Multiphase Modulation Research Articles

Multi-phase features interaction transformer network for liver tumor segmentation and microvascular invasion assessment in contrast-enhanced CT.

Precise segmentation of liver tumors from computed tomography (CT) scans is a prerequisite step in various clinical applications. Multi-phase CT imaging enhances tumor characterization, thereby assisting radiologists in accurate identification. However, existing automatic liver tumor segmentation models did not fully exploit multi-phase information and lacked the capability to capture global information. In this study, we developed a pioneering multi-phase feature interaction Transformer network (MI-TransSeg) for accurate liver tumor segmentation and a subsequent microvascular invasion (MVI) assessment in contrast-enhanced CT images. In the proposed network, an efficient multi-phase features interaction module was introduced to enable bi-directional feature interaction among multiple phases, thus maximally exploiting the available multi-phase information. To enhance the model's capability to extract global information, a hierarchical transformer-based encoder and decoder architecture was designed. Importantly, we devised a multi-resolution scales feature aggregation strategy (MSFA) to optimize the parameters and performance of the proposed model. Subsequent to segmentation, the liver tumor masks generated by MI-TransSeg were applied to extract radiomic features for the clinical applications of the MVI assessment. With Institutional Review Board (IRB) approval, a clinical multi-phase contrast-enhanced CT abdominal dataset was collected that included 164 patients with liver tumors. The experimental results demonstrated that the proposed MI-TransSeg was superior to various state-of-the-art methods. Additionally, we found that the tumor mask predicted by our method showed promising potential in the assessment of microvascular invasion. In conclusion, MI-TransSeg presents an innovative paradigm for the segmentation of complex liver tumors, thus underscoring the significance of multi-phase CT data exploitation. The proposed MI-TransSeg network has the potential to assist radiologists in diagnosing liver tumors and assessing microvascular invasion.

Использование мультифазных коэффициентов для анализа и совершенствования конструкций лопастных машин, работающих на газожидкостных, парожидкостных смесях, смесях из жидкости и твердых частиц

To increase the oil recovery factor, the bottom-hole pressure is reduced, which is accompanied by an increase in the free gas and mechanical impurities content at the pump inlet. As a rule, the serial equipment is not providing reliable and efficient operation in such conditions. In oil producing wells with the high free gas content, efficiency of the multiphase modules blade stages could be increased by correct selection of the serial equipment and introduction of the new design solutions. The paper analyzes specifics of the gas-liquid mixture flow in the flow path of the blade multiphase stages pumping the gas-liquid mixtures. Recommendations are provided for improving the flow path taking into account the multiphase specific speed coefficient formula. It is proposed to use the multiphase coefficient along with the cavitation specific speed coefficient in development of the blade pumps operating under the steam cavitation conditions.

A Novel Approach for Radar Passive Jamming Based on Multiphase Coding Rapid Modulation

Electromagnetic controlled surface (ECS) which can regulate the amplitude and phase of electromagnetic wave reflection characteristics has attracted extensive attention in recent years because of its radar stealth effect by reducing the radar cross section (RCS). However, radar detection cannot be avoided only by stealth in the energy field gradually. It is a novel pulse Doppler radar jamming mode proposed in this paper to utilize the self-correlation of radar-transmitted waveforms to result in signal processing and radar detection failure through the rapid time-domain variation of phase coding ECS. In principle, phase modulation alters the intra-pulse characteristics of the original signal and fundamentally interferes with the processing of the radar signal. In this paper, random and periodic phase coding sequences are proposed according to different forms of radar jamming. And through the derivation formula and simulation experiment, the jamming effect under multi-phase modulation is verified. Among them, the target energy is dispersed to the surroundings to form a wide envelope through random coding modulation, which leads to noise barrage jamming. While we use periodic sequence coding modulation, the target is shifted in the range-Doppler domain, causing misplaced coherence on the radar echo and deceptive jamming to the radar. Moreover, the technology can also be widely used in synthetic aperture radar (SAR) imaging, microwave measurement and other remote sensing fields. To further confirm the accuracy and efficiency of the proposed method, multi-parameter contrast experiments and parameter sensitivity analyses are conducted.

