On the design of high-performance wide-band continuous-time sigma-delta converters using numerical optimization

Abstract

Continuous-time (CT) sigma-delta (61) modulators are growing increasingly popular in wide-band analog-digital conversion. High orders of quantization noise shaping, and multibit quantizers, are used to compensate for the low oversampling ratios in wide-band applications. These, however, add circuit complexities and excess loop delay that are detrimental to the 61 control loop. This paper presents an exact mathematical analysis technique, based on the CT-discrete time equivalence, that can take these effects into account. A design-by-optimization approach based on that analysis is used to compensate for these effects, avoid intractability issues and to gain flexibility in the design. It is also shown that it is advantageous not to fix the position of the quantization noise-shaping zeros in the signal band.Index Terms-Continuous-time (CT) sigma-delta (61), CT-discrete-time (DT) equivalence, design by optimization, impulse invariance.

A novel optimization method for CT sigma-delta-modulators using a switched system model

“…The desired DT noise transfer function NTF(z) is obtained by means of the Schreier-Toolbox [10] in MATLAB: The corresponding open loop noise transfer function H noise (z) of the NTF is transformed to its CT equivalent H noise (s) using the method proposed in [11]:…”

Hardware-Accelerated Simulation Environment for CT Sigma–Delta Modulators Using an FPGA

“…The time-discrete representation of a CT integrator stage is attained by a ZOH CT-to-DT transformation given by (2) and (3). Additionally, the model has to be extended by two inputs for error correction according to (4) and (5). A digital representation is achieved by choosing appropriate signal bit widths for all signals and replacing the DT integration by a register in a feedback loop.…”

“…Afterward, the NTF is mapped by a DT-to-CT transformation onto a CT filter, where modifications are done by expert knowledge and simulations in the CT domain in order to meet the overall specification. During this transformation step, it is also possible to add nonideal behavior to the CT modulator model (e.g., [5]). The major disadvantage of designing a CT ΣΔ modulator in the DT domain is that not all DT modulator filters can be realized in the CT domain.…”

Accurate Time-Domain Simulation of Continuous-Time Sigma–Delta Modulators

“…When the delay is nonzero, (1) has no solution because a degree of freedom is missing, making it impossible to map the transfer function. An optimization method, such as in [16], can be used to optimize the coefficients of the CT filters in order to maintain the stability and performance of the loop. As explained in [17], in order to ensure the equivalence, a feedback term can also be added between the DAC output and the ADC input.…”