List of Figures. List of Tables. List of Abbreviations and Symbols. Preface. Acknowledgments. 1. DeltaSigmaMu Concepts. 2. Designing CT Modulators. 3. DeltaSigmaMu Implementation Issues. 4. Excess Loop Delay. 5. Jitter and Metastability. 6. DeltaSigmaMu Design Procedure. 7. A 4GHZ 4TH-Order BP DeltaSigmaMu. 8. Conclusions.

Continuous-time delta-sigma modulators for high-speed A/D conversion: theory, practice and fundamental performance limits

This paper presents an analytical algorithm for optimizing the dynamic range of continuous-time active filters under a fixed power dissipation constraint. Assuming weak third-order nonlinearities, we model distortion as a small signal disturbance of the linear solution and use linear techniques in the distortion analysis. Due to the generality of the formulation many important distortion phenomena can be described, e.g., the compression of the desired in-band signal due to large out-of-band interferers, intermodulation distortion, etc. Simple, closed-form expressions are derived for the noise and the distortion of the filter as functions of power dissipation. These expressions are used to optimize the noise, distortion and dynamic range, of the filter. The validity of the proposed algorithm is verified with simulation.

Dynamic range optimization of weakly nonlinear, fully balanced, Gm-C filters with power dissipation constraints

The Volterra series is commonly used for the modeling of nonlinear dynamical systems. In general, however, a large number of terms are needed to represent Volterra kernels, with the number of required terms increasing exponentially with the order of the kernel. Therefore, reduced-order kernel representations are needed in order to employ the Volterra series in engineering practice. This paper presents an approach whereby multiwavelets are used to obtain low-order estimates of first-, second-, and third-order Volterra kernels. A family of multiwavelets is constructed from the classical finite element basis functions using the technique of intertwining. The resulting multiwavelets are piecewise-polynomial, orthonormal, compactly-supported, and can be constructed with arbitrary approximation order. Furthermore, these multiwavelets are easily adapted to the domains of support of the Volterra kernels. In contrast, most wavelet families do not possess this characteristic. Higher-dimensional multiwavelets can easily be constructed by taking tensor products of the original one-dimensional functions. Therefore, it is straightforward to extend this approach to the representation of higher-order Volterra kernels. This kernel identification algorithm is demonstrated on a prototypical oscillator with a quadratic stiffness nonlinearity. For this system, it is shown that accurate kernel estimates can be obtained in terms of a relatively small number of wavelet coefficients. These results indicate the potential of the multiwavelet-based algorithm for obtaining reduced-order models for a large class of weakly nonlinear systems.

Multiwavelet Constructions and Volterra Kernel Identification

State space harmonic distortion modeling and estimation are introduced for G/sub m/-C filters with fully balanced, weakly nonlinear tranconductors. The proposed method provides compact closed-form answers expressed explicitly in terms of the values of the circuit elements. It can be easily implemented in MATLAB and applied to G/sub m/-C filters of any order. The filter is viewed as a composition of three operators in signal space representing the input stage, the filter core, and the output stage. Each operator is then decomposed into the superposition of a linear operator and a nonlinear operator. The total distortion at the output is shown to be approximately the sum of the distortion introduced by the nonlinear operator of each stage. The theoretical results are found to be in good agreement with Cadence simulations for the cases of a lossy integrator and a third-order Butterworth low-pass filter.

State-space harmonic distortion modeling in weakly nonlinear, fully balanced G/sub m/-C filters-a modular approach resulting in closed-form solutions

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Theory, practice, and fundamental performance limits of high-speed data conversion using continuous-time delta-sigma modulators.

In this paper we consider the nonlinear mixing products that arise and cause distortion in weakly nonlinear bandpass filters that might be used in a radio receiver. Volterra series analysis is applied to a G/sub m/-C filter with weak cubic nonlinearities in the transconductance amplifiers so that explicit formulae for the amplitudes of the mixing products can be derived and an architecture for the reduction of distortion proposed, The analysis is used to aid in the characterization of distortion in practice, both in SPICE simulation and laboratory work.

J.A. Cherry

Papers

On the characterization and reduction of distortion in bandpass filters