Phase-frequency Characteristics Research Articles

Modeling Thermal Impedance of IGBT Devices Based on Fractional Calculus Techniques

The thermal impedance characteristics of insulated gate bipolar transistor (IGBT) modules are critical for the thermal management and design of electronic devices. This paper proposes a fractional-order equivalent thermal impedance model, which is inspired by the correlation between multi-time-scale dissipation characteristics of heat conduction processes and fractional calculus. The fractional-order equivalent thermal impedance model is derived based on the connection between fractional-order calculus and the Foster thermal network model in mathematical operations, with only two parameters to be identified: heat capacity C and fractional order α. Moreover, this paper provides a parameter identification method for the proposed fractional-order equivalent thermal impedance model based on the multi-objective particle swarm optimization (MOPSO) algorithm. In order to validate the effectiveness and superiority of this work, experiments and comparative works are provided in this paper. The results indicate that the fractional-order equivalent thermal impedance model can accurately describe the frequency domain characteristic curves of the thermal impedance of the Foster thermal network model for IGBT modules, with the difference between the amplitude frequency characteristics not exceeding 1 dB and the difference between the phase frequency characteristics not exceeding 1° within the operating frequency range of (1 kHz, 1 MHz).

Realizing Multi-Parameter Measurement Using PT-Symmetric LC Sensors.

With the rapid development in sensor network technology, the complexity and diversity of application scenarios have put forward more and more new requirements for inductor-capacitor (LC) sensors, for instance, multi-parameter simultaneous monitoring. Here, the parity-time (PT) symmetry concept in quantum mechanics is applied to LC passive wireless sensing. Two or even three parameters can be monitored simultaneously by observing the frequency response of the reflection coefficient at the end of the readout circuit. In particular, for three-parameter detection, a novel detection method is studied to extract the three resonant frequencies of the system through the phase-frequency characteristics of the reflection coefficient, which has never appeared in the previous literature on PT symmetry. The changes in three resonant frequencies are in response to changes in the three parameters in the environment. We show theoretically and demonstrate experimentally that the PT-symmetric LC sensor can realize multi-parameter measurement using a series LCR circuit as the sensor and a symmetric adjustable LCR circuit as the readout circuit. Our work paves the way for applying PT symmetry in multi-parameter detection.

Impedance modeling and quantitative stability analysis of grid-connected voltage source converters under complex unbalanced conditions

The stability issues caused by voltage source converters (VSCs), which are commonly used in renewable energy systems, are investigated in this paper. Much literature has investigated the impedance models and quantitative stability analysis for converters under the weak and unbalanced grid. However, on the one hand, harmonic-transfer-function (HTF)-based modeling methods are complex, and the established infinite-order models may suffer from unreasonable truncation. On the other hand, these existing impedance models without considering all unbalance factors are inaccurate. Both of these may bring wrong stability analysis results. Therefore, this paper proposes a simple impedance extension method and considers all unbalance factors to derive the impedance model of the converter. However, due to the established higher-order impedance model, the traditional impedance-ratio based stability analysis method is not applicable to multi-input multi-output (MIMO) systems. The commonly used eigenvalue-based GNC and diagonalization-based methods applicable to MIMO systems are cumbersome and not suitable for quantitative analysis. Therefore, in this paper, a quantitative analysis tool of system stability based on the phase-frequency characteristics of determinants is developed. Then, stability regions in the multi-parameter space are obtained. Finally, the established impedance model and the quantitative analysis results are validated via both simulations and hardware experiments.© 2017 Elsevier Inc. All rights reserved.

Gyroscopic rotor dynamics simulation with anisotropy of elastic and damping characteristics of the support

In the work, the differential equations of motion of the gyroscopic rotor, built taking into account the anisotropy of stiffness and damping of the flexible support, are solved analytically, by the method of harmonic balance, convenient for obtaining separately amplitude-frequency and phase-frequency characteristics in the direction of oscillations. The equations of the non-stationary process are obtained by the method of changing amplitudes. It has been found that when the linear stiffness of the elastic support is different in two orthogonal directions, two critical velocities and the corresponding resonant regions arise. In the area of each critical speed, there are two amplitude-frequency curves of oscillations of the main direction and the direction perpendicular to it, respectively. The geometric nonlinearity of damping suppresses the elevations of these amplitude-frequency curves more significantly than linear damping. If only one of the two directions has a damping nonlinearity, then its effect is on the amplitude-frequency curves of the corresponding critical speed. It is more efficient to control resonant amplitudes for smooth resonant transitions by enhancing the linear damping with geometrically nonlinear damping. The results of the analytical solution of the equations of motion agree well with the results of direct modeling and experimental studies.

