Function Of Reflection Coefficient Research Articles

Method for synthesis of matching devices for broadband radio engineering systems with unstable load impedance based on the method of real frequencies

The aim of this work is to develop a method for the synthesis of matching devices for broadband radio engineering systems with varying impedance in different operating conditions. To achieve this goal, a criterion (complex criterion) is proposed for minimizing the value of the modulus of the sensitivity invariant of the reflection coefficient function to a change in the load impedance with restrictions on the square of the deviation of the power transmission ratio from a given level. It is proposed to use a combination of methods of real frequencies together with the shown complex criterion, which made it possible to implement an effective approach to the synthesis of matching devices for broadband radio engineering systems with an unstable load impedance. To verify the approach, a matching device was synthesized, which made it possible to reduce the loss of the power transmission factor level transmitted to the UHF/VHF antenna of the AD-44 / CW-TA-30-512 range when it is located in various operating conditions by at least 50 % in relation to losses obtained with a standard matching device.

Метод синтеза широкополосных устройств с оптимальной характеристикой коэффициента преобразования мощности, согласующих изменяющийся во времени импеданс нагрузки.

A method is proposed for the synthesis of broadband matching devices that adapt radio engineering systems to the changing load impedance in a wide range of natural conditions of their operation. The results of experimental studies of the effect of operating conditions on the impedance of VHF and UHF radio antennas with matching devices are presented. An invariant of the sensitivity of the reflection coefficient function to changes in the load impedance is obtained, on the basis of which a complex criterion for the synthesis of broadband matching devices is developed. A broadband matching circuit was synthesized for the AD-44/CW-TA-30-512 antenna device, which provides a gain in the potentially achievable radio line range of up to 5% in relation to the standard matching device. An analytical mathematical model of a broadband matching device is developed and based on it, a matching device adaptive to the changing impedance of the AD-25/CW-3512 antenna is synthesized, providing an average gain in the potentially achievable range of the radio line from 2% to 15% in the framework of the presented experimental studies.

THE METOD OF SYNTHESIS OF MULTIBAND MATCHING DEVICE

The purpose of this work is to provide the estimation of the potential abilities of analytic broadband matching methods for complicated load terminations. The article covers the problem of synthesis of mylti-band frequency response matching circuits. Results presented in the article are of prime interest for communications systems from one point and the lack of advanced analytic methods from another. The problem of multiband impedance matching is under consideration. Presented is the method of synthesis of multiband matching circuits for arbitrary complex loads, based on the generalized Darlington approach to the lumped circuits design. Frequency response for the synthesis is obtained as a result of double-band reactance transformation in the process of reflection coefficient factorization. The factorization results in the analytic representation of the reflection coefficient function on the complex surface. This method allows to identify functional limitations on broadband matching and for the first time to obtain analytical solutions for the loads of practical value. Application of the method is demonstrated in the detailed procedure of realization of double-band Batterworth frequency response for the resonance load (RLC-load). It would be pertinent to stress, that presented results concerning the double-band synthesis of resonance load have no coverage in technical literature. The method also features the analytic description of the design parameters as functions of load termination parameters which provides a road-map to conceptual design of multiband matching circuits.

Coulomb Blockade of a Nearly Open Majorana Island

We consider the ground-state energy and the spectrum of the low-energy excitations of a Majorana island formed of topological superconductors connected by a single-mode junction of arbitrary transmission. Coulomb blockade results in e-periodic modulation of the energies with the gate-induced charge. We find the amplitude of modulation as a function of reflection coefficient R. The amplitude scales as sqrt[R] in the limit R→0. At larger R, the dependence of the amplitude on the Josephson and charging energies is similar to that of a conventional-superconductor Cooper-pair box. The crossover value of R is small and depends on the ratio of the charging energy to superconducting gap.

