Small-signal Limit Research Articles

A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction

We present a variance-reduced method for efficiently solving the Boltzmann equation in all rarefaction regimes. The proposed method is based on the VRDSMC method of Al-Mohssen and Hadjiconstantinou (2010) [50], which exploits the correlation between two DSMC simulations using the same random numbers to significantly reduce the statistical uncertainty associated with moment estimation. This variance-reduction formulation is preferred here because it requires minimal change to the underlying DSMC method and code base. The instability reported in the collision-dominated regime in this previous work is removed via a combination of Kernel Density Estimation, a hierarchy of moment conservation constraints and a Maximum Entropy formulation for minimizing the bias introduced by the stabilization process. The resulting method is referred to as maximum-entropy variance-reduced direct simulation Monte Carlo (ME-VRDSMC). Computational experiments show that the proposed algorithm provides an efficient and accurate method for solving the Boltzmann equation in the low-signal limit. We also show that, similar to VRDSMC, the relative statistical noise of the proposed method is decoupled from the signal magnitude, leading to a substantial speedup compared to DSMC in the small-signal limit.

Analytical Models for the Pulse Shape of a Superconductor-Ferromagnet Tunnel Junction Thermoelectric Microcalorimeter

The superconductor-ferromagnet thermoelectric detector (SFTED) is a novel ultrasensitive radiation detector based on the giant thermoelectric effect in superconductor-ferromagnet tunnel junctions. We demonstrate analytical models and solutions in the time domain for a SFTED operated as a microcalorimeter (pulse excitation), in the linear small-signal limit. Based on these solutions, the signal current and temperature pulse response were studied for two different electrical circuit models, providing design conditions for stable and non-oscillatory response.Kindly check and confirm whether the corresponding author is correctly identified.The corresponding author is correct.

A Double-PLLs-Based Impedance Reshaping Method for Extending Stability Range of Grid-Following Inverter Under Weak Grid

Conventional vector current control scheme has been widely used in grid-connected inverter systems. However, it suffers from severe power limitation issues under weak grids. This article reveals that the coupling effect between the power delivery and the voltage at the point of common coupling causes the static power limit, which only depends on physical parameters of the system. When the stability of the control scheme is considered, negative resistance characteristics of the phase-locked loop (PLL) mainly result in the small-signal stability limit, which is called the dynamic power limit in this article. Because the small-signal stability limit can be improved by using different control methods, it attracts lots of research attention. In this article, a simplified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> small-signal impedance model is introduced to show the destabilizing factors. Then, an initial small-signal impedance reshaping method is proposed to counteract the major destabilizing factor caused by the PLL. Based on the initial impedance reshaping method, an improved control scheme is proposed. Through exhaustive mathematical analysis, it is proved that the dynamic power limit can be extended almost to the static power limit by using this proposed method. Finally, simulation and experimental results verify the effectiveness of the proposed method.

The Athena X-IFU Instrument Simulator xifusim

We present the instrument simulator xifusim developed for the X-ray Integral Field Unit X-IFU aboard the planned Athena mission. xifusim aims to be an accurate representation of the entire instrument, starting from a full simulation of the Transition-Edge Sensor (TES) array receiving impact photons unconstrained by the small signal limit. Its output current is then propagated through the entire readout chain, including multiplexing, amplification and the digital readout. The final output consists of triggered records, which can be post-processed to reconstruct the photon energies. The readout chain itself is separated into individual, modular blocks with several possible models for each, allowing the simulation of different readout schemes or models of varying physical accuracy at the expense of run time. New models are implemented as necessary to enable studies of the overall readout chain. Such studies are also facilitated by fine-grained control of the simulation output, including the internal state of intermediate simulation blocks. In addition to its modularity, xifusim also allows the manipulation of certain internal parameters during a run, enabling the simulation of readout chain characterization measurements, environmental drifts or various kinds of crosstalk.

High aspect ratio transition edge sensors for x-ray spectrometry

We are developing large Transition Edge Sensor (TES) arrays in combination with a frequency domain multiplexing readout for the next generation of X-ray space observatories. For operation under an AC-bias, the TESs have to be carefully designed and optimized. In particular, the use of high aspect ratio devices will help us to mitigate non-ideal behavior due to the weak-link effect. In this paper, we present a full characterization of a TES array containing five different device geometries, with aspect ratios (width:length) ranging from 1:2 up to 1:6. The complex impedance of all geometries is measured in different bias configurations to study the evolution of the small-signal limit superconducting transition parameters α and β, as well as the excess noise. We show that high aspect ratio devices with properly tuned critical temperatures (around 90 mK) can achieve excellent energy resolution, with an array average of 2.03±0.17 eV at 5.9 keV and a best achieved resolution of 1.63±0.17 eV. This demonstrates that AC-biased TESs can achieve a very competitive performance compared to DC-biased TESs. The results have motivated a push to even more extreme device geometries currently in development.

