Some Techniques for Network Synthesis

The recurrent-continuant method of synthesizing a ladder network due to Holbrook is limited to the lossless quadrupoles terminated in resistance at only one end. The technique has been modified to cover the general class of lossless quadrupoles terminated in resistances at both the ends. The proposed synthesis procedure starts with a given realizable polynomial which is separated into two realizable component polynomials, one of the same order and the other of one order less under the condition that the continuants corresponding to the component polynomials are such that one becomes the first minor of the other. By applying simple mathematical manipulations, the final continuant is formed out of these continuants. The element values of the final continuant are evaluated by solving certain sets of equations. The sensitivity of the transfer function of the network with respect to the terminal resistance, the non-realizability of the characteristic polynomial for a given terminal resistance ratio, and the multiple sets of values of the circuit elements for a given characteristic have also been investigated.In the case of active RC low-pass ladder networks Nesbitt has presented a technique for transforming the recurrent determinant into the continuant determinant provided the elements of the main diagonal of the latter are specified. His method however does not provide a solution for active RC ladder networks which are terminated in a resistance at the output end. In this paper a modified transformation technique, applicable to resistively-terminated active RC ladder networks, is proposed.

A digital computer program for the design of an all-pass function, with n natural modes, to correct the phase of a prescribed transfer function is discussed. The program is based on the expansion of both the desired phase and that of the all-pass function as a Tchebycheff polynomial series, together with the selection of the all-pass natural modes, so that the first n coefficients in the two series agree. If the over-all delay is unimportant, it may be chosen either to increase the number of matched coefficients by one, or to seek a minimum peak error over the approximating bandwidth. The design process is based on a continued fraction expansion, and a detailed technique for adjusting the over-all delay is discussed. Recurrence relationships are established for expanding the phase of any transfer function as a Tchebycheff polynomial series. The dependence of peak error on approximating bandwidth is discussed, and a routine for the automatic adjustment of the bandwith to meet a specified peak error is described. The design accuracy depends primarily on the root extraction technique, and on the loss of significant figures during continued fraction expansion. Adequate results have been obtained with 8 or 10 natural modes. The speed of the program depends on the number of basic iterations of the design process, which varies from one to ten. On a Ferranti Mercury Computer with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 8</tex> , the basic iteration time is 20 seconds.

New solutions of Novozhilov's equation of toroidal shells

It is known that many structural schemes can be used to implement digital filters. Some structures of digital filters are characterized by low sensitivity of the characteristics to the accuracy of the representation of the coefficients. A separate group of methods for the structural synthesis of digital filters is based on the expansion of rational fractions, including transfer functions, into continued fractions. Because of this decomposition, ladder structures are obtained. The sensitivity of such ladder structures is analyzed in this paper. As a measure of the structure sensitivity, estimations of the partial derivatives of the transfer function coefficients with respect to the expansion coefficients in continued fraction were used. The analysis showed that the sensitivity of the transfer function coefficients to some expansion coefficients is very small. However, the presented examples show that the sensitivity to certain coefficients of expansion can exceed the sensitivity of the classical direct and the canonic forms.

In this research work, aHOS(high order system)remains decreased into LOS (lower order system) by usage of MCF (modified cauer form) method. The ROM is founded upon CF (Continued fraction) technique also find comes out to be LOM (low-order model). For the reduction of HOS indirect method is used. Presents article, show the graphical comparison of simulation results between MCF ROM and another diminution technique presented in literature. In the simulation, the response comparison displays improved performance of proposed ROM than further approaches obtainable in literature and discuss the result technics of peak time, settling time, rise time also peak amplitude information for higher order and ROM.

The results of filter design obtained by solving non-linear coefficient derived polynomial equations is reported. Taking Butterworth filters as an example, and working within the machine precision of the software package Mathematica (Wolfram 1991 WOLFRAM , S. , 1991 , Mathematica, a System for doing Mathematicas by Computer ( New York Addison-Wesley ). [Google Scholar]), many solutions are obtained. The results provide experimental evidence supporting the low sensitivity of the transfer function with result to the element value variations of doubly terminated LC networks. In addition, element value sets are found which support the Butterworth transfer function, but do not result from classical synthesis techniques.

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.

A method for harmonic measurements in EHV systems is proposed that is based on the measurement of currents in capacitor voltage transformers (CVT) and values of capacitor elements of CVTs. This is the basis of a new technique, which uses current sensors installed within CVTs. Simulation studies and field tests have confirmed the validity and practicability of the technique. In the new method the input terminal voltage is directly determined and no information about transfer function and burden is required. In order to verify the field test results, errors in the CVT output voltage recorded during tests were compensated by the use of the transfer function determined independently in transfer function tests for the same burden. A very good correlation was observed between the two results. The results of field measurements are also presented.

This paper presents theory for multivariable system identification using matrix fraction descriptions and the matrix continued fraction description approach which, in turn, yields a lattice-type order-recursive structure. Once the matrix continued-fraction expansion has been determined, it is straightforward to obtain solutions to both the left and right coprime factorizations of transfer function estimates and, in addition, solution to problems of state estimation (observer design) and pole-assignment control. An important and attractive technical property is that calculation of transfer functions in the form of right and left coprime factorizations, calculation of state variable observers and regulators all can be made using causal polynomial transfer functions defined by means of matrix sequences of the continued-fraction expansion applied in causal and stable forward-order and backward-order recursions. >

The problem of minimal state space realization of two-dimensional systems is considered. The approach followed is, initially, to derive a circuit realization of the given transfer function involving a minimum number of delay elements. To facilitate this realization, the transfer function is expanded into a continued fraction. Using this circuit realization, an algorithm is proposed which readily provides the matrices of the state space model. The simplicity in deriving this model is due to a novel state space model introduced, which is of cyclic structure. Several examples are presented to illustrate ihe proposed algorithm.

On the use of continued fraction filter structures for the design of 2-D digital filters

A simple and straightforward procedure for active realization of a class of biquadratic RC voltage transfer functions with minimum number of passive elements, minimum active sensitivity and minimal spread in element values is given.

A realizable, low-pass, minimum-phase transfer function is constructed which produces "maximally flat" time delay as a function of frequency, and which is associated with an impulse response that resembles closely a Gaussian curve properly delayed with respect to t= 0. The delay and loss characteristics are particularly easy to evaluate, since this transfer function can be expressed in terms of conveniently tabulated functions. It is shown how to realize this transfer function as the transfer impedance of a ladder network containing only low-Q elements, and the response of this network is put into perspective to those of conventionally designed delay networks. Also, a class of nonminimum-phase transfer functions is generated from the above transfer functions in order to offer added flexibility. The delay and loss characteristics of the nonminimum-phase transfer functions are described, but their network realization is not considered in this paper.

A method is presented for solving the one-dimensional Schrodinger equation in which the potential is approximated by a step function. This effective Hamiltonian is then solved exactly by a continued fraction technique which enables the convergence properties to be studied. The method is particularly suitable for the solution of scattering problems for which upper and lower bounds can be obtained for the phase shifts.

Error analysis of code AROSA for quantal coulomb excitation calculations