A Knowledge-Guided Framework for Fine-Grained Classification of Liver Lesions Based on Multi-Phase CT Images.

Automatic and accurate differentiation of liver lesions from multi-phase computed tomography imaging is critical for the early detection of liver cancer. Multi-phase data can provide more diagnostic information than single-phase data, and the effective use of multi-phase data can significantly improve diagnostic accuracy. Current fusion methods usually fuse multi-phase information at the image level or feature level, ignoring the specificity of each modality, therefore, the information integration capacity is always limited. In this paper, we propose a Knowledge-guided framework, named MCCNet, which adaptively integrates multi-phase liver lesion information from three different stages to fully utilize and fuse multi-phase liver information. Specifically, 1) a multi-phase self-attention module was designed to adaptively combine and integrate complementary information from three phases using multi-level phase features; 2) a cross-feature interaction module was proposed to further integrate multi-phase fine-grained features from a global perspective; 3) a cross-lesion correlation module was proposed for the first time to imitate the clinical diagnosis process by exploiting inter-lesion correlation in the same patient. By integrating the above three modules into a 3D backbone, we constructed a lesion classification network. The proposed lesion classification network was validated on an in-house dataset containing 3,683 lesions from 2,333 patients in 9 hospitals. Extensive experimental results and evaluations on real-world clinical applications demonstrate the effectiveness of the proposed modules in exploiting and fusing multi-phase information.

Efficiency-Oriented Parameter Design and Comparison of Medium Voltage Isolated Bidirectional DC/DC Converters

In a medium voltage (MV) solid state transformer(SST), the isolated bidirectional DC/DC converter (IBDC) is the core circuit for controlling power flow and galvanic isolation. Current research works on MV single-cell IBDC mainly focus on two directions: resonant and non-resonant topologies. However, for different scenarios with various voltage regulation ranges and power ranges, which topology should be adopted to achieve better efficiency performance is unclear. To effectively illustrate the two IBDCs’ respective benefits, a comparison between the two IBDCs is conducted in this study along with the optimization design method. For resonant IBDC, a complex objective optimization-based parameter design strategy is developed to realize rapid automatic design under various operating conditions. For non-resonant IBDC, a multi-phase modulation scheme aimed at minimizing the current stress under different voltage and power ranges is introduced. The optimal operating range of the two IBDCs has been derived. A 4 kV/1 kV 200 kW non-resonant IBDC experimental prototype has been built and its efficiency is tested under various operating conditions. The test data were compared with the established power loss model to derive the converter's full range efficiency, and the efficiency of the converter over a wider power range could then be projected.

Heat-mass transfer coupling effects in water-ice phase transformation of water-bearing coal frozen with liquid nitrogen