Small-Signal Stability Limit of a Grid-Connected PMSG Wind Farm Dominated by the Dynamics of PLLs

This paper presents a derivation of the small-signal stability limit of a grid-connected wind farm with M permanent magnet synchronous generators (PMSGs) as determined by the dynamics of phased locked loops (PLLs). The stability limit reveals the mechanism whereby the PLLs can destabilize the wind farm in the case of a weak grid connection. Computation of the derived stability limit is simple and obviates the need to establish a parametric model of the wind farm. The stability limit can approximately indicate the potential instability risk collectively posed by the PLLs in the wind farm. Case studies are presented to evaluate the analytical conclusions obtained and the derived small-signal stability limit. Application of the stability limit during the planning and operating stages of a grid-connected wind farm is also demonstrated. Various factors that can affect the stability of the wind farm, and that must be considered during planning and operation, are examined and useful conclusions are obtained. These factors include the length of the transmission line connecting the wind farm to the AC grid, the topology of the wind farm, the wind speed, and its distribution over the wind farm, as well as the parameters of the PLLs.

Superlinearity, saturation, and the PMT-Tailoring and calibration methodology for prompt radiation detectors.

This work illustrates predominant measureable nonlinearities in photomultiplier tubes (PMTs) and introduces a controllable one called "Superlinearity," signifying both a positive nonlinear response and the ability to extend linear operation by counteracting gain saturation mechanisms - charge depletion, space-charge field limitation, and secondary emission surface effects. Recognizing superlinearity and its effect on the temporal step response leads to a true definition of linearity, free of a small-signal linear assumption. Furthermore, given the prevalent use of glass microchannel-plate (MCP) PMTs in favor of a faster impulse response in spite of a small charge limit, we are motivated to examine their nonlinear amplitude response and deploy tailored gain bias string methods to fully harness the maximum linear gain as is usually done for transmissive metal mesh and reflective metal dynode PMTs. Our characterization methodology applies standard NIST-traceable calibrated laboratory equipment with absolute input-referenced techniques, examining step responses over many orders of magnitude in controlled illumination. By doing so, we quantitatively reveal the superlinearity strength independent of charge depletion, yielding true linear responsivity and effectively doubling the small-signal linear limit; this is very relevant to PMT modeling and charge deconvolution efforts. With further development, the tailoring strategies we introduce could be applied to MCP detectors, extracting all useful capillary charge with a significant improvement in large linear signal quality.

Small-signal transient response and turn-on delay of polariton laser diodes

We present a theoretical description of the small-signal transient response of polariton laser diodes (pol-LDs) based on simplified coupled rate equations describing the exciton reservoir and the ground-state polariton populations. The analytic expressions derived for two pumping geometries, which are valid for all inorganic semiconductors suitable for the realization of pol-LDs, are compared to exact numerical calculations performed for the specific case of GaN-based devices. The two approaches show excellent agreement provided the current step transient remains within the small-signal limit. We report that the temporal attenuation of the envelopes of the oscillations matches half the value of the damping factor () of the pol-LDs, which is proportional to the square of the oscillation relaxation resonance frequency. An explicit expression for the dependence of on both the exciton-photon detuning and the driving current (equivalently the optical pump power) is also obtained. In a further step, we derive the expression for the turn-on delay (td) associated with the build-up of the exciton reservoir population up to its threshold value before coherent light emission occurs. We show that td has the same functional form for the two pumping geometries. It is equal to the effective exciton lifetime () weighted by a logarithmic dependence on the initial and final driving currents. In addition, is shown to be approximately equal to the exciton lifetime, which proves to be the main parameter governing the build-up of polariton lasing/condensation. Beyond electrically driven polariton lasers, we highlight that the temporal shape of the transients could also be easily tested by monitoring the time dependence of the output power of optically pumped polariton lasers subjected to a sudden increase in the continuous wave pump power within the small-signal limit.

Impact of atmospheric molecular absorption on the temporal and spatial evolution of ultra-short optical pulses.

