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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Issue 8 • Date Aug 1992

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Displaying Results 1 - 15 of 15
  • Approximate solution of a transient tolerance problem for linear circuits

    Page(s): 666 - 673
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    The transient tolerance analysis problem for linear circuits or systems is considered. More specifically, the worst-case tolerance problem is treated in the setting of transient analysis. Two approximate solutions to the tolerance problem considered are suggested. It is shown theoretically that these are good approximations to the exact interval solution to the tolerance problem. This is confirmed by numerical examples. The second approximate solution is found in a very efficient manner and can be used for transient tolerance analysis of circuits (systems) of increased dimensionality. The results obtained are based on an approach using some basic concepts and techniques from interval analysis View full abstract»

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  • Canonical piecewise-linear approximations

    Page(s): 697 - 699
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    The canonical representation of piecewise-linear functions is considered as a universal approximation scheme of multivariate functions. Meanwhile, two universal approximation schemes in terms of combinations of univariate canonical piecewise-linear functions are proposed. The discussion supports the application of these schemes in mapping networks, e.g. neural networks or adaptive nonlinear filters View full abstract»

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  • Criteria for the approximation of nonlinear systems

    Page(s): 673 - 676
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    Conditions for the approximation of discrete-time time-invariant nonlinear systems that act between bounded real sequences are considered. It has been shown in different contexts that if the output of a nonlinear system at each moment is dependent on the remote past of the input only to an arbitrary small extent in a certain sense, then the system can be uniformly approximated arbitrarily well by the maps of certain simple structures such as lattice-map structures, finite Volterra-series structures, dynamic multilayered neural networks with sigmoidal hidden units, and dynamic radial-basis-function networks. Results are given to the effect that, for a certain broad class of system approximation problems, conditions introduced earlier and certain variations of other conditions are all equivalent, and are in fact necessary as well as sufficient View full abstract»

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  • Linear algebraic properties of the realization matrix with applications to principal axis realizations

    Page(s): 628 - 640
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    Examines the realization matrix R=[A b; c d] defined by a state variable model of a linear, shift invariant, discrete time, scalar system. Several properties concerning the eigenvalues and singular values are derived, which are used to obtain tests for the minimality of the state variable model. An inequality is derived between the spectral norm of R and the LΩ-norm of its frequency response. The realization matrices of principal axis realizations are characterized in terms of their eigenvalues and singular values. qr-factorizations and bounds for the spectral norms of such realization matrices are derived View full abstract»

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  • On piecewise-linear approximation of nonlinear mappings containing Gummel-Poon models or Schichman-Hodges models

    Page(s): 694 - 697
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    An effective technique for the piecewise-linear approximation of nonlinear mappings containing Gummel-Poon models or Shichman-Hodges models is presented. The basic idea is to exploit the pairwise-separability of the nonlinear mappings containing these nonseparable models. The proposed approximation is much more effective than the conventional piecewise-linear approximation using a simplicial subdivision View full abstract»

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  • How near is a stable polynomial to an unstable polynomial?

    Page(s): 676 - 680
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    Frequency response techniques are applied to the problem of robust Hurwitz stability of a family of polynomials with complex coefficients. The distance between two polynomials is measured by a weighted lp norm, 0>p⩽Ω. Necessary and sufficient conditions for robust stability, as well as formulas for the stability radius and a minimal norm destabilizing polynomial are provided. This work is motivated by and follows the spirit of a result reported by Y.Z. Tsypkin and B.T. Polyak (see IEEE Trans. on Autom. Control, vol.36, p.1464-9, 1991) View full abstract»

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  • On L2-sensitivity minimization of linear state-space systems

    Page(s): 641 - 648
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    Properties of the solution to the L2-sensitivity minimization problem are discussed. In particular, a specific form of the solution is derived together with a bound. This bound gives an insight into the difference between a pure L2-sensitivity optimal realization and a mixed L 2/L1-sensitivity optimal one. The question of L2-sensitivity balanced truncation is addressed, and a counterexample is presented to show that two main properties associated with model reduction by truncating a Lyapunov balanced realization are lost in the case of L2-sensitivity balanced truncation View full abstract»

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  • Optimal dynamic range integrators

    Page(s): 614 - 627
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    The design of optimal dynamic range integrators that are meant as building blocks for optimal dynamic range analog continuous-time filters is discussed. A fundamental limit for the dynamic range of an integrator is given. This limit is a function of the supply voltage and the available amount of capacitance. It is shown how integrators are to be designed if this limit is to be reached. Different conventional integrator realizations are evaluated and optimized so that they can be compared to the fundamental limit. A design example of a filter with integrators that approach this limit is given View full abstract»

