M. V. Andreev

Determination of Parameters of Fractional-Rational Model using Interpolation by Continued Fraction

The opportunity of realization of fractional-rational approximation using model in the form of continued fraction is considered. A simplified approach to selection of suboptimal samples for the formation of the approximating continued fraction is offered. The accuracy of the suggested method is analyzed and its application for processing the resonant response is considered.

Rational representation in spectrum conjugate domain for parameters determination of reflecting structures

An opportunity of use of rational representation in the spectrum conjugate domain for determination of parameters of reflecting structures using measured frequency reflection characteristics has been considered. An opportunity of use of the linear approaches for spectral data approximation by unipolar function and use of rational interpolation of the spectral data with the purpose of acceleration of a procedure of parameter determination of the additive exponential model has been considered. The properties of these methods and their comparison with analogous properties of other methods are presented.

Measurement of dielectric material properties using coupled biconical resonators

The paper considers the advantages of using coupled biconical resonators in microwave measurement of dielectrics. The advantage of technique is application of resonance frequency of empty resonator as reference one and replacement of Q-factor measurement by measurements of the ratio of amplitudes of maxima of frequency transmission coefficient.

Rational model of E-cross for six-port measurements

Automated analyzers, based on six-port reflectometers (SPR), are widely used for measuring the parameters of the microwave devices. In the measurement transducer of SPR the matched multiport passive microwave connection is used for the complex composition of the reference wave generator and the wave reflected from the object. In this case the parameters of the measurement system are found by preliminary calibration using at least four standards of the complex reflection coefficient (RC).

Wide-band reflection coefficient measurements using direct and inverse frequency-time domain transformations

The problem of measurement of modulus of the reflection coefficient (RC) in wide frequency band in presence of additional reflections such as reflections in a horn antenna is considered. The Pronys method and the method of separation of autocorrelation function of layered structure by windowing in time domain for the restoration of the square modulus of the RC in wide frequency band were compared. The values of the error of restoration methods under consideration in the chosen frequency band have been calculated. It has been shown the advantage of the Pronys method application in sliding frame by the results of the numerical simulations and real measurement data processing. The technique of data extrapolation at the edges of the frequency band for applying Pronys method is proposed.

Analysis of Q-factor of dielectric resonator by means of fractional-rational approximation of reflection response

Estimation of Q-factor of the open resonator by means of fractional-rational approximation of the reflection response has been considered. An advantage of the proposed technique in comparison with classical methods has been demonstrated. Dependence of Q-factor of the half-disk dielectric resonator and estimations of poles and zeros of resonance response against coupling coefficient value has been analyzed.

Analysis of natural frequency and Q-factor estimation for open dielectric resonators with variation of coupling by means of fractional-rational approximation of reflection response

The analysis of the natural frequency and estimation of Q-factor of the open resonator by means of fractional-rational approximation of the reflection response has been considered. An advantage of the proposed technique in comparison with the classical methods has been demonstrated. Dependence of Q-factor of the shielded half-disk dielectric resonator and estimations of the poles and the zeros of the resonance response against the coupling coefficient value has been analyzed.

Determination of parameters of closely spaced resonances using fractional-rational approximation of resonator frequency response

The paper discusses the use of a fractional-rational approximation for estimation of the parameters of resonant oscillations if resonance frequencies are situated rather close with substantial overlapping. Limits of applicability of the method of fractional-rational approximation by continued fractions have been determined for two closely spaced resonances in presence noise.

Feature of Prony's method application for natural frequencies estimation from the frequency response

Specifics of use of the Pronys method to determine the natural frequencies from the frequency response of the object in comparison with direct fractional-rational approximation has been examined.

The possibility of using the fractional-rational approximation to determine the parameters of closely spaced resonances

The paper discusses the problem of determining the parameters of closely spaced resonances. The overlapping ratio was introduced for estimation of the degree of the resonance peaks overlapping and analysis of its dependence against the width and magnitude of the peaks. The dependence of the error of poles estimation against the degree of resonance peaks overlapping was examined. The limits of applicability of the method of fractional-rational approximation by continued fractions were determined for two coupled resonators.