Dynamic and Phase-Frequency Characteristics of Rotor Instability Induced by Steam Flow Excited Vibration in Seals

Steam flow excited vibration in seals seriously affects the seal-rotor stability. A mesh deformation based on user-defined functions was adopted to establish the multi-frequency whirl model, and the reliability of the simulation method was verified by experiments. The average effective damping and working ability of the fluid were proposed to analyse the stability of the seal. The mechanism of seal instability induced by steam flow excited vibration was revealed through the phase-frequency characteristics of exciting forces and displacements. The results show that direct damping decreases gradually with an increase in frequency, and the cross-coupling damping tends to be stable over 15 Hz. The average effective damping is more sensitive and accurate in predicting the seal stability. Effective damping decreases with increased frequency. Therefore, the rotor stability is decreased. Near the 12 Hz and 24 Hz frequencies, the average effective damping of eccentricity fluctuates, so the seal stability is poor. The negative effect of exciting forces increases, and the seal stability is improved when the eccentricity increases. When the phase difference between the excitation force and displacement changes, the seal stability decreases. The fundamental reason for rotor instability induced by steam flow excited vibration in seals is the sharp changes of phase difference caused by pressure fluctuations.

High impedance fault detection method based on improved Mayr Arc model and fitting curve coefficients

To solve the problem of weak transient fault currents and significant nonlinear characteristics caused by arcs in resonant grounding systems, proposing a high-impedance fault (HIF) detection method based on an improved Mayr arc model and fitting curve coefficients. Firstly, to address the issue of low accuracy in simulating fault waveforms in existing HIF models, construct an improved arc model based on Mayr and control the parameter values under different feature dimensions, achieving accurate simulation of arc waveforms. Secondly, based on the impedance characteristics of the feeder, analyze the phase frequency characteristics, determine the first capacitive frequency band, and then determine the cutoff frequency of the Chebyshev filter to improve the ability of waveform feature extraction and fault recognition. Finally, by fitting the voltage and current geometric characteristic curve within the characteristic frequency band, using the least squares method and the quadratic coefficient values of the fitting curve to construct detection criteria, accurate detection of HIF is possible. Research shows that the improved arc model can fully characterize the current arc waveform under various working conditions. Simulations and real-world measurements verify that HIF can be accurately detected using the quadratic coefficient value of the fitting curve.

Fractional order modelling and optimal control of dual active bridge converters

As the construction of new power systems centred around renewable energy gains traction, the installed capacity of new energy sources has experienced explosive growth. Research has shown that the actual external characteristics of inductors and capacitors in circuits exhibit fractional order characteristics. As a core device in dual active bridge converters, the non-integer order of inductors and capacitors has an important impact on their dynamic performance, frequency domain characteristics, and control system design. This paper conducts modelling and control research on dual active bridge converters based on fractional-order calculus theory. First, based on the definition of fractional-order calculus, according to the operating mode of the fractional-order dual active bridge converter and the characteristics of fractional-order components, The fractional-order state space average model was established, and the influence of the order of inductance and capacitance on the amplitude frequency characteristics, phase frequency characteristics and dynamic performance of the converter was analyzed. Secondly, the average model and circuit model were built on the MATLAB/Simulink simulation platform, and the simulation results under different fractional orders were compared. Finally, in order to further improve the control performance of the converter, a fractional-order P I λ control strategy is designed based on the established state space average model of the fractional-order dual active bridge converter and based on the transfer function from the control to the output of the fractional-order dual active bridge converter. The research results show that the fractional-order model can more accurately describe the actual characteristics of the converter. In addition, the fractional-order controller P I λ enables the fractional-order dual active bridge converter to obtain better robustness and improve the dynamic performance of the converter.