Evolution of the ultrasonic resonance modes in a three-layer structure with change of material and interface adhesion properties

The quantitative non-destructive evaluation (NDE) of interface adhesion has long been a challenge for the safe use of bonding structures. It is difficult to predict the adhesion resistance force between adhesive and adhered material without performing destructive testing. Ultrasonic approach seems to be the only potential way for its NDE based on the reason of mechanical nature of the problem. Different ultrasonic techniques, such as bulk wave echography, reflection resonance, and Lamb guided waves, have been used to evaluate the interface adhesion strength. But no direct relation between the interfacial bonding strength and the ultrasonic measurement has been established. The most used compression wave echography and resonance at normal incidence are less sensitive to the interface condition, except for a disbond. It is essential that the interface should be excited with a shear stress component to increase the measurement sensibility. But it is not easy to excite the interface by using shear waves in experiment, while the use of guided waves will encounter the problems of high attenuation and mode selection as all modes are not sensitive to a certain interface in a bonded structure. A previous study has shown that the V (z) inversion technique can be used to perform a multimode measurement on a layered structure, where both compression and shear stress resonance occur. This method has the advantage in using a simple experimental setup working at the normal incidence with a focus transducer of large angular aperture. The inversed angular-frequency reflectance function R(; f) gives the resonance modes which are equivalent to the Lamb type guided modes, while it is a local determination of the wave mode, thus the difficulty in guided wave measurement above mentioned can be avoided. The first part of the paper contains the development of the theoretical model for wave propagation in a multilayered structure where three-layer sandwich bonded structures can be considered as a particular case. A weak interfacial adhesion is described by two interface compression and shear stiffness parameters, namely km and kt. By integrating the transfer matrix formalism under the non-ideal boundary conditions, the plane wave angular (incident angle) and frequency reflection coefficient function R(; f) for a liquid immersed asymmetric metal-adhesive-metal three-layer and its dispersion curves of guided mode waves with or without charge are calculated. It is confirmed that the evolutions of the reflection zeros (mode resonances) correspond to the dispersion curves of the guided waves of the same structure without charge. Furthermore, the resonance modes observed in R(; f) can be considered as a combination of the respective Lamb modes of the top and bottom single metal layers coupled through the modes conditioned by the middle adhesive layer and the its interface conditions. The second part of the paper shows the behaviors of the resonance modes by changing the parameters related to the bonding strength. The acoustical impedance, the mass density and the thickness of the adhesive layer, which are related to the cohesive property, and the shear interfacial stiffness coefficient kt which conditions the adhesive property, are changed respectively to observe the resonance mode evolutions. The mode evolutions due to each parameter are analyzed and differentiated. It can be concluded that the change in the adhesion strength of the bonding structure does not affect significantly the modes belonging to those inherent to the two adhered aluminum layers, while the coupling modes will be shifted in frequency and exchange with or replace the said inherent modes. It is expected that the obtained results in this study will be of significance for quantitatively characterizing the interfacial properties of an adhesively bonded layered structure by using the V (z) inversion technique.

The V(z) Inversion Technique for Evaluation of an Adhesively Bonded Structure**Supported by the Key Program of the National Natural Science Foundation of China under Grant Nos 10834009 and 11374230

Based on the fact that the evolution trace in incident angle and frequency of the resonance zeros of the reflection coefficient function for a water charged layered medium is equivalent to its guided wave mode dispersion, the interfacial adhesion of a three-layer aluminum–adhesive–aluminum bonding structure is characterized nondestructively by determining the interface shear stiffness kt associated with the interfacial strength. The resonance reflection function is obtained experimentally by the V(z) inversion technique using an ultrasonic focused transducer of wide-band and large angular aperture (up to ±45°). The dispersion curves are numerically calculated, adjusting the parameter kt so that the difference between the dispersion curves and the angular-frequency tracing of the reflection zeros is minimum. The parameter kt at an interface of weakly adhered aluminum epoxy-resin is estimated to be 1014 N/m3.

Polarized Channel Model for Body Area Networks Using Reflection Coefficients

A geometry-based propagation model is proposed for wideband polarized body area network (BAN) channels. Reflection coefficient functions ( $\Gamma$ -functions) are derived as a function of geometry-based channel modeling parameters for more precise modeling of polarized BAN channels than existing polarized channel models, which exclude the reflection coefficients or use constant-valued reflection coefficients. Conservation-of-polarization (CoP) propagation planes along with geometrical $\Gamma$ -functions, which we call the CoP - ${\mit\Gamma} $ plane methodology , are used to derive the channel polarization functions. Statistical characteristics of polarized BAN channels such as the cross-polarization discrimination (XPD) and time–frequency correlation function (TF-CF) are provided based on this new CoP- $\Gamma$ plane methodology. The model is validated with measurement data taken at 13 GHz and shown to be in excellent agreement.

