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Circuits and Systems, IEEE Transactions on

Issue 12 • Date December 1981

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Displaying Results 1 - 10 of 10
  • Jump behavior of circuits and systems

    Page(s): 1109 - 1124
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1803 KB)  

    Some circuits exhibit jump behavior. for example, this occurs when the velocity field specified by thedot{i}_Landdot{upsilon}_cof the inductor and capacitor characteristics cannot be "lifted" on to the resistive constraint manifold. The (jump) behavior is viewed as the limit asepsilon rightarrow 0of the solutions of a regularized system of equations obtained by introducing suitably locatedepsilon-parasiticL's andC's: this leads to a consistent way of defining discontinuous solutions. In particular, the behavior near a fold and cusp is examined. The concept of physically measurable operating point is defined and is related to that of strict local dissipativeness (which generalizes that of strict local passivity). Two examples are included. View full abstract»

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  • On the sensitivity of a class of wave digital filters

    Page(s): 1158 - 1164
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    The first-order sensitivity of Fettweis' wave digital filter is expressed in terms of those of its reference filter from which the wave digital filter is derived. With this explicit relation the numerically observed properties of the wave digital filter sensitivity are explained and the relation itself can be used as an efficient computing method when the sensitivities of the reference filter are available. In obtaining the above mentioned relation, the summed sensitivity invariants are used. We show that such invariants can be obtained as a consequence of impedance scaling and frequency scaling property of the reference filter. View full abstract»

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  • A high-quality double integrator building-block for active-ladder filters

    Page(s): 1174 - 1177
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    Active-ladder filters, at high frequencies, require doubleintegrator building-blocks meeting certain stringent requirements, which are not completely satisfied by most of the existing active-compensated double-integrator units. These restrictions are discussed here, and a highquality circuit is pointed out, having all the necessary properties. View full abstract»

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  • Broadbanding:Gain equalization directly from data

    Page(s): 1125 - 1137
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    This paper begins by presenting a powerful method which is easy to apply to many broad-band circuit design problems. Anyone with a broad-band design problem, which in the narrow-band case amounts to finding a point inside of a certain circle (say on the Smith chart), might find the method here very useful (Section I). Gain equalization problems fall into this category and the main subject of this paper is a conceptually appealing, highly practical, and very flexible theory of gain equalization. The clever matching theory developed by Fano and Voula in principle handles passive one-ports well except for some difficulty in computing gain-bandwidth limitations. It converts the main problem into computing solutions to a system of nonlinear equations which are in practice so formidable that typical text book treatments [8], [9] never address the issue of solving them systematically. Also classical theory requires the load and gains to be specified as rational functions. Our theory does a good job on gain-bandwidth limitations, reduces all problems to ones of finding eigenvalues and eigenvectors of a given matrix, and only requires the load and gains be specified as data on a frequency band. Our theory is highly effective for multiports and so settles the old impedance matching problem for passive multiport circuits. The concrete results which we present here are: (1) Two numerically efficient ways to determine theoretical gain bandwidth limitations for one-ports and n-ports; (2) For one-ports a quick way to compute the frequency response function for the optimal coupling circuit directly from the answer obtained in (1). The recent advance of broad-band microwave technology has produced a need for more general and more flexible theories of gain equalization. The type of theory called for is based on measured data and avoids rational functions and spectral factorizations until late in the design process. One typically specifies a desired gain profileG(jomega)and then wants to find the largest multiplekappa Gof it which is realizable. The procedure described herein is well suited to these needs since is requires only measured data and since determination ofkappais automatic. A very different method for broadbanding which - fills these needs was developed by Carlin [10]. It is a clever approach with quite a few compromises. One possible use of the lengthier rigorous procedure here would be to check the accuracy of Carlin's method. In addition to quantitative results we present some (much more easily learned) qualitative properties which every circuit (passive or active) designed to optimize gain possesses. They might be of considerable practical use in that any designer can learn them instantly and thereby obtain a certain (small) amount of general orientation very cheaply. The section on qualitative results, Section Ill, can be read independently of the rest of the paper (except for Fig. 1.1 and environs) and that might be best for some practical designers who have little taste for theory. Also in this paper we describe a certain viewpoint to the matching problem itself. From this perspective the matching problem is an elegant mathematical problem which fits solidly into a long line of classical mathematics. The classical mathematics underlies the computation of "prediction error" in Wiener's prediction theory. Our contention is that the matching problem is a very natural nonlinear analog of the classical prediction error problem. This formulation might broaden the appeal of impedance matching theory since it is easy to remember and is intriguing to the many systems theorists who are schooled in linear prediction theory (Section IV). View full abstract»