Accurate detection method of traveling wave shape based on EEMD and L1 norm regularization

Aiming at the problem of waveform distortion of the secondary traveling wave obtained from the primary traveling wave signal transmitted by the voltage traveling wave sensor, an accurate detection method of voltage traveling wave based on ensemble empirical mode decomposition (EEMD) and L1 norm least squares regularization is proposed in this paper. Firstly, the forward transfer function model of the specialized voltage traveling wave sensor is established, and the inversion model is derived to analyze the phase frequency and amplitude frequency characteristics of the secondary traveling wave after transmission. EEMD is used to decompose the secondary traveling wave into the intrinsic modal function (IMF) components of different frequency bands. The L1 norm least square regularization inversion algorithm was used to invert each IMF component. Finally, the IMF' components after inversion are synthesized to obtain the primary traveling wave. Simulation and experimental results demonstrate that the proposed method is not affected by noise, mode aliasing effect and regularization parameter accuracy, and the obtained waveform has high similarity to the simulated waveform, which enables precise identification of fault traveling wave.

Design of the Monopulse Feeding Network for a Slotted Waveguide Array on an Annular Disk

Design of a monopulse feeding network including a compact power distribution network and a monopulse comparator for a dual polarization slotted waveguide array fabricated on an annular disk is presented in this paper. As the slotted waveguide array is arranged on an annular disk, the feeding network is more complicated than that of a regular array such as a rectangular array. The design details of some key waveguide components, such as the compact assembly of H-plane T-junctions and E-plane elbows used to connect power distribution networks and radiation waveguides, are provided. Quasiplanar magic tees are designed and used to construct the compact sum and difference comparator. The antenna system contains two comparators, which are used to generate sum and difference beams for horizontal polarization and vertical polarization, respectively. Finally, the monopulse slotted waveguide array antenna is divided into two modules, a comparator module and an antenna module (including power distribution network), and fabricated with the layered processing and bonding process. The comparator module is measured using a network analyzer to verify its amplitude-frequency characteristics and phase-frequency characteristics. Screwing the comparator module and the antenna module together, a monopulse slotted waveguide array antenna is obtained, and the sum beam and difference beam characteristics of the antenna are measured in a microwave chamber and presented.

Electrical characteristics of a fractional-order 3 × n Fan network

In this article a new achievement of fractional-order 3 × n Fan networks is presented. In the first step, the RT-I method is used to derive the general formulae of the equivalent impedance of fractional-order 3 × n Fan networks. In the second part, the effects of five system parameters (L, C, n, α and β) on amplitude-frequency and phase-frequency characteristics are analyzed. At the same time, the amplitude-frequency and phase-frequency characteristics of the fractional order 3 × n Fan network are revealed by Matlab drawing. This work has important theoretical and practical significance for resistor network models in the field of natural science and engineering technology.

Determining vertical oscillations of front-plow tractor without support wheel

The object of this study is a tractor with a front plow without a support wheel. One way to avoid the use of ballast is to use front-mounted plows that operate under the "push" mode. As a rule, such plows are equipped with at least one supporting wheel. The presence of the latter complicates the structure of the plow and, of course, affects the degree of vertical load on the steered wheels of the mobile vehicle. With the help of the constructed mathematical model and the corresponding amplitude and phase frequency characteristics, the dynamics of vertical oscillations of the front axle of a tractor with a front mounted plow without a support wheel were investigated. Vertical fluctuations of the total force acting on the tractor from the side of the plow were considered as a disturbing influence. According to the simulation results, an increase in the vertical load of the front axle of the tractor by 600 kg causes a desired decrease in the value of the amplitude and an increase in the phase of external disturbances of the dynamic system. The higher the frequency of disturbance oscillations, the more acceptable these characteristics become. It was established that in order to improve the response of the studied dynamic system to disturbances, it is necessary to reduce the stiffness coefficient of the tires of the front wheels. In practice, this is achieved by adjusting the air pressure in the tires. The amplitude-frequency characteristics of the system almost do not change when the damping coefficient of the tires of the front wheels of the tractor is increased in the range from 1 to 3 kN·s/m, while the phase-frequency characteristics improve. This is especially noticeable at the frequencies of oscillations of the disturbing influence in the range of 0–10 s-1. The results could be used as a basis for evaluating the efficiency of tractors with a front plow without a support wheel in tillage operations. Such efficiency can be achieved under the condition of practical implementation of the recommendations proposed in this paper regarding the selection of design parameters of tires for the front wheels of the tractor

Justification of the Unit Design Diagram for Mowing Agricultural Crops Simultaneously with Their Stuble Chopping