Effect of Primary Source Location on Fabry-Perot Resonator Antenna with PEC or PMC Ground Plate

The radiation property of Fabry-Perot Resonator antennas made of PEC or PMC ground plate covered with a partially-reflecting surface effected by the primary source location is investigated theoretically, respectively. It is shown that the location of primary source affects the gain of Fabry-Perot Resonator antenna greatly, and the maximum of gain can be obtained when primary source is located at certain positions for these two types of ground plate. But the pattern bandwidth does not vary obviously with the source location, as long as the resonant condition on the height of Fabry-Perot cavity is satisfied. At the same time the normalized product of maxium of gain and its bandwidth act as a reasonable criterion for evaluating the performance of such kind of antenna, a function of reflection coefficient of partially reflective surface, trending to a certain limitation with increase of reflection coefficient is firstly proposed. Finally the simulated results of planar Fabry-Perot Resonator antenna are validated to have good agreement with the calculated theoretically, which is of great significance to antenna designing.

Design of Dielectric Waveguide Filters Using Topology Optimization Technique

Topology optimization technique is applied to the design of a dielectric waveguide filter. The objective function is defined as a function of reflection coefficient, and the design variable is relative density of dielectric material in each unit cell. To calculate sensitivity information that is needed during topology optimization, adjoint variable method is used. The results of numerical examples show feasibility of the proposed method

Discrete Systems and their Characteristic Spectral Functions

We define first-order discrete systems in the matrix-valued case. They are characterized by sequences of pair of matrices, called admissible sequences. We present two important examples of such sequences, called Szego and Nehari sequences. We introduce the characteristic spectral functions associated to a first-order system. We define in particular the scattering function, the Weyl function and the reflection coefficient function and we study the relationships between these functions.

Inverse problem for Sturm-Liouville operators with rational reflection coefficient

In this paper we give exact formulas for the potential associated to a Sturm-Liouville equation when the reflection coefficient function is rational. The solution is given in terms of a minimal realization of the reflection coefficient function.

Acoustic waves in a piezoelectric plate loaded by a dielectric fluid

Measurements and calculations of reflection spectra of an X-cut LiNbO3 plate immersed in a dielectric fluid have been performed, with the numerical results presented in an innovative image data format. The influence of dielectric fluid loading on all branches of the reflection coefficient function has been investigated. Strong piezoelectric coupling leads to unexpected plate wave dispersion in the fundamental symmetric mode, where the group velocity exceeds the phase velocity at low frequency. The experimental data are in excellent agreement with the results of an exact partial wave analysis. These phenomena and their effect on plate wave behavior can play an important role in the performance of chemical or physical liquid sensing devices.

Multiple Suppression By a Wave-equation Extrapolation Method

The wave-equation-based multiple suppression method, unlike predictive deconvolution and stacking, makes no assumptions on periodicity or moveout patterns of multiples, and can cope with complex sea-bottom and sea-surface variations. It entails multiple prediction by wave equation extrapolation of the seismic data and then multiple subtraction from the recorded seismograms. In general, the multiple subtraction method requires the calculation of a subtraction scalar (a reflection coefficient function), which is a function of the ratio of the original data to the extrapolated multiple model traces. The success of the method depends on establishing the correct scalar. However, it is difficult to get a good subtraction scalar when the wavelet of the original data is different from that of the multiple model traces. This occurs for the long offset traces because of geophone ghosting, and changes of amplitude and phase in the reflection waveform beyond the critical angle. In this paper, we develop a superior alternative scheme, based on a simple 2-D Butterworth-type gain function, calculated from the original data and the (extrapolated) multiple model data. This gain function will attenuate the multiples and preserve the primaries. A simple synthetic example is used to demonstrate the efficacy of the method in multiple suppression.