We present a rigorous study on the impact of atmospheric molecular absorption on the linear propagation of ultrashort pulses in the mid-infrared wavelength region. An ultrafast thulium-based fiber laser was employed to experimentally investigate ultrashort-pulse propagation through the atmosphere in a spectral region containing several strong molecular absorption lines. The atmospheric absorption profile causes a significant degradation of the pulse quality in the time domain as well as a distortion of the transverse beam profile in the spatial domain. Numerical simulations carried out in the small signal limit accurately reproduce the experimental observations in the time domain and reveal that the relative loss in peak power after propagation can be more than twice as high as the relative amount of absorbed average power. Although their nature is purely linear (i.e. the intensities considered are sufficiently low) the discussed effects represent significant challenges to performance-scaling of mid-infrared ultrafast lasers operating in spectral regions with molecular absorption bands. Guidelines for an efficient mitigation of the pulse quality degradation and the beam profile distortion are discussed.

Modeling third-harmonic generation from layered materials using nonlinear optical matrices.

A matrix approach is formulated to describe third-harmonic (TH) generation in stacked materials in the small signal limit, in both transmission and reflection geometries. The model takes into account the contribution from the substrate to the total generated TH, interference of fundamental and nonlinear fields inside the stack, the nonlinear signal generation in forward and backward direction, the beam profile of the focused incident beam in the substrate, and the finite spectrum associated with short laser pulses. The model is applied to design stacks of thin films for efficient TH generation.

Theoretical analysis of carbon nanotube photomixer-generated terahertz power

On the basis of mixer circuit model of light, the terahertz power generated by the carbon nanotubes (CNT) photomixer is analyzed. By simulating mixer conductance, impedance of the antenna, and light plus paranoid voltage, it is shown that the improved mixer conductance, antenna impedance and light plus paranoid voltage can improve the output power of terahertz waves. The output power can reach dozens of microwatt level in the small-signal limit.

Weak-Periodic Stochastic Resonance in a Parallel Array of Static Nonlinearities

This paper studies the output-input signal-to-noise ratio (SNR) gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.

Analysis of saturation phenomena in Cerenkov free-electron lasers with a planar waveguide

In this paper, the operation of the stimulated emission in Cerenkov free-electron laser (CFEL) is studied on the basis of the modulations of electron velocity and density by the electromagnetic (EM) field. The influence of the electron relaxation, due to mutual electrons collisions, on the electron dynamics is taken into account. We investigate the growth characteristics of Cerenkov laser operating in the small-signal and saturation regimes. In the saturation regime, the effect of velocity reduction of the electron beam on the gain dynamics is demonstrated. We also show that our results match with those of other well-known treatments in the small-signal gain limit.

Dynamic Non-Detection Zones of Positive Feedback Anti-Islanding Methods for Inverter-Based Distributed Generators

Positive feedback anti-islanding methods have been widely applied to inverter-based distributed generators recently due to their high cost-performance ratio. The effectiveness of these anti-islanding methods is usually demonstrated by means of steady-state non-detection zones (NDZs) represented in a load parameter space (LPS). However, these NDZs cannot accurately describe the impact of the inverter interface controls on the anti-islanding methods' detection performance, especially in multi-inverter systems. In addition, the intrinsic destabilization characteristic of the positive feedback anti-islanding scheme cannot be exhibited by these NDZs. This paper proposes an improved dynamic NDZ in the LPS to evaluate the islanding detection effectiveness of the positive feedback anti-islanding methods. The modal analysis approach is employed to determine the critical RLC load quality factor which is defined as the small-signal stability limit index of the islanded distributed generation (DG) systems for the dynamic NDZs. The sensitivity analysis of the dynamic NDZs for different DG system parameters is conducted in this paper. The applications of the proposed dynamic NDZs in multi-DG systems are also presented.

Suppression of current fluctuations in an intense electron beam

When an intense beam encounters an aperture, the transmitted current depends on the properties of the beam and the transport channel, as well as those of the aperture itself. In some cases, an increase in the incident beam current will be exactly compensated by an increase in the incident beam area, so that the current density at the aperture remains unchanged. When this occurs, the transmitted beam current becomes independent of changes in the incident beam current, providing a passive means for suppressing current fluctuations in the beam. In this article, a key requirement for the existence of this condition is derived. This requirement is shown to be fulfilled in the case of an idealized uniform focusing channel in the small-signal limit, but to be violated when the current fluctuations are not small. Even in this case, the apertured transport system retains the ability to suppress—but not totally eliminate—fluctuations in the transmitted beam current for a wide range of incident beam currents.

An analytical model for pulse shape and electrothermal stability in two-body transition-edge sensor microcalorimeters

High-resolution superconducting gamma-ray sensors show potential for the more accurate analysis of nuclear material. These devices are part of a larger class of microcalorimeters and bolometers based on transition edge sensors (TESs) that have two distinct thermal bodies. We derive the time domain behavior of the current and temperature for compound TES devices in the small signal limit and demonstrate the utility of these equations for device design and characterization. In particular, we use the model to fit pulses from our gamma-ray microcalorimeters and demonstrate how critical damping and electrothermal stability can be predicted.