Abstract The two-phase method is quite widespread when harvesting grain crops and forage grasses. For its implementation, farmers prefer harvesting units with a front-mounted header. The main disadvantage of such units is that after their passage in the space between the swaths of mown crops, open soil falls under the direct influence of sunlight. Subsequently, this leads to an intensive loss of its moisture. A harvesting unit has been designed to eliminate this shortcoming, consisting of a tractor with a front harvester and a soil-cultivating machine (disc harrow) mounted at the rear. The latter chops stubble and soil in the space between the swaths of the mowed crop, contributing to soil moisture conservation. In the diagram plan, the tillage machine can have a swivel or fixed conjunction with the tractor in a horizontal plane. A mathematical model of the harvesting unit plane-parallel movement in the horizontal plane has been designed to choose these conjunctions better. In the study, it is used to analyze the corresponding amplitude (AFC) and phase (PFC) frequency characteristics of a dynamic system when it is working out a control action in the form of the sighting point transverse shift. As a mathematical modeling result, it was found that the fixed conjunction of a tillage machine with a tractor is preferable. In this case, the natural AFC practically approaches the perfect one for servo dynamical systems. The correlation degree between the tractor‘s steered wheels‘ rotation and heading angles increases by almost 37%. As a result, this leads to a significant decrease in this parameter variance fluctuations, which contributes to an increase in the harvesting unit controllability movement as a whole.

Sine Approximation-Based Comparison Method for Determining the Phase–Frequency Characteristic of Analog-to-Digital Converters

The analog-to-digital converters (ADCs) have been widely used in the applications of such as precision metrology, motion control, position and pose estimation, whose phase-frequency characteristic usually brings in an inevitable influence. In order to ensure the performance of these applications, the phase-frequency characteristic of ADCs has to be definitely determined before they are used. In this study, a new sine approximation-based comparison measurement method is presented, which accurately deter- mines this characteristic by utilizing the linear frequency modulation signal with high carrier frequency and narrow bandwidth instead of the sinusoidal signal. Experimental results demonstrate that the presented method is able to obtain the satisfactory accuracy for the phase-frequency characteristic of general ADCs and promote the improve- ment of their applications.

Frequency criterion for stability «as a whole» of modulation-type pulse voltage converters according to Lyapunov

Background. The use of methods for researching and designing stable nonlinear dynamic systems by constructing the frequency characteristics of the loop gain of the negative feedback of a pulsed voltage converter through time characteristics obtained by numerical methods for solving nonlinear differential equations that describe electromagnetic processes in the converter takes a lot of time and has low accuracy in calculating optimal modes, when you need to calculate hundreds of options.
 Aim. Therefore, it seems necessary to further develop the theory of stability of modulation-type pulse voltage converters using frequency stability criteria, Lyapunov functions, amplitude and phase frequency characteristics of the converter loop gain.
 Methods. Stability in the «small» is solved using linearized models, which are constructed using the so-called first Lyapunov method - the «first approximation» method. The second method for studying the stability of nonlinear dynamic systems is the harmonic linearization method, when the nonlinear element is replaced by a harmonically linearized link with a transmission coefficient only for the first harmonic.
 Results. The Lyapunov function for a pulse voltage converter with nonlinear relay-type elements was found. Conclusion. The results obtained in the work make it possible to simplify the design of Lyapunov-stable pulse voltage converters through the use of the method of amplitude-frequency characteristics used for stationary linear systems.

Modeling of dynamic characteristics for hydraulic drive under nonstationary load

The methodology for estimating the transient response and frequency characteristics for volumetric hydraulic drive under nonstationary load is proposed. The methodology is based on obtaining the transfer function for the speed of movement for the drive output link according to the load. To obtain the transfer function, the nonlinear mathematical model of translational hydraulic drive has been compiled, including the motion equations for the hydraulic cylinder piston, the equations of continuity in the pressure and drain cavities, taking into account compressibility of the working fluid. Hydraulic losses are described by quadratic dependence. In addition to the generally arbitrary load acting on the hydraulic cylinder rod, the resistance force proportional to the speed of movement of the hydraulic cylinder piston is also considered. By linearization of the mathematical model, the transfer function for the speed of movement on load is established in the form of fractional rational function of the third order. The dependences for calculating the coefficients of the transfer function is determined. The example of calculating the transient response, amplitude and phase frequency characteristics is given. The presented results can be used in the design and modernization of technological equipment with hydraulic drives.

