Electronic Phase Shifter Research Articles

A Survey of Phase Shifters for Microwave Phased Array Systems

ABSTRACTPhased Array Systems (PASs) are extensively used in radar and telecommunication systems for diverse applications, including military surveillance and wireless broadband communication. Besides, they are becoming increasingly indispensable in modern applications such as multi‐function phased array radars for weather monitoring and aircraft tracking or high‐throughput satellite systems, which aim to provide fast broadband connectivity in remote areas. Despite the numerous advantages of phased array systems with RF phase shift, including high signal‐to‐noise and signal‐to‐interference ratios, as well as low complexity, they present a few limitations, including high cost and large chip areas. The cost and size of PASs are mainly dependent on the RF phase shifters, which are essential to their operation. This article describes the different types of phase shifters (mechanical, ferromagnetic/magnetic, electromechanical, and electronic). It compares their performance metrics, highlighting that electronic phase shifters are the most common type used in modern PASs. In this regard, a comparative study of different subcategories of electronic phase shifters, such as the switched‐type, reflective‐type, loaded‐transmission line, and vector‐sum phase shifters, are explored along with their advantages, drawbacks and state‐of‐art techniques used to address their limitations. Therefore, this article may serve as a reference for research milestones on RF phase shifters.

Scale transformations in model exchange potentials in low energy electron-atom scattering

Model exchange potentials are particularly interesting to account for the indistinguishability between the projectile and target electrons in electron-atom scattering in vacuo and plasma environments. It is well known that their performance is pretty satisfactory in the high energies but also that discrepancies from the results obtained with exact exchange are found toward the zero energy limit. In this article, we examine how well established model exchange potentials based on the free electron gas approach compare to phase shifts calculated considering exchange in exact form. In particular, we show that the Hara and the semiclassical exchange potentials are able to reproduce reference low energy phase shifts through a simple scale transformation, in opposition to the previous approaches where energy dependent corrections to the local momentum were adopted. We provide the scale factors and phase shifts for electron scattering by He, Ne and Ar atoms for k< 1,0 a0−1. Such scaling factors can be determined reproducing the scattering length and the number of s-wave bound states from exact exchange calculations. We also show that the scaling procedure works for electronic densities that present the physically correct asymptotic behavior. The present results are important to the research field, since they form the basis to construction of scattering models based on optical potential approaches.

Advanced processing of differential phase contrast data: Distinction between different causes of electron phase shifts

Differential phase contrast, in its high resolution modification also known as first moment microscopy or momentum resolved STEM [1–7] , basically measures the lateral momentum transfer to the electron probe due to the beam interaction with either electrostatic and/or magnetic fields, when the probe transmits the specimen. In other words, the result of the measurement is a vector field p→(x,y) which describes the lateral momentum transfer to the probe electrons. In the case of electric fields, this momentum transfer is easily converted to the electric field E→(x,y) causing the deflection, and from ϱ=ɛ0∇⋅E→ the local charge density can be calculated from the divergence of the electric field.However, from experimental data it is known that also the calculation of the vector field’s curl ∇→×p→ in general yields non-zero results. In this paper, we use the Helmholtz decomposition (Wikipedia contributors, 2022), also known as the fundamental theorem of vector calculus, to split the measured vector fields into their curl-free and divergence-free components and to interpret the physical meaning of these components in detail. It will be shown, that non-zero curl components may be used to measure geometric phases occurring from irregularities in crystal structure such as a screw dislocation.

Flight demonstration of a miniature atomic scalar magnetometer based on a microfabricated rubidium vapor cell.

We have developed an atomic magnetometer based on the rubidium isotope 87Rb and a microfabricated silicon/glass vapor cell for the purpose of qualifying the instrument for space flight during a ride-along opportunity on a sounding rocket. The instrument consists of two scalar magnetic field sensors mounted at 45° angle to avoid measurement dead zones, and the electronics consist of a low-voltage power supply, an analog interface, and a digital controller. The instrument was launched into the Earth's northern cusp from Andøya, Norway on December 8, 2018 on the low-flying rocket of the dual-rocket Twin Rockets to Investigate Cusp Electrodynamics 2 mission. The magnetometer was operated without interruption during the science phase of the mission, and the acquired data were compared favorably with those from the science magnetometer and the model of the International Geophysical Reference Field to within an approximate fixed offset of about 550 nT. Residuals with respect to these data sources are plausibly attributed to offsets resulting from rocket contamination fields and electronic phase shifts. These offsets can be readily mitigated and/or calibrated for a future flight experiment so that the demonstration of this absolute-measuring magnetometer was entirely successful from the perspective of increasing the technological readiness for space flight.