• The equation of coal freezing and water-ice phase transformation under the action of cryogenic LN 2 is derived. • A new discretization method is proposed to solve the equation of coal temperature and water-ice phase transformation. • The water-ice phase transition law of LN 2 flowing through water-bearing coal is studied quantitatively. • The influence of ice water conversion process on temperature distribution in water-bearing coal at low temperature is analyzed. • The law of heat and mass transfer in the process of LN 2 flowing through water-bearing coal is revealed. Liquid nitrogen (LN 2 ) fracturing, as a waterless and environmentally friendly fracturing technology, has a broad application prospect in coalbed methane (CBM) exploitation. Currently, there is a lack of sufficient understanding of the heat mass transfer mechanism of LN 2 fractured coal mass. In this paper, the heat-flow coupling problem of LN 2 frozen coal mass was systematically studied by means of numerical simulation. A fluid-solid coupled multiphase module was mathematically modeled on LN 2 flow, coupling between LN 2 and coal mass temperature, and the variation law of coal temperature and water-ice phase with time and geometric position during LN 2 flow was obtained under the coal seam freeze-thaw simulation analysis program by FORTRAN language. The results showed that the most obvious heat mass transfer occurred in the coal mass area close to the LN 2 inlet and the fluid-solid interface. Along the direction of coal burial depth, the changes of temperature and water-ice phase are broadly divided into rapid change zone, slow change zone and stable zone, and along the horizontal direction of LN 2 flow, the temperature and unfrozen water volume first peaked, then decreased and gradually stabilized, while the ice content was diametrically opposed, which indicating that the change of temperature and water-ice phase have significant anisotropic characteristics, and the hydrothermal coupling effect out to be one of the most important factors affecting the effect of LN 2 fracturing coal. The main findings of this study are the keys to the research of LN 2 fracturing physical mechanisms in CBM reservoirs.

Humidity-Controlled Dynamic Engineering of Buckling Dimensionality in MoS2 Thin Films

Dynamic engineering of buckling deformation is of vital importance as it provides multiphase modulation of thin film devices. In particular, dynamic switch of buckles between one-dimensional (1D) and two-dimensional (2D) configurations in a single film system on rigid substrates is intriguing but very challenging. The current approach to changing buckling configuration is mainly achieved by varying the built-in stress at the film-substrate interface, but it is difficult to realize dynamic engineering on rigid substrates. Herein, we report a dynamic engineering of buckling deformation in MoS2 thin films by humidity-tuned interfacial adhesion. With the change of humidity, the MoS2 thin films deform from 1D telephone-cord buckles to 2D web-like buckles due to the hydrophilic nature of both MoS2 and substrate. Such 1D-to-2D evolution of buckles is attributed to the weakened interfacial adhesion of mixed deformation modes induced by humidity, which is verified by finite-element modeling. These buckled films further find potential applications as patterned templates for liquid condensation and sensing units for tactile sensors. Our work not only demonstrates the humidity-controlled dimensionality engineering of buckles in MoS2 thin films but also sheds light on the functional applications of buckled films based on their profile features.

An enhanced ultra-wideband single phase hybrid supply envelope tracking modulator for modern wireless communications

This paper presents a Single Phase Hybrid Supply Envelope tracking Modulator (HSEM) for RF-Power Amplifiers (RF-PAs) used in modern wireless communication systems such as 5G and 6G applications. The proposed HSEM consists of an ultra-wideband linear amplifier to track the input signals with several Mega Hertz of bandwidth, a switching amplifier to provide a high-efficiency supply voltage for the main power amplifier, and a new sensing circuit to generate the required voltage for the switching amplifier. The designed HSEM uses a two-stage rail-to-rail linear class-AB amplifier with constant Gm, high gain bandwidth (GBW), high slew rate (SR), and good phase margin (PM). Most conventional modulators use a sensing resistor or a resistor structure that increases the output ripple and the power loss. The proposed structure uses a linear amplifier output stage sensing circuit and a hysteresis low power current comparator without any resistors, external capacitors, filters, or multi-phase modulator structures. Additionally, using a current comparator eliminates the need for an external reference voltage or a current-to-voltage converter. The proposed structure does not need to remove the switching ripple through the linear amplifier, leading to a more relaxed linear amplifier design. A comprehensive analysis and guide on how to optimally select the inductor values, and the mathematical equation for the switching frequency of the hybrid modulator is given. The efficiency of the proposed structure is 84.3 %, and the maximum output power is 27.3dBm. The average output ripple is 4.16 mV in the wide range of the input voltages, and its minimum is 0.4 mV. In addition, the new structure can track a signal with 400 MHz bandwidth with FOM of the HSEM about 18. The proposed modulator is suitable for broadband and emerging telecommunications applications such as 5G and 6G, and as a power supply for RF power amplifiers. The proposed HSEM is evaluated with TSMC 180 nm CMOS technology parameters.