ДОСЛІДЖЕННЯ ЗАЛЕЖНОСТІ ШВИДКОСТІ ПЕРЕДАВАННЯ ДАНИХ В СИСТЕМІ BPL ВІД КІЛЬКОСТІ НАВАНТАЖЕНИХ ВІДГАЛУЖЕНЬ МЕРЕЖІ ВНУТРІШНЬОБУДИНКО-ВОЇ ЕЛЕКТРОПРОВОДКИ

The work is devoted to research of the characteristics of Broadband over Power Lines (BPL) transmission systems (TS) when working on domestic house electrical wiring networks (HEWN). The object of research is the component of domestic electrical wiring network (HEWN) – branch. The influence of the branch load resistance on attenuation and data transmission rate acros HEWN fragment with one branch in the cases of the idle and short type of load, the load with active and reactive resistance type in the case of traditional orthogonal harmonic signals and generalized class orthogonal harmonic signals used in BPL TS was reviewed previously. The influence of number and position of active and reactive character load of branch on attenuation, phase and data transmission rate acros HEWN fragment in the case of traditional orthogonal harmonic signals on BPL TS uses is researched in the paper. Calculations are carried out and the results of research of frequency characteristics of attenuation, phase and data transmission rate acros HEWN fragment, formed with widely used in Ukraine PPV type wire (the cross-sectional area of the conductor is 2,5 mm2), in the range of 2 MHz to 30 MHz are given. The research of dependence between BPL TS data transmission rate acros HEWN fragment (in the case of 25ºMHz-PB frequency plan uses) and number and position of the load branches in the case of the idle type of load, the load with active and reactive resistance type (R, L, C) that connected to the poles of the load on the branch is researched in the paper. A comparison of the data transmission rate acros HEWN fragment for different numbers and variants of the position of the loaded branches that poles of which connected to the loads of different types (idle, R, L, C) was made.

Determining the dynamic characteristics of a class B fire in the case of extinguishing by water spray

The object of this study is a class B fire, which is extinguished with sprayed water. The subject of the study is the characteristics of class B fires when they are extinguished with sprayed water. Diffusion burning of a flammable liquid is considered as such a fire, and its extinguishing is carried out by cooling the flame. Heat and oxygen balance equations are used to build a mathematical model describing the fire extinguishing process. The components of the heat balance equation are the power of heat during heat release due to the chemical reaction of liquid combustion and the power of heat dissipated to the environment. The second component takes into account heat removal due to radiation, convection, and evaporation. The component of removed heat due to evaporation takes into account the Sreznevsky constant. The mathematical model that describes the process of extinguishing a class B fire is built in the class of models belonging to differential equations with constant coefficients. Analytical expressions were obtained for these static and dynamic coefficients, which include thermophysical, kinematic, and geometric parameters of the flame and fire extinguishing agent. To determine these characteristics, the constructed mathematical fire model was transformed using the integral Laplace transform. The dynamic characteristics of the fire were obtained in the time domain – the transient function of the fire, and in the frequency domain – the amplitude-frequency and phase-frequency characteristics of the fire. It is shown that the parameters of these dynamic characteristics should be determined experimentally. Experimental methods for determining parameters of dynamic fire characteristics have been devised. The presence of dynamic characteristics of class B fire makes it possible to spread the proven methods of the theory of control systems to design effective fire extinguishing systems

Research on Phase-to-phase Fault Location Method of Active Distribution Network

Due to the weak feed characteristic of active distribution networks, the sensitivity of the original fault phase selection method and the accuracy of fault location are decreased. Most of the existing fault section location methods focus on the phase selection and location of the earth fault, and there is a lack of relevant research on the location of the fault section to the phase-to-phase fault. Moreover, most of the methods need to install the signal measuring device in the system as large as possible, which is not economical. The operation condition of active distribution networks is complicated, the fault characteristics are weak, and the location result is easily affected by non-fault disturbances such as DG access capacity and location. In this paper, the phase-to-phase fault of active distribution networks is taken as the research object. Firstly, phase current and zero-sequence current combined criterion is used for fault phase selection, and then combined with the phase-frequency characteristics of mode impedance of distribution line and photovoltaic power line, a fault section location method based on transient characteristic frequency band is proposed, which is not affected by non-fault disturbance such as photovoltaic control strategy and DG access capacity and location. Simulation results show that the method is effective.