Current noise and Keldysh vertex function of an Anderson impurity in the Fermi-liquid regime

We present a complete microscopic Fermi-liquid description for next-to-leading order transport through an Anderson impurity under a finite bias voltage $V$. It is applicable to multilevel quantum dots without particle-hole or time-reversal symmetry and is constructed based on the nonequilibrium Keldysh formalism, taking into account the current conservation between electrons in the impurity levels and the conduction bands. Specifically, we derive the formula for the current noise generated in the steady flow up to terms of order ${(eV)}^{3}$ at zero temperature $T=0$. To this end, we calculate the Keldysh vertex functions ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\sigma}{\ensuremath{\sigma}}^{\ensuremath{'}};{\ensuremath{\sigma}}^{\ensuremath{'}}\ensuremath{\sigma}}^{{\ensuremath{\nu}}_{1}{\ensuremath{\nu}}_{2};{\ensuremath{\nu}}_{3}{\ensuremath{\nu}}_{4}}(\ensuremath{\omega},{\ensuremath{\omega}}^{\ensuremath{'}};{\ensuremath{\omega}}^{\ensuremath{'}},\ensuremath{\omega})$, which depend on branches ${\ensuremath{\nu}}_{1},\phantom{\rule{4pt}{0ex}}{\ensuremath{\nu}}_{2},\phantom{\rule{4pt}{0ex}}{\ensuremath{\nu}}_{3}$, and ${\ensuremath{\nu}}_{4}$ of the time-loop contour and on spin degrees of freedom $\ensuremath{\sigma}$ and ${\ensuremath{\sigma}}^{\ensuremath{'}}$, up to linear order terms with respect to $eV$, $T$, and frequencies $\ensuremath{\omega}$ and ${\ensuremath{\omega}}^{\ensuremath{'}}$. The coefficients of these linear order terms are determined by a set of the parameters, defined with respect to the equilibrium ground state: the phase shift, static susceptibilities, and nonlinear three-body susceptibilities of the impurity electrons. The low-energy expressions of the vertex components are shown to satisfy the Ward identities with the Keldysh Green's functions expanded up to terms of order ${\ensuremath{\omega}}^{2}$, ${(eV)}^{2}$, and ${T}^{2}$. We also find that the imaginary part of the Ward identities can be described in terms of the $eV$-dependent collision integrals for a single-quasiparticle excitation and that for a single quasiparticle-quasihole pair excitation. These collision integrals ensure the current conservation of the next-to-leading order Fermi-liquid transport due to the quasiparticles with a finite damping rate.

Analog Radio Over Fiber-Aided Multi-Service Communications for High-Speed Trains

High speed trains (HST) have gradually become an essential means of transportation, where given our digital world, it is expected that passengers will be connected all the time. More specifically, the on-board passengers require fast mobile connections, which cannot be provided by the currently implemented cellular networks. Hence, in this article, we propose an analogue radio over fiber (A-RoF) aided multi-service network architecture for high-speed trains, in order to enhance the quality of service as well as reduce the cost of the radio access network (RAN). The proposed design can simultaneously support sub-6GHz as well as millimetre wave (mmWave) communications using the same architecture. Explicitly, we design a photonics aided beamforming technique in order to eliminate the bulky high-speed electronic phase-shifters and the hostile broadband mmWave mixers while providing a low-cost RAN solution. Finally, a beamforming range of 180° is demonstrated with a high resolution using our proposed system.

