance measure. An algorithm based on principles of optimal control is presented for designing general m-dimensional ADCs. The design process involves numerical computation of the candidate value function of the underlying dynamic program, which is computed iteratively, in parallel with the quantization law. A procedure is presented for certifying the numerical solution and providing an upper bound for performance of the designed ADC. Furthermore, an exact analytical solution to the optimal one-dimensional ADC is presented. It is shown that the designed one-dimensional optimal ADC is identical to the classical Delta-Sigma Modulator (DSM) with uniform quantization spacing.National Science Foundation (U.S.). (Grant number 0835947)Los Alamos National Laboratory. Information Science and Technology Institut