Computer-Aided Design of Switched-Capacitor Filters

This thesis describes a series of computer methods for the design of switched-capacitor filters. Current software is greatly restricted in the types of transfer function that can be designed and in the range of filter structures by which they can be implemented. To solve the former problem, several new filter approximation algorithms are derived from Newton's method, yielding the Remez algortithm as a special case (confirming its convergency properties). Amplitude responses with arbitrary passband shaping and stopband notch positions are computed. Points of a specified degree of tangency to attenuation boundaries (touch points) can be placed in the response, whereby a family of transfer functions between Butterworth and elliptic can be derived, offering a continuous trade-off in group delay and passive sensitivity properties. The approximation algorithms have also been applied to arbitrary group delay correction by all-pass functions. Touch points form a direct link to an iterative passive ladder design method, which bypasses the need for Hurwitz factorisation. The combination of iterative and classical synthesis methods is suggested as the best compromise between accuracy and speed. It is shown that passive ladder prototypes of a minimum-node form can be efficiently simulated by SC networks without additional op-amps. A special technique is introduced for canonic realisation of SC ladder networks from transfer functions with finite transmission at high frequency, solving instability and synthesis difficulties. SC ladder structures are further simplified by synthesising the zeros at +/-2fs which are introduced into the transfer function by bilinear transformation. They cause cancellation of feedthrough branches and yield simplified LDI-type SC filter structures, although based solely on the bilinear transform. Matrix methods are used to design the SC filter simulations. They are shown to be a very convenient and flexible vehicle for computer processing of the linear equations involved in analogue filter design. A wide variety of filter structures can be expressed in a unified form. Scaling and analysis can readily be performed on the system matrices with great efficiency. Finally, the techniques are assembled in a filter compiler for SC filters called PANDDA. The application of the above techniques to practical design problems is then examined. Exact correction of sinc(x), LDI termination error, pre-filter and local loop telephone line weightings are illustrated. An optimisation algorithm is described, which uses the arbitrary passband weighting to predistort the transfer function for response distortions. Compensation of finite amplifier gain-bandwidth and switch resistance effects in SC filters is demonstrated. Two commercial filter specifications which pose major difficulties for traditional design methods are chosen as examples to illustrate PANDDA's full capabilities. Significant reductions in order and total area are achieved. Finally, test results of several SC filters designed using PANDDA for a dual-channel speech-processing ASIC are presented. The speed with which high-quality, standard SC filters can be produced is thus proven

Digital filter structures from classical analogue networks

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The doubly terminated lossless digital two-pair in digital filtering

A digital lossless two-pair terminated at both ends with "passive" multipliers is studied. Conditions for low sensitivity of the transfer-function magnitude with respect to the digital multiplier coefficients are derived. It is shown that low sensitivity property can be achieved by forcing certain "matching" conditions, at the terminations. The application of these results to the understanding of some well-known digital filter structures is outlined. In particular, it is shown that the coupled-form biquad can be interpreted as a doubly terminated lossless digital two pair, and that it satisfies the "termination matching conditions" for almost all pole locations. All results derived in the paper are based on independentz-domain arguments

Model-Based Calibration of Filter Imperfections in the Random Demodulator for Compressive Sensing

The random demodulator is a recent compressive sensing architecture providing efficient sub-Nyquist sampling of sparse band-limited signals. The compressive sensing paradigm requires an accurate model of the analog front-end to enable correct signal reconstruction in the digital domain. In practice, hardware devices such as filters deviate from their desired design behavior due to component variations. Existing reconstruction algorithms are sensitive to such deviations, which fall into the more general category of measurement matrix perturbations. This paper proposes a model-based technique that aims to calibrate filter model mismatches to facilitate improved signal reconstruction quality. The mismatch is considered to be an additive error in the discretized impulse response. We identify the error by sampling a known calibrating signal, enabling least-squares estimation of the impulse response error. The error estimate and the known system model are used to calibrate the measurement matrix. Numerical analysis demonstrates the effectiveness of the calibration method even for highly deviating low-pass filter responses. The proposed method performance is also compared to a state of the art method based on discrete Fourier transform trigonometric interpolation.Comment: 10 pages, 8 figures, submitted to IEEE Transactions on Signal Processin

Theory and Methodology of Integrated Ladder Filter Design

This thesis presents a systematic study of integrated ladder filter design. A theoretical model of ladder structures is first established in terms of a family of symmetric matrix polynomial systems (SMPS's). It is shown that SMPS's are a natural mathematical abstraction of ladder circuits. The properties of stability, canonical (or minimal) realisation, low-sensitivity and low-noise, are proved for SMPS's under certain very simple conditions. A design methodology is then presented for active-RC, SC and digital ladders. The basic principle is that a SMPS can be decomposed by means of matrix factorisation into several linear systems, which can then be easily realised by active or digital circuits. It is shown that many existing methods, such as leapfrog or coupled biquads, result from some special decompositions. It is further shown that LU and UL factorisations drawn from numerical methods can be used to develop several novel structures (so-called LUD and ULD structures) which demonstrate significant improvments over existing ones regarding sensitivity, component area and dynamic range. This is confirmed by examples and statistical investigations. Besides the matrix methods applicable to standard lowpass and bandpass cases, further research is undertaken for bandstop, highpass and allpass filter designs. It is demonstrated that frequency transformations can be used to reduce the hardware cost in many classical filtering cases. A novel building block, the so called TWINTOR, is introduced in bandstop design to reduce the switching rate. Active-RC and SC allpass ladders are constructed and proved to have significant advantages over the existing biquad circuits. Matrix methods also provide an efficient vechicle for the development of a filter design software package called PANDDA. Its many outstanding features are described. Finally measured results from two fabricated LUD SC filters are presented. They confirm the high quality of the novel circuit structures developed by this research

Switched capacitor networks : a novel prewarping procedure

Bibliography: leaves 152-157.Novel methods for prewarping filter specifications prior to realization. in Switched Capacitor (SC) form are presented. These allow the design of arbitrary response requirements, exhibiting a low amount of error that normally results from the frequency warping associated with sampled-data networks. Adjustment is applied to the pole and zero locations of a reference filter, using three distinct approaches (Center frequency "CF", Selectivity "S" and Complex Mapping "CM" pole/zero prewarping), developed for both the Lossless Discrete Integrator (LOI) and Bilinear (Bil) analog to digital transformations. The derivation of the prewarping expressions is explained with reference to these mappings, and the effect they have on the apparent pole and zero locations of an SC filter realization

Switched-current filter structure for synthesizing arbitrary characteristics based on follow-the-leader feedback configuration

This document is the Accepted Manuscript version of the following article: Wenshan Zhao, Yigang He, and Yichuang Sun, ‘Switched-current filter structure for synthesizing arbitrary characteristics based on follow-the-leader feedback configuration’, Analog Integrated Circuits and Signal Processing, (2015), Vol. 82 (2): 479-486. The version of record is available online at doi: 10.1007/s10470-014-0477-8 © Springer Science+Business Media New York 2015Peer reviewedFinal Accepted Versio

Analogue filter networks: developments in theory, design and analyses

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