THEORETICAL BACKGROUNDS OF NONLINEAR THz SPECTROSCOPY OF SEMICONDUCTOR SUPERLATTICES

We consider terahertz absorption and gain in a single miniband of semiconductor superlattice subject to a bichromatic electric field in the most general case of commensurate frequencies of the probe and pump fields. Using an exact solution of Boltzmann transport equation, we show that in the small-signal limit the formulas for absorption always contain two distinct terms related to the parametric and incoherent interactions of miniband electrons with the alternating pump field. It provides a theoretical background for a control of THz gain without switching to the negative differential conductivity state. For pedagogical reasons we present derivations of formulas in detail.

Multiple Diffractions of Guided Optical Waves with Multifrequency Magnetostatic Forward Waves in Magnetooptic Film Waveguides

The multifrequency diffraction effects of guided optical waves with multiple magnetostatic forward volume waves (MSFVWs) excited in magnetooptic (MO) film waveguides under a normal bias magnetic field are theoretically studied for the first time. Multifrequency MO coupled-mode equations and the analytic solution for small-signal approximation are presented. It is shown that, in the small-signal case, the second or higher order diffraction can be neglected in multifrequency MO coupling and the principal diffraction efficiency (PDE) is proportional to the MSFVW power. Thus, the method of determining the small-signal or linear dynamic range is very important for the design of MO spectrum analyzers. The process of multiple diffractions caused by two MSFVW signals in a third-order MO coupling approximation is analyzed in detail. The small-signal limit can be determined according to the MSFVW power dependences of the PDEs, instead of those of the depletions. The multi-frequency diffraction theory can be applied to the quantitative evaluation of linear and nonlinear effects occurring in MO multi-frequency applications.

Multitone large-signal analysis of superconducting transition-edge sensors for astronomy

A simple transition-edge sensor (TES) is governed by two coupled, nonlinear equations, which when solved give the behavior of the device given the initial conditions. The two equations describe the full electrical and thermal characteristics of the device and the way in which the device interacts with the external electrical and thermal circuits. To date these coupled nonlinear equations have been solved analytically in the small-signal limit, by linearizing the equations about some operating point. The resulting coupled linear equations contain a wealth of interesting physics, and form the principal tool by which all detectors are currently designed and modeled. In this article we describe a numerical technique for solving the coupled nonlinear equations rigorously, without any assumptions about the magnitudes of the various signals and parameters that determine the behavior of a device. The technique is based on a harmonic balance algorithm that searches, in the frequency domain, for voltage, current, and temperature wave forms that are consistent with the solid-state physics of the device. Indeed, both the small and large signal limits can be simulated, and the full harmonic content of the system retrieved. In this article, we will outline the principal features of the algorithm, and show various results such as I−V curves, saturation when signal power is modulated, impedance response when the bias current is modulated and signal power kept constant, and pulsed signal power analysis that shows the dynamics of a device. Numerous extensions of this fundamental technique are now possible including multitone nonharmonic analysis, large-signal impedance calculation, modeling of complicated thermal circuits, noise models, and frequency-domain multiplexing. We believe that our algorithm will become the principle technique for analyzing the large-signal behavior of all TES detectors and on that basis we are developing computer aided design software.

Harmonic gain and noise in a frequency-doubling gyro-amplifier

Nonlinear gain in a 34-GHz three-stage frequency-doubling gyro-traveling wave tube (gyro-TWT) has been experimentally studied. The device consists of a thermionic electron gun, TE/sub 01//spl rarr/TE/sub 02/ fundamental gyro-TWT input section, second harmonic TE/sub 03/ intermediate buncher section, and a second harmonic TE/sub 02//spl rarr/TE/sub 04/ complex output circuit. Nonlinear bunching in the electron orbital phase generates harmonics of the input signal in the beam current, which excite the subsequent circuits at the second harmonic frequency. Since the gain is nonlinear, noise or applied sideband signals intermodulate with the carrier generating high-order products in the output. Therefore, it has been suggested that the noise figure of these devices may be unreasonably high. In this study, the complex harmonic transfer characteristics were experimentally measured and compared with calculations based on the assumption that the gyro-amplifier gain can be described, in the narrowband sense, as a classical frequency-doubling circuit. The results show that narrowband intermodulation gain is 6 dB higher than the carrier as predicted in the small signal limit, but as the device reaches saturation the nonlinear products become suppressed with respect to the carrier. Tests on the broadband gain characteristics show that output noise consists of second harmonic shot noise spontaneously excited in the output circuits along with the products of the intermodulation between external noise and the carrier. Good agreement between the experimental results and the calculations is demonstrated.