Continuous Frequency Range Research Articles

Design of an efficiency enhanced wideband Doherty power amplifier based on synthesising of a modified harmonic‐control load modulation network

AbstractA design of a broadband Doherty power amplifier (DPA) using a novel harmonic control network (HCN) is presented. The DPA structure focused on manipulating harmonic components using this new HCN to enhance the bandwidth of operation and power efficiency. The proposed HCN combines a third harmonic suppression network (THSN) with the second harmonic impedance inverter circuit (SHIIC). In the design, the second harmonic component of the main transistor and the peaking transistor are short‐circuited by their associated SHIIC. Additionally, the carefully designed SHIIC and THSN circuit placed between the main and peaking transistors realise open circuit conditions at the third harmonic for both transistors at the saturation state and back‐off regions. Side by side with the aid of the properly designed post‐matching tuned network (PMTN), these harmonic loading conditions make both amplifiers to operate in continuous Class‐F modes with enhanced‐added efficiencies over wideband conditions. As a result, a succession of highly efficient DPA modes can be formed over a continuous frequency range in the full Doherty region, resulting in a reduced‐size enhanced power efficiency wideband DPA. For verification, a wideband DPA operating from 1.1 to 1.8 GHz was designed and implemented using the proposed topology. The measured drain efficiency of the implemented DPA at 6‐dB back‐off is 52.5%–67.5%, while the saturated power across the specified bandwidth is 43–43.7 dBm. The fabricated DPA exhibits an average efficiency of 48.7%–59.4%, when supplied by a 40‐MHz long‐term evolution (LTE) signal with a 7.5‐dB peak‐to‐average power ratio (PAPR). Performing digital pre‐distortion (DPD) improves the adjacent channel power ratio (ACLR) from −25.8 dBc to −47.6 dBc.

Nanoscale Rheology: Dynamic Mechanical Analysis over a Broad and Continuous Frequency Range Using Photothermal Actuation Atomic Force Microscopy.

Polymeric materials are widely used in industries ranging from automotive to biomedical. Their mechanical properties play a crucial role in their application and function and arise from the nanoscale structures and interactions of their constitutive polymer molecules. Polymeric materials behave viscoelastically, i.e., their mechanical responses depend on the time scale of the measurements; quantifying these time-dependent rheological properties at the nanoscale is relevant to develop, for example, accurate models and simulations of those materials, which are needed for advanced industrial applications. In this paper, an atomic force microscopy (AFM) method based on the photothermal actuation of an AFM cantilever is developed to quantify the nanoscale loss tangent, storage modulus, and loss modulus of polymeric materials. The method is then validated on styrene-butadiene rubber (SBR), demonstrating the method's ability to quantify nanoscale viscoelasticity over a continuous frequency range up to 5 orders of magnitude (0.2-20,200 Hz). Furthermore, this method is combined with AFM viscoelastic mapping obtained with amplitude modulation-frequency modulation (AM-FM) AFM, enabling the extension of viscoelastic quantification over an even broader frequency range and demonstrating that the novel technique synergizes with preexisting AFM techniques for quantitative measurement of viscoelastic properties. The method presented here introduces a way to characterize the viscoelasticity of polymeric materials and soft and biological matter in general at the nanoscale for any application.

Mechanical characterization of human skin—A non-invasive digital twin approach using vibration-response integrated with numerical methods

This paper proposes an innovative approach to identify elastic material properties and mass density of soft tissues based on interpreting their mechanical vibration response, externally excited by a mechanical indenter or acoustic waves. A vibration test is performed on soft sheets to measure their response to a continuous range of excitation frequencies. The frequency responses are collected with a pair of high-speed cameras in conjunction with 3-D digital image correlation (DIC). Two cases are considered, including suspended/fully-free rectangular neoprene sheets as artificial tissue cutout samples and continuous layered human skin vibrations. An efficient theoretical model is developed to analytically simulate the free vibrations of the neoprene artificial sheet samples as well as the continuous layered human skins. The high accuracy and validity of the presented analytical simulations are demonstrated through comparison with the DIC measurements and the conducted frequency tests, as well as a number of finite element (FE) modeling. The developed analytical approach is implemented into a numerical algorithm to perform an inverse calculation of the soft sheets' elastic properties using the imported experimental vibration results and the predicted system's mass via the system equivalent reduction/expansion process (SEREP) method. It is shown that the proposed frequency-dependent inverse approach is capable of rapidly predicting the material properties of the tested samples with high accuracy.