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  • An l_m norm bound for state variables in second-order recursive digital filter

    Page(s): 1170 - 1171
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    We introduce a new approach for determining anl_mnorm estimation of state variables in a second-order recursive digital filter. A bound with closed-form analytical expressions is obtained for any minimum realization configurations. For the uniform grid structure, it is shown that if the poles of the filter lie in a specific region, the proposed bound is better than the existing bounds. View full abstract»

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  • A new class of very low sensitivity and low roundoff noise recursive digital filter structures

    Page(s): 1152 - 1158
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    A class of new structures is proposed, for the realization of the recursive digital filter with poles near the unit circle, by introducing the particular type of delay replacement scheme in the existing digital filter structure and then, inserting, delays at the. proper places to avoid the delay-free loops. By applying the proposed method to the second-order direct form structures, new structures are found with very low magnitude transfer function sensitivities with respect to multiplier coefficients and low roundoff noises. Some numerical results are also presented. View full abstract»

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  • Synthesis of lossy-lumped-distributed cascaded networks

    Page(s): 1137 - 1152
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    The synthesis of lossy lumped-distributed networks is important for many applications; for example, in the analysis of large systems such as the interconnections of the circuits on an LSI or VLSI silicon chip, such networks have been used as models, and a solution of the synthesis problem will thus aid in the design of these chips. In this paper singlevariable realizability conditions and synthesis procedures are established for the class of lossy and/or lossless lumped-distributed cascade networks described by an input-impedance expression of the formZ_0 = frac{sum_{i=0}^{6n}a_i(s)e^{sT(2i-n)}}{sum_{i=0}^{n}b_i(s)e^{sT(2i-n)}}witha_i(s), b_i(s)real polynomials ins. The cascade networks consist of commensurate, uniform, lossless transmission lines interconnected by passive, lumped (lossless and/or lossy) two-ports and terminated in a passive load which can be prescribed as part of the specifications. Moreover, the results of this paper are also applicable to lumpeddistributed cascade networks which contain noncommensurate, tapered and/or lossy transmission lines (e.g., RC lines, distortionless lines) and to nonelectrical systems which can be modeled as distributed or lumpeddistributed cascades of types similar to the ones described above (e.g., acoustic filters). View full abstract»

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  • An efficient residue-to-decimal converter

    Page(s): 1164 - 1169
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    One of the fundamental problems with residue arithmetic is the difficulty associated with residue-to-decimal conversion. In this paper, several new efficient conversion algorithms are presented. They span a practical fixed-point dynamic range.running from 12 to 36 bits with execution speed measured in nanoseconds. The mathematical foundations of the developed methods are discussed in detail and realizable architectures presented. View full abstract»

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  • A digital all-pass transfer function with all possible coefficient combinations

    Page(s): 1171 - 1174
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    Characteristics of a second-order digital all-pass network with all possible combinations of two coefficients are discussed, and the constraints that the system should be stable and the group delay characteristic on extremum are described. Approximation formulas are given for the maximum group delay and for the angular frequency at which the group delay attains its maximum value. Digital all-pass transfer functions realizable with two finite wordlength multipliers and their maximum group delay characteristics are also described. View full abstract»

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  • A Monte Carlo method of one-sided tolerancing

    Page(s): 1177 - 1180
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    A method of one-sided tolerancing is given to determine an optimum set of minimum dc current gains in transistorized circuitry. The method has been used to select transistors in economical low-frequency power amplifiers which must survive a severe environment with a specified probability of failure. View full abstract»

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