Nonlinear Fermi liquid transport through a quantum dot in asymmetric tunnel junctions

We study the nonlinear conductance through a quantum dot, specifically its dependence on the asymmetries in the tunnel couplings and bias voltages $V$, at low energies. Extending the microscopic Fermi liquid theory for the Anderson impurity model, we obtain an exact formula for the steady current $I$ up to terms of order ${V}^{3}$ in the presence of these asymmetries. The coefficients for the nonlinear terms are described in terms of a set of the Fermi liquid parameters: the phase shift, static susceptibilities, and three-body correlation functions of electrons in the quantum dots, defined with respect to the equilibrium ground state. We calculate these correlation functions, using the numerical renormalization group approach (NRG), over a wide range of impurity-electron filling that can be controlled by a gate voltage in real systems. The NRG results show that the order ${V}^{2}$ nonlinear current is enhanced significantly in the valence fluctuation regime. It is caused by the order $V$ energy shift of the impurity level, induced in the presence of the tunneling or bias asymmetry. Furthermore, in the valence fluctuation regime, we also find that the order ${V}^{3}$ nonlinear current exhibits a shoulder structure, for which the three-body correlations that evolve for large asymmetries play an essential role.

Analog Radio Over Fiber Aided C-RAN: Optical Aided Beamforming for Multi-User Adaptive MIMO Design

Given the increasing demand for high data-rate, high-performance wireless communications services, the demand on the radio access networks (RAN) has been increasing significantly, where optical fiber has been widely used both for the backhaul and fronthaul. Additionally, advances in signal processing such as multiple-input multiple-output (MIMO) techniques, have improved the performance as well as transmission rate of communications networks. Beamforming has been used as an efficient MIMO technique for providing a signal to noise ratio (SNR) gain as well as reducing the multi-user interference. However, beamforming requires the employment of phase-shifters, which suffers from reduced phase resolutions, degraded noise figures as well as beam-squinting in addition to the implementation challenges. Hence, in this paper we employ an analogue radio over fiber (A-RoF) aided architecture for supporting the requirements of the current and future mobile networks, where we design a photonics aided beamforming technique in order to eliminate the bulky electronic phase-shifters and the beam-squinting effect, while also providing a low-cost RAN solution. Additionally, this photonics aided beamforming is combined with a reconfigurable multi-user MIMO technique, where users can communicate with one or multiple remote radio heads (RRHs), while employing stand-alone beamforming, beamforming combined with diversity or with multiplexing depending on the available resources and the user channel information as well as the quality of service requirements.

Nonlinear Interactions Between Relativistic Electrons and EMIC Waves in Magnetospheric Warm Plasma Environments

AbstractWith the kinetic dispersion relation and test particle simulation, we examine the effect of hot protons on the nonlinear interactions of relativistic electrons with electromagnetic ion cyclotron (EMIC) waves. We find that hot protons alter the refractive index of EMIC waves at a given wave frequency along latitude and thus modify resonance latitude. Consequently, resonance refractive index gradient along the magnetic field line, which plays a dominant role in controlling the electron behaviors, changes. Overall, the involvement of hot protons enlarges the resonance region (linear and nonlinear) but narrows the nonlinear resonance region. Additionally, hot protons weaken the electron phase bunching process and shift the electron phase trapping region to larger equatorial pitch angles. When the abundance or temperature anisotropy of hot protons increases, their effects on electron behaviors become more significant.

Quantifying leakage fields at ionic grain boundaries using off-axis electron holography

The electrical properties of interfaces in semiconductors and ionic conductors are immensely important in a wide range of applications. Electron holography is ideally suited for the direct measurement of the electrostatic potential of such interfaces. A key challenge with this approach is the contribution of the leakage field from the sample to the observed electron phase shift. This leakage field cannot be a priori independently determined and can cause an overestimation of the phase shift. In this work, we use finite element simulations to compute the three-dimensional electrostatic potential in the vicinity of an interface associated with a given interfacial charge density distribution. We then evaluate the predicted phase shift and demonstrate that the leakage field strongly affects the recovery of the projected interface potential. From the difference between the true potential and uncorrected, recovered potential, we propose a method to correct for this effect. We then demonstrate the application of this methodology to the analysis of experimental off-axis electron holography data acquired from the grain boundaries in lightly doped ceria.