Development of the theory of root crop head cleaner movement in the longitudinal-vertical plane mounted behind a wheeled tractor

The relevance of developing analytical methods for studying the stability of root crop cleaners on tractors is determined by the need to improve the efficiency and quality of root crop head cleaning, as this affects the quality of the final product and its marketable properties. The research aims to increase the stability of the cleaner movement by constructing a mathematical model of its oscillatory motion in the longitudinal-vertical plane and its numerical solution to determine the influence of parameters in response to external disturbances. To achieve this goal, a new theory of the movement of a root crop head cleaner in the longitudinal-vertical plane, mounted behind a wheeled tractor, under the influence of the disturbing effect of irregularities in the longitudinal profile of the soil surface on the amplitude and phase frequency characteristics of its angular oscillations was developed. Using numerical calculations carried out on a personal computer, the conditions were found under which the stability of the cleaner’s movement in the specified plane will increase when the stiffness coefficient of the pneumatic tyres of the doubler wheels is 315 kN×m–1. This result is achieved when the pressure in the pneumatic wheel tyres is 135 kPa. As for the damping characteristics of the doubler wheel tyres, which are determined by the coefficient μ, it was found that when it changes from 350 N×s×m–1 to 1350 N×s×m–1, there is an invariance of the delay in the reaction of the cleaner to the disturbing effect when its frequencies change from 0 to 24 s–1. It was also found that the influence of the geometric dimensions of the cleaner is insignificant in the range of frequencies of oscillations of the ordinates of the longitudinal profile of soil surface irregularities from 0 to 24 s–1. This follows from the nature of changes in the obtained amplitude-frequency and phase-frequency characteristics. The methodology for constructing a mathematical model of the plane-parallel oscillatory motion of the cleaner can be used in similar analytical studies of other agricultural machines mounted on a wheeled aggregating tractor

Изучение принципов построения широкополосной колебательной СВЧ системы на примере резонатора Фабри-Перо

In telecommunications and radar systems of the centimeter and millimeter wave ranges, span klystrons are widely used as medium and high power amplifiers. The use of high-quality resonators makes it possible to realize high efficiency and amplification factors. However, typical designs of 2 - 4 resonator klystrons have a bandwidth of 0.1 - 0.5 % due to the need to use resonators with a high Q – factor. The well-known method of expanding the amplified frequency band in the centimeter range up to 7 – 12 % and in the millimeter range up to 1 - 2 % consists in tuning the frequency of the intermediate klystron resonators by several percent of the central amplification frequency. But in this case, it is required to use 10 - 12 resonators. The authors of the work discovered that when a millimeter range electromagnetic wave is reflected from an electrodynamics system in the form of a metal film on the surface of a semiconductor layer, the input resistance phase-frequency characteristic of this system consists of a chain of frequency intervals with turnings from a positive phase-frequency characteristic to a negative one and vice versa. The possibility of constructing a phase shifter with a negative phase frequency response based on this phenomenon is demonstrated and its application for expanding the resonant frequency band is considered on the example of the Fabry - Perot interferometer model. This resonator contains a phase shifter in the form of a semiconductor layer F with a thickness DF, a conductivity σF, a relative dielectric eF and a magnetic mF permeability. The outer surface of the layer F contains a metal mirror, and the inner surface is adjacent to the layer W. The layer W which has the thickness of DW, eW, mW forms the internal space of the resonator. The external environment I with mI and eI. adjoins the layer W. A plane electromagnetic wave propagates in I media so that it excites the resonator at a wavelength of l0. The use of a phase shifter makes it possible to increase the resonant wavelength band Δl/l0 by 2 - 4 times and with an electromagnetic field amplification coefficient |G(l)| in the W layer by 10 - 20 times (the value of Dl/l0 corresponds to 0.707 max |G(l0)|). An increase of σF leads to an amplitude-frequency characteristic transforming of the field gain function G(l0) from two maxima to one maximum form with a transition through a flat top. In this case max |G(l0)| decreases and Dl/l0 increases. For the case, when the function |G(l)| has a flat top, an increase in the wave resistance ρW of the layer W with a corresponding decrease in sF and optimal values of DW leads to an increase in |G(l0)|. When this occurs, Dl/l0 becomes lower.