Experimental Investigation on Electric and Dielectric Properties of Thallium Ions Doped Sodium Zinc Phosphate Glass

Sodium zinc phosphate glasses modified by Tl2O addition of composition Na2−xTlxZnP2O7 (x = 0, 0.005, 0.01, and 0.015) are synthesized following the melt quenching technique. The structure of the glass samples is analyzed by the Fourier transform infrared absorption spectroscopy. The results suggest that the phosphate network is polymerized by the addition of Tl+ ions. The electrical conductivity, electric modulus, and dielectric constant characteristics of the glasses are measured over a wide continuous frequency range of 10−2 Hz–1 MHz and in the temperature range 293–473 K by the impedance spectroscopic method. The ac conductivity data are analyzed following the power law exponent (S) and the proposed correlated barrier hopping mechanism (CBH) is the most suitable conduction mechanism in the studied compositions. The electrical modulus formalism is applied to analyze the electric data to study their dielectric relaxation. Non‐Debye type relaxation is obtained. From the obtained results, the present glass can be used as a high‐energy capacitor.

A Concise and Time-efficient Method for Characterizing the Permittivity of Unknown Materials

We propose a simplified and time-efficient methodology to characterize the permittivity of unknown materials. Based on the transmission line method, this method enables permittivity extraction using a small number of dielectric materials under test (MUT). It is fully compatible with conventional electromagnetic measurement environments and does not require any modification, since the extraction is conducted simply by replacing the MUT above the coplanar waveguide (CPW). The proposed approach enables a more concise and faster measurement process compared to conventional methods previously reported in the literature. This method is then numerically and experimentally verified through various MUTs that have different permittivities or thicknesses. The results are determined to be valid over a continuous frequency range of 1.0 GHz–30.0 GHz with an average accuracy of over 95.0%.

A novel method for dominant oscillation estimation and harmony quantification through spectral leakage suppression

Several methods exist for the quantification of the underlying oscillation within a time series in terms of frequency, amplitude and phase. The evaluation of the discrete Fourier transform is limited to integer periods and therefore prone to spectral leakage. Other approaches detect the dominant oscillation on a continuous frequency range, but lead to a nonlinear optimization problem, resulting in high requirements for the solving algorithm. We propose a novel direct method for the quantification of the dominant oscillation based on a characteristic value – called “DOH” – which is defined both in frequency and time domain. This enables the assessment of the harmony and periodicity and is discussed for different signal-to-noise ratios and the number of periods. By iteratively calculating the DOH for a successive truncated time series, the method – called “LSDOH” – is extended to a high frequency resolution. The algorithm suppresses spectral leakage, though it does not require any windowing. The method is compared to the DFT based on a Monte Carlo simulation. It is shown that the proposed identification method is highly accurate in determining the oscillation parameters of a time series overlaid by different noise levels, especially for high sampling frequencies.