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  • Linear circuit models of PWM flyback and buck/boost converters

    Page(s): 688 - 693
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    A method for modeling PWM converters operating in continuous conduction mode (CCM) is introduced. First, static voltage and current transfer functions of the idealized switching part of the converters are found. Second, the linearization of these transfer functions at the operating point is carried out, and the idealized switching part is replaced by dependent current and voltage sources. Third, the equivalent average resistance of parasitic resistances and equivalent average voltage of offset voltage sources of switches are determined using the principle of energy conservation. The method leads to linear DC and small-signal circuit models of a PWM converter. To illustrate the method, the analysis of the PWM flyback converter is given. Design equations for DC voltage transfer function, efficiency, and small-signal characteristics are derived View full abstract»

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  • Bounded-input-bounded-output properties of nonlinear discrete difference equations-applications to fixed-point digital filters

    Page(s): 662 - 666
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    Input-output properties of discrete difference equations with sector-type nonlinearities are derived. The results are applied to direct form digital filters with combinations of quantization and overflow nonlinearities. Using these properties, the regions of global asymptotic stability of digital filters with two's complement quantization and overflow are provided. Previous stability results for combinations of roundoff quantization and any type of overflow are also improved upon View full abstract»

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  • Class E resonant low dv/dt rectifier

    Page(s): 604 - 613
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    A class-E resonant low dv/dt rectifier is analyzed and experimentally tested. All major parasitic reactive components are included in the rectifier topology. The diode capacitance and the leakage inductance of the isolation transformer and lead inductances are absorbed into the resonant inductance. Therefore, the rectifier is suitable for high-frequency applications such as resonant DC-to-DC converters. The rectifier is driven by a sinusoidal voltage source. Equations governing the circuit operation are derived using Fourier techniques. Experimental results are obtained at 1 MHz and an output voltage of 5 V. The design equations show good agreement with the measured circuit performance View full abstract»

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  • Chaos in a current-mode controlled boost DC-DC converter

    Page(s): 680 - 683
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    A mapping is derived in closed form, without approximations, for an idealized current-mode controlled boost converter. This circuit is known experimentally to behave chaotically for certain values of the reference current, and to produce subharmonics of the clock frequency at others. Numerical iteration of the mapping indicates chaotic operation and the presence of subharmonics. Two mechanisms of bifurcation are explained View full abstract»

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  • Stability of a set of multivariate complex polynomials with coefficients varying in diamond domain

    Page(s): 683 - 688
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    Recently, attention has been focused on the (open left half plane) stability of a family of polynomials with complex coefficients with their real and imaginary parts each varying in a diamond. It has been concluded that the stability of a diamond family of polynomials is equivalent to the stability of the specific 16-edge polynomials of the diamond. This result is extended to the n-variate case. It is proved that the scattering Hurwitz property of the certain 16n diamond edge polynomials can guarantee the scattering Hurwitz property of the whole diamond family of n-variate complex polynomials View full abstract»

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  • Transient simulation of nonuniform coupled lossy transmission lines characterized with frequency-dependent parameters. I. Waveform relaxation analysis

    Page(s): 585 - 603
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    Presents a waveform relaxation technique for simulating the transient response of nonuniform coupled transmission lines which are characterized with frequency-dependent parameters. The method consists of iterative waveform relaxation analysis of asymmetric disjoint resistive networks constructed with voltage-dependent voltage sources generated by applying the fast Fourier transform (FFT). The method requires neither convolution integration nor synthesis of lumped equivalent circuits for the simulation of the frequency-dependence of transmission-line parameters. Transient responses of uniform and nonuniform coupled transmission lines with and without skin-effect parameters and terminated with linear and nonlinear loads are simulated for illustration. The accuracy and efficiency of the relaxation technique are substantiated with exact analytical solutions and experimental data View full abstract»

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  • Steady-state analysis of nonlinear circuits based on hybrid methods

    Page(s): 649 - 661
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    Two efficient algorithms for calculating the steady-state responses of nonlinear circuits are proposed. They are based on both time-domain and frequency-domain approaches. A nonlinear circuit is partitioned into two subnetworks with substitution sources, and their responses are solved by a combined frequency-domain and time-domain method. The total response of the combined circuit can be calculated by an iterative technique based on either the Newton or the relaxation harmonic balance method. Since the methods are based on both time-domain and frequency-domain algorithms, they are called the Newton and the relaxation hybrid harmonic balance methods, respectively. The methods can be applied efficiently to strong nonlinear circuits containing high- Q subnetworks such as filter circuits and crystal oscillators. When a large-scale circuit is partitioned into large linear subnetworks and small nonlinear subnetworks, the method can also be applied efficiently View full abstract»

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