Fabrication of low aspect ratio three-element Boersch phase shifters for voltage-controlled three electron beam interference

A Boersch phase plate can shift the phase of electrons proportionally to the applied electrical potential, thereby allowing for in situ control of the electron phase shift. A device comprising multiple Boersch phase shifter elements will be able to modulate the wavefront of a coherent electron beam and control electron interference. Recently, fabrication of single and 2 × 2 element Boersch phase shifter devices by focused ion beam milling has been reported. Realization of a large-scale Boersch phase shifter array would demand further developments in the device design and the fabrication strategy, e.g., using lithographic processes. In the present work, we develop a fabrication method utilizing the state-of-the-art electron beam lithography and reactive ion etching processes, a combination that is widely used for high-throughput and large-scale micro- and nanofabrication of electronic and photonic devices. Using the developed method, we fabricated a three-element phase shifter device with a metal–insulator–metal structure with 100-nm-thick ring electrodes and tested its electron transmission characteristics in a transmission electron microscope with a beam energy of 200 keV. We observed voltage-controlled evolution of electron interference, demonstrating the voltage-controlled electron phase shift using the fabricated device with a phase shift of π rad per 1 V. We analyze the experimental results in comparison with a three-dimensional electrostatic simulation. Furthermore, we discuss the possible improvements in terms of beam deflection and crosstalk between phase shifter elements in a five-layer device structure.

Theory of exciton-electron scattering in atomically thin semiconductors

The realization of mixtures of excitons and charge carriers in van-der-Waals materials presents a new frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with Quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for Quantum Monte-Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.

Vacuum Resonance States as Atomic-Scale Probes of Noncollinear Surface Magnetism.

The reflection of electrons at noncollinear magnetic surfaces is investigated by spin-polarized scanning tunneling microscopy and spectroscopy on unoccupied resonance states located invacuo. Even for energies up to 20eV above the Fermi level, the resonance states are found to be spin split, exhibiting the same local spin quantization axis as the underlying spin texture. Mapping the spin-dependent electron phase shift upon reflection at the surface on the atomic scale demonstrates the relevance of all magnetic ground state interactions for the scattering of spin-polarized low-energy electrons.

Practical design of the voltage controllable quadrature oscillator for operation in MHz bands employing new behavioral model of variable-voltage-gain current conveyor of second generation

This paper introduces a new simple behavioral model of variable-voltage-gain (inverting) current conveyor of second generation (VG-(I)CCII) intended for experimental verification of linearly controllable quadrature oscillator operating above 1 MHz. The proposed novel topology implements two models of VG-(I)CCII. Next, its precise design procedure is presented. Operation with constant amplitude levels is ensured from 2.69 to 20.18 MHz, whereas the highest available oscillation frequency achieves 30.1 MHz. The oscillator employs high-speed off-the-shelf active elements, which emulate behavior of current conveyor of second generation with a variable voltage gain between Y and X terminals. The influence of the real features of active elements and printed circuit boards is considered for the estimation (design equations) of the operational conditions of the circuit. Experimental measurements confirmed the validity of the expected results. Novel behavioral model of active device brings significant advantages (variable voltage gain and its polarity control) for its implementation in applications. Simple circuitry of the newly proposed quadrature oscillator and its wideband linear electronic tuning, constant amplitudes and phase shift with frequency tuning are the most notable benefits of our proposed concept, compared to current state-of-the-art solutions.

Two-Frequency Undulators for Generation of X-Ray Radiation in Free-Electron Lasers

We present a theoretical study and a computer simulation of characteristics of the undulator radiation in single-pass free-electron lasers (FELs). Using a phenomenological model describing the dynamics of the radiated power in FELs with allowance for the basic loss, we study generation of harmonics in the X-ray range in a FEL with a two-frequency undulator. We study the possibility to achieve a hundredfold increase in the radiation intensity of the nth harmonic in a FEL, in which the electron-phase shift by kπ/n with respect to photons occurs between undulator sections, where k = 2, 4, . . . . The advantages of using a two-frequency undulator in a single-pass FEL and the possibility of generating the high-power X-ray radiation by the FEL at the harmonic wavelengths 2.3–3.3 nm in the linear regime are demonstrated. The FEL is compared with the two-frequency undulator and the conventional plane undulator. Additionally, generation of radiation having a power of tens of megawatts is studied at the wavelength λ ≈ 3.27 nm in a multistage FEL with a length of 40 m, an off-the-shelf excimer ultraviolet seed laser, which operates at a wavelength of 157 nm, and an electron beam having an energy of about 0.6 GeV.