Dynamic damping of vibrations of a solid body mounted on viscoelastic supports

The study of the problem of damping vibrations of a solid body mounted on viscoelastic supports is an urgent task. The paper considers the problem of reducing the level of vibrations on the paws of electric machines using dynamic vibration dampers. For this purpose, the paw of electric machines is represented in the form of a subamortized solid body with six degrees of freedom mounted on viscoelastic supports. The aim of the work is to develop calculation methods and algorithms for studying the oscillations of the resonant amplitudes of a solid body mounted on viscoelastic supports. Dynamic oscillation (vibration) damping method consists in attaching a system to the protected object, the reactions of which reduce the scope of vibration of the object at the points of attachment of this system. Applying the D’Alembert principle, the equations of small vibrations of a solid with dampers are derived. For practical calculations, a simplified system of equations was obtained that takes into account only three degrees of freedom. Numerical calculations were carried out on a computer to determine the amplitude-frequency characteristics of the main body. Numerical experiments were carried out using the Matlab mathematical package. Considering that a solid body is characterized by vibration, as a rule, in a continuous and wide frequency range, therefore, dynamic vibration dampers are used to protect a solid body mounted on viscoelastic supports. It was found that when the damper is set at a frequency of 50 Hz, the vibration level at the left end of the frequency interval of rotary motion of the rotor-converter, decreases to 37.5 dB, and at the right end — to 42.5 dB. At a frequency of 50 Hz, the paws do not oscillate. When setting the dampers to a frequency of 51.5 Hz, the maximum vibration level does not exceed 40 dB. The optimal setting of the dampers is within the frequency of 50.60...50.70 Hz, and a two-mass extinguisher is 10–15% more efficient than a single-mass one. Thus, the paper sets the tasks of dynamic damping of vibrations of a solid body mounted on viscoelastic supports, develops solution methods and an algorithm for determining the dynamic state of a solid body with passive vibration of the object in question.

AP/HTPB combustion response simulation with a new equivalent linear system method

In the study of solid rocket motor (SRM) combustion instability, modeling and analyzing the combustion response of the solid propellant is a laborious task. We propose a new idea, an equivalent linear system method, for modeling solid propellant combustion response with three steps: first, simulating the transient combustion process under pulse pressure excitation for only one CFD case; then, treating the combustion process as a black-box and obtaining the transfer function of the combustion process from the CFD result; finally, predicting and analyzing the combustion response based on the transfer functions. For the AP/HTPB sandwich propellant withp¯=3MPa, the amplitude, duration, and direction of excitation pulses are studied. The new method is also verified, with a maximum relative error of 4.3% for burning rate response under p˜≤1MPa (as high as one-third of the pressure DC). Applicability of this new method is demonstrated for another two AP/HTPB sandwich propellants with different configuration under p¯=8MPa and p¯=10MPa, showing that the system-simulated combustion responses of burning surface temperature and burning rate are consisted well with the CFD results and the maximum relative error of burning rate response is 2.1%. Asymmetric combustion response for positive and negative pressure perturbations is a new finding based on the CFD and simulation results. Besides, a new approach using dual transfer functions is proposed to ensure high accuracy for the simulation of solid propellant combustion. The pressure-coupled response function is predicted by this method for the sandwich propellant under p¯=5MPa and p˜=20kPa within a wide continuous frequency range (0–3000 Hz). The comparison with CFD results indicates that the relative bias of Rp is less than 2%. With the proposed method, the combustion response to arbitrary pressure excitations can be simulated with high accuracy, high time-resolution, and high speed. The method shows great advantage and potential in simulating and predicting combustion instability.

Continuous-Frequency Microwave Heterodyne Detection in an Atomic Vapor Cell

Atomic heterodyne dressed by a local oscillator resonant with Rydberg transitions allows high sensitivity and robust phase measurement of a microwave electric field, but it is typically limited to detection of discrete frequencies within the narrow bandwidth of Rydberg transitions. Here we demonstrate an atomic heterodyne scheme for continuous-frequency electric field measurement based on multilevel Rydberg atoms in a room-temperature vapor cell. Driven by two off-resonant microwaves acting as a tunable local oscillator field, the heterodyne receiver can retrieve the amplitude, phase, and frequency information of signal microwave in a continuous frequency band. In our experiment, the receiver achieves an electric field sensitivity of up to $1.5\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$, 80-dB linear dynamic range, and over 1 GHz of continuous frequency range. We also demonstrate the reliable reception of continuously tunable phase-modulated carriers in the digital communication. This work will facilitate the application of atomic heterodyne in the areas such as radar technique, radio monitoring, and radio astronomy.