Evaluation of the in vitro and in vivo antiplasmodial effect of water treated with Photonic Multiphase Modulators (PMM) designed with Advanced Physics System Engineering (APSE™) and BioPhoton-X™ technology.

In vitro and in vivo testing of new technology was performed to evaluate the antiplasmodial activity of Photonic Multiphase Modulators (PMM) in cultures and in mice previously infected with Plasmodium falciparum and Plasmodium berghei parasites. Cultures of P. falciparum infected-erythrocytes were exposed overnight to two generations of different APSE™ and BioPhoton-X™ PMM (C#1, R#1, R#2, D8 and D9). Growth of parasites was determined through flow cytometry or microscopy. Mice of the strain C57BL/6 were infected and treated with water exposed to second-generation APSE™ and BioPhoton-X™ PMM plus one previously untested first-generation PMM (AGN10). Parasitemia and weight loss were monitored throughout the infection until death or point of euthanasia was reached. After death, necropsy was performed on all animals and the number of days each survived was recorded. In vitro and in vivo testing using different APSE™- and BioPhoton-X™-designed PMM revealed an effect of D8 in lowering the growth of the parasite in vitro, while the best effect in mice was observed with D9 PMM, with a reduced weight loss and an increase in survival, although the results in lowering the parasitemia were inconclusive. D9 PMM did not generate ROS in vitro. APSE™ and BioPhoton-X™ optic circuit technologies can affect the growth of parasites and show protective effects in mice drinking from water treated with their PMM.

An Automotive LiDAR SoC for 240 × 192-Pixel 225-m-Range Imaging With a 40-Channel 0.0036-mm2 Voltage/Time Dual-Data-Converter-Based AFE

This article presents a 40-channel high-resolution automotive LiDAR system-on-chip (SoC), which utilizes the world's first dual-data converter (DDC). The proposed DDC consolidates the functions of ADC and TDC into a single circuitry and achieves acquisition of both high-precision time and voltage data from the input, realizing a 5× smaller analog front-end (AFE) area than prior arts. Such innovations lead us to a 40channel AFE integration of the SoC without silicon cost increase, which characterizes our LiDAR system with 2× higher pixel resolution. To enhance the ADC's signal-to-noise and distortion ratio (SNDR) without sacrificing the area efficiency, a calibrationfree and variation-tolerant voltage-controlled oscillator (VCO)based ADC with a multiphase pulse density modulator (MP-PDM)-based feedback is proposed. Our proof-of-concept LiDAR system achieves a measurement range of 225 m at 70-klx direct sunlight, with a resolution of 240 × 192 pixels at 10 frames per second (FPS). To quantitatively measure the effect of the resolution improvement of our LiDAR, we evaluate the LiDAR's detection accuracy of small targets 75 m away. Due to the 2× higher vertical pixel resolution, our LiDAR can detect targets with 2× smaller height. The 3-D point cloud of the LiDAR captured outdoor in the wild is presented.

Development of a vector control system of the semiconductor converter, which will provide a polyharmonic operating mode of a polyphase electric machine

A system for vector control of current in the circuit of a polyphase electric machine has been developed. For this, on the basis of the analysis of electromagnetic processes in a multiphase semiconductor converter of electrical energy, its discrete mathematical model was created, which takes into account the redistribution of electromagnetic energy by individual spatial harmonic components depending on the number of phases. Using this mathematical model and the scheme of injection of higher current harmonics, which provides a polyharmonic mode of operation of a semiconductor converter, a method for independent control of the spatial harmonic components of the input current of the converter has been developed. The formation in each of the phases of polyharmonic currents, conjugated in shape and phase with the voltage supplying the converter, is carried out by means of control actions in the form of voltage vectors of a semiconductor switch, the implementation of which is carried out by the method of multiphase space-vector modulation. To check the developed provisions, a simulation model of a nine-phase semiconductor converter of electrical energy with a vector control system was created. The results of the study of the model confirmed the adequacy of the developed technical solutions, the use of which will ensure the most complete realization of the own advantages of a multiphase electric machine in order to generally improve the weight, size and energy indicators of the autonomous power supply system.

