# A z plane Lerner switched-capacitor filter

TL;DR: The design of a switched-capacitor filter that optimizes both amplitude and phase response simultaneously is described, conceptually derived from a Lerner function.

Abstract: The design of a switched-capacitor filter that optimizes both amplitude and phase response simultaneously is described. Conceptually derived from a Lerner function, the filter architecture is efficient and simple.

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TL;DR: In this article, a pole-sharing technique was used for implementing bandpass filter banks using the non-minimum-phase Lerner approximation without placing additional speed requirements on the operational amplifiers and without resorting to complicated clocking strategies; only a biphasic clock was used.

Abstract: A pole-sharing technique was used for implementing bandpass filter banks using the nonminimum-phase Lerner approximation without placing additional speed requirements on the operational amplifiers and without resorting to complicated clocking strategies; only a biphasic clock was used. Substantial hardware saving has been achieved. The filter synthesis is shown to be micropower-compatible and parasitic-insensitive; phase reversal was easily accommodated while retaining all desirable features. A uniformly and nonuniformly spaced filter bank for typical speech applications have been simulated with SWITCAP and three channels of the uniformly spaced filter bank have been constructed on a breadboard using discrete components. The results obtained agreed with design specifications, yielding a good approximation to linear phase in the passband and sharp attenuation in the stopband. Single-parameter and statistical multiparameter sensitivity analyses are presented. >

12 citations

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07 Jun 1988TL;DR: In this article, a switched-capacitor time-division-multiplexed pole sharing technique for implementing bandpass filter banks is proposed, which is parasitic-insensitive and compatible with micropower techniques.

Abstract: A switched-capacitor time-division-multiplexed pole sharing technique for implementing bandpass filter banks is proposed. Using this technique, the hardware reduction is achieved in three ways. First, the efficient non-minimum-phase Lerner filter approximation is used to minimize the number of poles required to satisfy a given filter specification in frequency and time domains. Second, the number of poles is reduced by pole sharing and third, hardware for implementation is simplified by time-division-multiplexing. In the case of the 8th-order-per-channel 16-channel bandpass filter bank example discussed, the total hardware reduction is substantially greater than 50% when compared to a conventional direct design using minimum-phase filter approximations. Furthermore, the proposed technique is parasitic-insensitive and compatible with micropower techniques. >

3 citations

##### References

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01 Jan 1975TL;DR: Feyman and Wing as discussed by the authors introduced the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.

Abstract: sprightly style and is interesting from cover to cover. The comments, critiques, and summaries that accompany the chapters are very helpful in crystalizing the ideas and answering questions that may arise, particularly to the self-learner. The transparency in the presentation of the material in the book equips the reader to proceed quickly to a wealth of problems included at the end of each chapter. These problems ranging from elementary to research-level are very valuable in that a solid working knowledge of the invariant imbedding techniques is acquired as well as good insight in attacking problems in various applied areas. Furthermore, a useful selection of references is given at the end of each chapter. This book may not appeal to those mathematicians who are interested primarily in the sophistication of mathematical theory, because the authors have deliberately avoided all pseudo-sophistication in attaining transparency of exposition. Precisely for the same reason the majority of the intended readers who are applications-oriented and are eager to use the techniques quickly in their own fields will welcome and appreciate the efforts put into writing this book. From a purely mathematical point of view, some of the invariant imbedding results may be considered to be generalizations of the classical theory of first-order partial differential equations, and a part of the analysis of invariant imbedding is still at a somewhat heuristic stage despite successes in many computational applications. However, those who are concerned with mathematical rigor will find opportunities to explore the foundations of the invariant imbedding method. In conclusion, let me quote the following: "What is the best method to obtain the solution to a problem'? The answer is, any way that works." (Richard P. Feyman, Engineering and Science, March 1965, Vol. XXVIII, no. 6, p. 9.) In this well-written book, Bellman and Wing have indeed accomplished the task of introducing the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.

3,249 citations

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TL;DR: In this article, two closely related, low-sensitivity, active switched capacitor fitter topologies are presented, which are immune to the various parasitic capacitances normally present in switched capacitor networks.

Abstract: Two closely related, low-sensitivity, active switched capacitor fitter topologies are presented. Each of these circuits comprises two operational amplifiers and at most nine capacitors. The topologies have been carefully constructed so that they are immune to the various parasitic capacitances normally present in switched capacitor networks. One filter topology is capable of realizing any stable biquadratic z-domain transfer function, while the second one is only slightly less than fully general. Most commonly used transfer functions can be realized with either topology and will require only seven capacitors. The choice between the two topologies will generally be made on the basis of total capacitance required, dynamic range behavior, and sensitivity. A complete set of synthesis equations is given for both circuits which cover both the general and all the important special cases of the biquadratic transfer function. Finally, several examples are given which illustrate the synthesis procedures and the versatility of the filter topologies.

278 citations

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TL;DR: In this paper, a switched-capacitor filter is presented based on a pair of complementary integrators and has transfer functions independent of parasitic capacitances between any node and ground, and design equations are given for low-pass, bandpass, high-pass and notch biquads, as well as ladder simulation filters.

Abstract: New topologies for switched-capacitor filters are presented. The circuits are based on a pair of complementary integrators and have transfer functions independent of parasitic capacitances between any node and ground. Design equations are given for low-pass, bandpass, high-pass, and notch biquads, as well as ladder simulation filters. The ladder simulation filters are scaled for optimum dynamic range. Discrete prototypes of both cascade and ladder simulation filters are used to verify the theory.

188 citations

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01 Jan 1976TL;DR: The most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships can be found in this paper, where the derivation of filtering functions, Fourier, Laplace, Hilbert and z transforms, lowpass responses, the transformation of lowpass into other filter types, the all-pass function, the effect of losses on theoretical responses, matched filtering, methods of time-domain synthesis, and digital filtering are discussed.

Abstract: Long regarded as a classic of filter theory and design, this book stands as the most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships. Analysis and theory are supplemented by detailed design curves, fully explained examples and problem and answer sections. Discussed are the derivation of filtering functions, Fourier, Laplace, Hilbert and z transforms, lowpass responses, the transformation of lowpass into other filter types, the all-pass function, the effect of losses on theoretical responses, matched filtering, methods of time-domain synthesis, and digital filtering. This book is invaluable for engineers other than those who are filter design specialists who need to know about the possibilities and limits of the filtering process in order to use filters competently and confidently in their system designs.

183 citations

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TL;DR: The user aspects of a switched-capacitor network analysis program, SWITCAP, are discussed and the relation of the program's simulation facilities to actual laboratory measurement setups incorporating function generators, oscilloscopes, and spectrum analyzers is described in detail.

Abstract: The user aspects of a switched-capacitor network analysis program, SWITCAP, are discussed. The relation of the program's simulation facilities (such as frequency-domain analysis, time-domain analysis, and sampling functions) to actual laboratory measurement setups incorporating function generators, oscilloscopes, and spectrum analyzers is described in detail. Some examples illustrating the basic features of the program are also given.

105 citations