Red Noise in Steady‐State Multiphase Flow in Porous Media

AbstractUnderstanding the interaction between competing fluids in the pore space of rocks is key for predicting subsurface flow and trapping, such as with CO2 in a saline aquifer. These processes occur over a large span of timescales (from seconds to thousands of years), and length scales (from microns to kilometers). Understanding the link between these temporal and spatial scales will enable us to interpolate between observations made at different resolutions. In this work we explore the temporal scales present during macroscopically steady‐state multiphase flow in a porous carbonate rock using differential pressure measurements acquired over a period of 60 min. Nitrogen and brine were injected simultaneously into a sample 5 mm in diameter and 21 mm in length. We observe a cascade of timescales in the pressure differential that is, a continuous range of frequencies, with lower frequencies having greater amplitudes. We demonstrate a scaling of the spectral density with frequency of S ∼ 1/f2, or red noise, to describe the dynamics. This scaling is independent of the flow rate of the fluids or the fraction of the flow taken by water. This red, or Brownian, noise indicates a stochastic process where pressure fluctuations are seen throughout the pore space, resulting in intermittent filling of pores over a wide range of time‐scales, from seconds to minutes in these experiments. The presence of red noise suggests self‐organized critically, with no characteristic time or length scale.

Tracing the source of unsteady-state low-frequency noise based on wavelet coherence analysis

The original partial coherence analysis method can be used to analyze the contributions between different noise sources and field points under steady-state conditions. Nevertheless, coherence analysis cannot be used to deal with unsteady-state signals because the signals are time-varying. In this paper, the method of panel contribution under unsteady-state conditions based on wavelet coherence analysis is proposed to determine the largest noise contribution in the cab. First, the unsteady-state simulation signals are analyzed by wavelet coherence theory. This step not only verifies the effectiveness but also points out that wavelet coherence is more superior to crossed wavelet. Second, the measured unsteady-state signals of the eight measuring points are processed by time-frequency wavelet coherent analysis. According to the obtained two-dimensional time-frequency diagrams, the contribution of different panels to the noise of measuring field points in the continuous frequency range can be found out. Then, the total contribution coefficient sum of each panel in a certain frequency band is calculated. Finally, the above analysis results are used to determine the panels with the largest contribution to the cab noise. The corresponding noise reduction scheme is also proposed. The results show that the overall sound pressure level is obviously decreased after optimization. The noise in the cab is reduced by 4.5dBA ∼ 7dBA. The effectiveness of this method has been further verified by the above results.

A continuous broadband electromagnetic energy harvester based on amplitude and phase adjustments

Broadening the bandwidth of vibration energy harvesters is a critical issue for their practical implementations. Although utilizing multi-degree-of-freedoms is a frequently used solution to widen the operating frequency range, the resultant effective bandwidth could consist of discrete peaks (existing local minimum points lower than the half-power level) if the modal amplitudes have large differences at different frequencies. To solve these problems, we designed a new electromagnetic multi-modal energy harvester, which works in a broad and continuous low-frequency bandwidth. This is achieved by attaching the magnet and the coil to a compliant frame integrated with two different kinked beams, respectively. In this way, the voltage can be generated in a continuous and wide frequency range by adjusting the amplitudes and phases of the magnet and the coil in different modes according to a proposed design requirement. Finite element results and experimental results are in good agreement with each other, which validate the performance of the proposed harvester. The experimental results demonstrate that the half-power bandwidth can be achieved in the range of 15.0 Hz and the maximum peak power is 1.56 mW at the center frequency of 40.5 Hz under base excitation of the root-mean-square acceleration of 0.24 g. The broadband and high power density feature are also validated in a random excitation test, so that this harvester has great potential for practical applications.