Experimental and modeling study on the hydrodynamics in multiphase monolith modules with different distributors

Three commonly used distributors (i.e., nozzle, packed bed, and foam) were introduced into a multiphase monolith reactor in this work to investigate the pressure drop, liquid holdup and gas–liquid distribution performance by combining experimentation and CFD simulation. The experimental results showed that the nozzle distributor exhibited the better gas-liquid phase distribution and the lowest pressure drop. However, so far, the gas and liquid velocities at the top of the monolith bed, which are crucial for the transition from a single channel to bed scale, have not been studied. Thus, a discrete phase and continuous phase coupling 3D model using CFD simulation was established for the nozzle distributor, and the magnitude and distribution of the gas and liquid velocities at the entrance of the monolith module were investigated. The simulation results showed that the droplets’ velocity reaching the monolith module was very high and had a strong influence on the gas velocity distribution. The increase in superficial gas velocity could enhance the gas distribution to some extent.

Prevention of Seabed Subsidence of Class-1 Gas Hydrate Deposits via CO2-EGR: A Numerical Study with Coupled Geomechanics-Hydrate Reaction-Multiphase Fluid Flow Model

The geomechanics effects and seabed subsidence are critical issues that should be considered in the development of a hydrate reservoir. The purpose of this study is to couple the geomechanics, hydrate reaction, and multiphase fluid flow modules to investigate the feasibility of CO2 enhanced gas recovery (CO2-EGR) of a Class-1 hydrate deposit by observing the formation deformation, and the seabed subsidence. The production methods of depressurization and CO2-EGR are modeled, respectively. The production behaviors and seabed subsidence of different production methods are compared. The positive influence on the gas recovery for a Class-1 hydrate deposit via CO2-EGR is observed. The calculations of seabed subsidence showed a significant improvement can be achieved when CO2-EGR was used. The subsidence is only 6.8% of that from the pure depressurization in the case of a pressure drop of 30%. The effects of production pressure drop and production gas rate are investigated. The association between the gas production and the pressure drop of the well is different from the cases of pure depressurization and the CO2-EGR. The appropriate initial time for the CO2 injection is tested. Slighter seabed subsidence is observed when the CO2 injection is initiated earlier. The case of different injection pressure control showed that a lower injection pressure leads to a heavier seabed subsidence. A higher CO2 fraction allowed in the produced gas stream results in a higher cumulative gas production, but there is no significant impact on the seabed subsidence.

Numerical simulation of streamwise fluidelastic instability of tube bundles subjected to two-phase cross flow

This work aims to develop and validate a numerical model to simulate the flow-structure interaction in tube bundles subjected to two-phase flow. The model utilizes a mixture multiphase module in which a drift flux formulation is used to account for the slip between the phases. Two methods of numerical flow-structure interaction are used to predict the onset of fluidelastic instability (FEI) in the streamwise direction for a two-phase air–water flow mixture in parallel triangular tube bundles. These models are the hybrid analytical-flow field model and the direct numerical flow/structure coupling model. This work investigates the effects of void fractions in the range of 20% to 80% and several pitch-to-diameter ratios (P/D) in the range of 1.3 to 1.7. The results of the fluidelastic forces and the stability threshold are validated against the experimental data available in the literature and show an excellent agreement. The streamwise FEI threshold shows a significant dependency on the pitch-to-diameter ratio while the void fraction exhibits a lesser effect. Generally, the stability threshold increases as the pitch-to-diameter ratio increases. The model that was developed paves the way for devising of more reliable prediction tools for FEI in steam generators.