Magnetization measurements for grain boundary phases in Ga-doped Nd-Fe-B sintered magnet

The magnetism of grain boundary (GB) phases in the Nd-rich Ga-doped Nd-Fe-B sintered magnet that shows unusually high improvement in coercivity by post-sinter optimal heat treatment was studied using electron holography. Transmission electron microscopy observations identified three types of GB phases with distinct structures, i.e., Ia3¯-type, amorphous-type, and Nd6(Fe,Ga)14-type. The magnetic flux densities of these three GB phases were systematically analyzed by measuring the phase shifts of incident electrons, and all of these GB phases are concluded to be nonferromagnetic. Unlike the standard commercial sintered magnets, this study has shown that the Nd2Fe14B grains in the optimally heat treated Nd-rich Ga-doped sintered magnet are exchange decoupled by the formation of the three types of nonferromagnetic GB phases. The observations provide useful information for GB engineering of Nd-Fe-B sintered magnets, which is key for further improvements of their coercivities without relying on grain size refinement.

Fermi Liquids and the Luttinger Integral

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral IL, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of IL with IL = ±π/2, occur in impurity models classified as singular Fermi liquids. Here we show the same values, IL = ±π/2, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.

Joint Space-Time Block-Coding and Beamforming for the Multiuser Radio Over Plastic Fiber Downlink

An all-optical processing aided multifunctional wireless multiple-input multiple-output architecture is designed, where both diversity and beamforming gains can be attained. Explicitly, we propose an architecture, where the twin-antenna Alamouti space-time block coded symbols are transmitted using a single Mach–Zenhder Modulator (MZM) over a plastic optical fiber. The signal is then transmitted through a set of fiber Bragg gratings for attaining the appropriate phase shifts for beamforming, followed by transmission over the wireless channel. The attainable angular beamsteering range is about 150°, where beamsteering is realized without the need for a large number of complex electronic phase shifter networks. The tuning of the beamsteering angle can be readily implemented by carefully controlling the drive voltage in the MZM, where we use MZM aided multiwavelength generation for supporting a large number of antennas.

Photonic-Delay Line Cross Correlation Method Based on DWDM for Phase Noise Measurement

A dual photonic-delay line cross-correlation method for phase noise measurement of microwave signal based on dense wavelength division multiplexing (DWDM) is proposed and experimentally demonstrated. The kilometer-long delay fiber is used together by the two mutually independent channels through the DWDM technology, which makes it easier to get the same delay between two channels. And it reduces the cost of the system by reducing the use of several kilometers of fiber and a Mach-Zendher modulator. Then, it uses variable optical fiber delay lines to replace the electronic phase shifters and a broader operation bandwidth can be obtained. A lower phase noise floor has been obtained by more averaging of the cross-correlation spectrum. In the experiments, the phase noise of a 10-GHz microwave signal has been measured accurately. A large operation bandwidth of 4-11 GHz is achieved and a measurement phase noise floor of -152.6 dBc/Hz at 10 kHz offset at 10 GHz in a 20 μs delay measurement system is realized by averaging 100 times.

Radio Over Fiber Downlink Design for Spatial Modulation and Multi-Set Space-Time Shift-Keying

Spatial modulation (SM) and multi-set space-time shift-keying (MS-STSK) are capable of striking a flexible design trade-off between the multiplexing and diversity gains attained. These techniques can also be combined with beamfoming for the sake of supporting reliable millimeter-wave (mmWave) communications. In this treatise, we propose an analogue radio-over-fiber (RoF) downlink network relying on SM and MS-STSK combined with beamforming and up-conversion to mmWave carrier frequencies, whilst using all-optical processing. In the proposed analogue RoF (A-RoF) system, most of the digital processing of the baseband SM and MS-STSK is carried out by the central unit and the implicitly carried bits of SM/MS-STSK, such as the antenna index selection and dispersion matrix selection bits, are recovered by the remote radio head of our A-RoF network for creating a multi-functional multiple-input multiple-output arrangement. As detailed by Hanzo et al. , the classic modulated bits are conveyed by the radio signal, without requiring any additional analogue-to-digital conversion and digital-to-analogue conversion before transmission from the antennas. Moreover, A-RoF-aided techniques are invoked for achieving optical processing-aided beamforming and optical up-conversion to an mmWave carrier frequency. Thus, we invoke A-RoF techniques for the generation of our SM/MS-STSK signal with the aid of optically up-converted millimetre-wave beamforming without using any electronic oscillators, mixers, or phase shifters. Furthermore, our A-RoF-aided system’s bit error ratio performance is similar to the conventional all-electronic SM/MS-STSK scheme.