Analyzing the Intrinsic Magnetic Field in the Galactic Center Radio Arc

Abstract The Radio Arc is a system of organized nonthermal filaments (NTFs) located within the Galactic center (GC) region of the Milky Way. Recent observations of the Radio Arc NTFs revealed a magnetic field that alternates between being parallel and rotated with respect to the orientation of the filaments. This pattern is in stark contrast to the predominantly parallel magnetic field orientations observed in other GC NTFs. To help elucidate the origin of this pattern, we analyze spectro-polarimetric data of the Radio Arc NTFs using an Australian Telescope Compact Array data set covering the continuous frequency range from ∼4 to 11 GHz at a spectral resolution of 2 MHz. We fit depolarization models to the spectral polarization data to characterize Faraday effects along the line of sight. We assess whether structures local to the Radio Arc NTFs may contribute to the unusual magnetic field orientation. External Faraday effects are identified as the most likely origin of the rotation observed for the Radio Arc NTFs; however, internal Faraday effects are also found to be likely in regions of parallel magnetic field. The increased likelihood of internal Faraday effects in parallel magnetic field regions may be attributed to the effects of structures local to the GC. One such structure could be the Radio Shell local to the Radio Arc NTFs. Future studies are needed to determine whether this alternating magnetic field pattern is present in other multi-stranded NTFs, or is a unique property resulting from the complex interstellar region local to the Radio Arc NTFs.

Protostellar Interferometric Line Survey of the Cygnus X region (PILS-Cygnus)

Context. Complex organic molecules (COMs) are commonly detected in and near star-forming regions. However, the dominant process in the release of these COMs from the icy grains – where they predominately form – to the gas phase is still an open question. Aims. We investigate the origin of COM emission in a high-mass protostellar source, CygX-N30 MM1, through high-angular-resolution interferometric observations over a continuous broad frequency range. Methods. We used 32 GHz Submillimeter Array observations with continuous frequency coverage from 329 to 361 GHz at an angular resolution of ~1″ to do a line survey and obtain a chemical inventory of the source. The line emission in the frequency range was used to determine column densities and excitation temperatures for the COMs. We also mapped out the intensity distribution of the different species. Results. We identified approximately 400 lines that can be attributed to 29 different molecular species and their isotopologues. We find that the molecular peak emission is along a linear gradient, and coincides with the axis of red- and blueshifted H2CO and CS emission. Chemical differentiation is detected along this gradient, with the O-bearing molecular species peaking towards one component of the system and the N- and S-bearing species peaking towards the other. The chemical gradient is offset from but parallel to the axis through the two continuum sources. The inferred column densities and excitation temperatures are compared to other sources where COMs are abundant. Only one deuterated molecule is detected, HDO, while an upper limit for CH2DOH is derived, leading to a D/H ratio of <0.1%. Conclusions. We conclude that the origin of the observed COM emission is probably a combination of the young stellar sources along with accretion of infalling material onto a disc-like structure surrounding a young protostar and located close to one of the continuum sources. This disc and protostar are associated with the O-bearing molecular species, while the S- and N-bearing species on the other hand are associated with the other continuum core, which is probably a protostar that is slightly more evolved than the other component of the system. The low D/H ratio likely reflects a pre-stellar phase where the COMs formed on the ices at warm temperatures (~30 K), where the deuterium fractionation would have been inefficient. The observations and results presented here demonstrate the importance of good frequency coverage and high angular resolution when disentangling the origin of COM emission.

Time-domain formulation of electromagnetic scattering based on a polarization-mode expansion and the principle of least action

An approach to the full wave analysis of the time evolution of the polarization induced in the electromagnetic scattering from dispersive nonmagnetic particles is presented. It is based on the combination of the Hopfield model for the polarization field, the expansion of the polarization field in terms of static longitudinal and transverse modes of the particle, the expansion of the radiation field in terms of transverse wave modes of free space, and the principle of least action. The polarization field is linearly coupled to the electromagnetic field. The losses of the matter are described thorough a linear coupling of the polarization field to a bath of harmonic oscillators with a continuous range of natural frequencies. The set of linear ordinary differential integral equations of convolution type of the overall system is reduced by eliminating both the radiation degrees of freedom and the bath degrees of freedom, and the reduced system of equations is studied. The role played by the radiation field in the coupling between the longitudinal and transverse mode amplitudes of the polarization is described. The principal characteristics of the temporal evolution of the mode amplitudes are found as the particle size varies, including the impulse response. Results are presented for the analytically solvable spherical particle. The proposed approach leads to a general method for the analysis of the temporal evolution of the polarization field induced in dispersive particles of any shape, as well as for the computation of transients and steady states.