Krein signature and Whitham modulation theory: the sign of characteristics and the “sign characteristic”

AbstractIn classical Whitham modulation theory, the transition of the dispersionless Whitham equations from hyperbolic to elliptic is associated with a pair of nonzero purely imaginary eigenvalues coalescing and becoming a complex quartet, suggesting that a Krein signature is operational. However, there is no natural symplectic structure. Instead, we find that the operational signature is the “sign characteristic” of real eigenvalues of Hermitian matrix pencils. Its role in classical Whitham single‐phase theory is elaborated for illustration. However, the main setting where the sign characteristic becomes important is in multiphase modulation. It is shown that a necessary condition for two coalescing characteristics to become unstable (the generalization of the hyperbolic to elliptic transition) is that the characteristics have opposite sign characteristic. For example the theory is applied to multiphase modulation of the two‐phase traveling wave solutions of coupled nonlinear Schrödinger equation.

Sensorless Speed Control of Five-Phase PMSM Drives in Case of a Single-Phase Open-Circuit Fault

This paper introduces a new method to track saliency in a five-phase permanent magnet synchronous motor in case of a single-phase open-circuit fault. The proposed method depends on measuring the dynamic current response of the motor line currents due to the insulated-gate bipolar transistor switching actions. In case of a single-phase open-circuit fault, a fault-tolerant control strategy to control the remaining healthy currents results in minor system performance degradation. The new strategy that is proposed in this paper to track the saliency includes software modifications only to the saliency tracking algorithm used in healthy mode in order to make it applicable in the cases of a single-phase open-circuit fault. It uses the fundamental pulse width modulation waveform obtained using a symmetric multi-phase space vector pulse width modulation only. Simulation results are provided to verify the effectiveness of the proposed design over a wide speed range under different load conditions.

Synthesis of the Algorithm of the Vector Width-Pulse Modulation in a Nine-Phase Active Voltage Rectifier

The article is devoted to the problems of synthesis of multiphase electromechanic modules consisting of a multiphase electrical machine (m > 3) and a multiphase controlled converter. In the multi-phase design of the electric machine, it is possible to obtain a trapezoidal electromotive force and to increase the specific power conversion provided that the EMF and the current at the output of the m-phase generator are matched. The development of the vector pulse width modulation algorithm for the m-phase active voltage rectifier is considered, which will make it possible to match the shape and phase of the currents and voltages at the output of the m-phase generator in order to obtain the maximum active power of the module under study. The analysis of possible combinations of states of the keys of a nine-phase active rectifier is carried out. Each key state is assigned a base vector in a fixed coordinate system. It is noted that there are a number of combinations in which two or more different key states correspond to one base vector. The system of basic vectors is differentiated into its constituent levels, sectors and subsectors. In order to obtain any given voltage vector that does not coincide with the base vectors, the method of spacevector modulation is used. This method provides using 100 % DC link voltage as compared with sinusoidal pulse width modulation (86.6 %). The goal of space-vector modulation for a nine-phase active voltage rectifier is to implement the resultant spatial vector of the output voltage with a given average value within the modulation period. For this, the three vectors nearest to the given base vector must be found. To implement a given voltage vector, a sequence of sampling the base vectors in the modulation period is given, providing one commutation (commutation of two complementary keys) while passing from one basic vector to another to reduce switching losses. Analytic relationships of the weight coefficients for the generators of vectors are obtained, as well as the equations of the boundaries of the subsectors that form a diagram of combinations of states of the circuit. The sequence of the calculations presented in the paper is a technique for realizing the vector pulse-width modulation in nine-phase controlled electrical energy converters.

