Robust Calibration of an Improved Delta-Sigma Data Converter Using Convex Optimization

TY - JOUR

T1 - Robust Calibration of an Improved Delta-Sigma Data Converter Using Convex Optimization

AU - Yang, Fuwen

AU - Gani, Mahbub

PY - 2007/12

Y1 - 2007/12

N2 - In this paper, we analyze that analog circuit imperfections in the cascaded Delta-Sigma modulators may lead to the incomplete noise cancellation from the earlier stages, as well as non-unit transfer function from the input signal to the output, resulting in the degradation of signal-to-noise ratio (SNR) performance. It is difficult to design one digital filter to compensate the effects from both the incomplete noise cancellation and non-unit transfer function. We therefore proposed a novel architecture of cascaded Delta-Sigma modulators which consist of feedforward and feedback loops. Under this structure, the transfer function from the input signal to the output is always unit even though there exist analog circuit imperfections. The rest of the design therefore, is only to consider to reduce the effect of the incomplete noise cancellation as small as possible, which is formed as a robust H-2 optimization problem. This problem can be recast as a convex optimization problem by the change of variables, congruence transformations and Schur complement, which is easily solved by reliable and efficient numerical algorithms. To prove the advantages of the architecture and the design method, we conduct numerical simulations on 2-2 cascaded Delta-Sigma modulators. Simulation results for a range of parameter excursions show that our proposed filter improves SNR performance over the nominal filter greatly.

AB - In this paper, we analyze that analog circuit imperfections in the cascaded Delta-Sigma modulators may lead to the incomplete noise cancellation from the earlier stages, as well as non-unit transfer function from the input signal to the output, resulting in the degradation of signal-to-noise ratio (SNR) performance. It is difficult to design one digital filter to compensate the effects from both the incomplete noise cancellation and non-unit transfer function. We therefore proposed a novel architecture of cascaded Delta-Sigma modulators which consist of feedforward and feedback loops. Under this structure, the transfer function from the input signal to the output is always unit even though there exist analog circuit imperfections. The rest of the design therefore, is only to consider to reduce the effect of the incomplete noise cancellation as small as possible, which is formed as a robust H-2 optimization problem. This problem can be recast as a convex optimization problem by the change of variables, congruence transformations and Schur complement, which is easily solved by reliable and efficient numerical algorithms. To prove the advantages of the architecture and the design method, we conduct numerical simulations on 2-2 cascaded Delta-Sigma modulators. Simulation results for a range of parameter excursions show that our proposed filter improves SNR performance over the nominal filter greatly.

U2 - 10.1109/JSTSP.2007.910280

DO - 10.1109/JSTSP.2007.910280

M3 - Article

SN - 1941-0484

VL - 1

SP - 678

EP - 685

JO - Ieee Journal Of Selected Topics In Signal Processing

JF - Ieee Journal Of Selected Topics In Signal Processing

IS - 4

ER -