Optimization of a type of elastic metamaterial for broadband wave suppression

The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.

Electrical conductivity and dielectric properties of rare earth ions (Ce3+, Pr3+ and Eu3+) doped in zinc sodium phosphate glass

The zinc phosphate glass (composition Na2–3xMxZnP2O7) doped with different rare earth ions (x = 1 mol% where M = Ce, Pr and Eu), were synthesized by the classical melting and quenching processes. Electrical and dielectric properties including dielectric constantε′(ω), loss tangenttanδ, as well as electric conductivityσac, have been investigated over a wide continuous frequency range from 10−2 Hz to 106 Hz over a temperature range 283 K to 473 K using complex impedance spectroscopy (CIS). The results revealed that the conductivity decreases and activation energy increases with the ionic radii of cations (from Eu3+to Ce3+) likely due to the size mismatch. This behaviour could be attributed to the depolymerization of the glass network by Eu3+. This induces the decrease of the electrostatic binding and strains energies facilitating the passage of sodium ions. The average value of the power law exponent s is interpreted by the correlated barrier hopping (CBH) model.

Rheology of rounded mammalian cells over continuous high-frequencies

Understanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1–40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

Design and characterization of microstrip patch antennas for high-Tc superconducting terahertz emitters.

We designed and characterized a microstrip pattern of planar patch antennas compatible with a cuprate high-Tc superconducting terahertz emitter. Antenna parameters were optimized using an electromagnetic simulator. We observed repeatable sub-terahertz emissions from each mesa fabricated on identical Bi2Sr2CaCu2O8+δ base crystals in a continuous frequency range of 0.35-0.85 THz. Although there was no significant output power enhancement, a plateau behavior at a fixed frequency was observed below 40 K, indicating moderate impedance matching attributable to the ambient microstrip pattern. A remarkably anisotropic polarization at an axial ratio of up to 16.9 indicates a mode-locking effect. Our results enable constructing compactly assembled, monolithic, and broadly tunable superconducting terahertz sources.

Chirped pulse propagation in a quasi-PT-symmetric medium with a broadband exceptional-point condition.

The boundary problem of dynamical Bragg diffraction of a chirped optical pulse in a dispersive quasi-PT-symmetric photonic crystal (PhC) in the Laue geometry ("on transmission") is solved by the analytical spectral method. It is shown that, in a quasi-PT-symmetric medium, in which an inhomogeneous spectral line width is much larger than the spectrum of investigated field, the exceptional-point (EP) condition is realized in a wide continuous frequency range, i.e., so-called broadband exceptional-point (BEP) condition takes place. If the Bragg condition is satisfied in a much narrower spectral range than the pulse spectrum, it leads to dramatic changes in the propagation dynamics and parameters of broadband chirped pulses in a quasi-PT-symmetric PhC. Indeed, for a positive Bragg angle of incidence in the case of diffraction in the Laue geometry, the entire spectrum of a broadband chirped pulse fulfills the BEP condition. The diffractionally reflected wave is absent in the BEP regardless of whether the Bragg condition is satisfied, and the pulse propagates as in a homogeneous conservative medium, i.e., without diffraction, gain and loss - unidirectional invisibility. When the sign of the angle of incidence changes, a unidirectional enhancement of the chirped diffracted pulse is observed in that part of it whose frequency simultaneously satisfies both the BEP condition and the Bragg condition. The rest part of the pulse, for which the Bragg condition is not satisfied, propagates as in the case of a positive angle of incidence - there is no diffracted wave. With a smooth change in the angle of incidence of the chirped pulse, a change in frequency that satisfies the Bragg condition occurs and, as a consequence, a smooth change appears in the frequency of the amplified output pulse, as well as in its duration and transverse size. It is also shown that the dispersion of the group velocity of the pulse is suppressed in the frequency range of the BEP condition. Therefore, all its frequency components propagate at a speed close to the speed of light in a conservative homogeneous medium.