Nonlinear theory considering harmonic interaction using Eulerian hydrodynamic analysis

Traveling wave tube amplifiers are one of the most widely used vacuum electronic devices which are employed in various applications, in the areas of such as radar, wireless communication and electronic countermeasures system. Among traveling wave tubes, space-borne helix traveling wave tubes which are of high power, high efficiency, high reliability, long life and radiation hardened, are extensively used in satellite transmitter, data communication system and global positioning system. With the rapid development of the multiphase digital modulation schemes, communication systems are placing greater demands on the output power, electronic efficiency and nonlinear distortion characteristics of space-borne helix traveling wave tubes. However, the nonlinear beam-wave interaction will lead to the generation of harmonics, and thus reduces the output power and electronic efficiency. The harmonics can also act to create beats with the fundamental wave, and thus generate these beat frequencies which are commonly known as intermodulation products. As a result, the bit-error-rate will be increased and the system performance will be compromised. Therefore, the generation of harmonics is of significant current interest in space-borne helix traveling wave tubes. Understanding this effect provides a strong motivation for nonlinear analysis of a helix traveling wave tube. In this paper, a continuous electron phase distribution is obtained by treating the discrete electron beam as a charge fluid based on the Lagrangian theory. Then, to obtain a nonlinear Eulerian theory considering harmonic interaction, the electron phases in Lagrangian theory have been expanded into a series of harmonic components. Considering the 0th component and 1st component of the electron phases only and integrating over the initial phase distribution with the help of the relation of Bessel function, the nonlinear Eulerian theory considering harmonic interaction is established. The nonlinear Eulerian theory considering harmonic interaction is compared to a Lagrangian theory on a set of traveling wave tube parameters which are based on a single section of L-and C-bands traveling wave tubes. It is found that the nonlinear Eulerian theory considering harmonic interaction agrees accords well with the Lagrangian theory before the saturation effect occurs. But, it begins to make a difference near saturation point where the electron overtaking happens. The maximum error in gain between the nonlinear Eulerian theory considering harmonic interaction and the Lagrangian theory is less than 4% at 1 dB gain compression point. So the present nonlinear Eulerian theory considering harmonic interaction can effectively describe harmonic generation at 1 dB gain compression point. The simulation results validate the correctness and effectiveness of our nonlinear Eulerian theory considering harmonic interaction. In futuristic future efforts, it is hoped that the present nonlinear Eulerian theory considering harmonic interaction may provide insights into the behavioral mechanisms of nonlinear effects in space-borne helix traveling wave tubes.

A Multiphase Class-D Automotive Audio Amplifier With Integrated Low-Latency ADCs for Digitized Feedback After the Output Filter

A $5 \times 80$ W class-D audio power amplifier for automotive applications is presented. The amplifier is implemented in a 140-nm bipolar CMOS DMOS SOI. Configurable digital-loop filters can compensate for a range of LC output filters and their high loop gain (>50 dB between 20 Hz and 20 kHz) suppresses non-idealities of the output filter and enables low-cost output filter components. Key elements are the integrated low-latency $\Delta \Sigma$ analog to digital converters (ADCs) which digitize the output signals directly at the speaker load, after the output filter. The ADCs use filtering finite impulse response digital to analog converters in their feedback path to create an input–output transfer with a negative group delay at low frequencies. The ADCs have 116-dBA DR and −108 dB total harmonic distortion (THD). The bridge-tied load amplifier supports multiphase pulse-width modulation for lower electromagnetic interference. It operates with supplies from 6 to 25 V and with loads down to $1\Omega$ and achieves 19- $\mu \text{V}$ idle noise (Awtd) and 0.004% THD + N.

Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation

AbstractIn recent years, a connection between conservation law singularity, or more generally zero characteristics arising within the linear Whitham equations, and the emergence of reduced nonlinear partial differential equations (PDEs) from systems generated by a Lagrangian density has been made in conservative systems. Remarkably, the conservation laws form part of the reduced nonlinear system. Within this paper, the case of double degeneracy is investigated in multiphase wavetrains, characterized by a double zero characteristic of the linearized Whitham system, with the resulting modulation of relative equilibrium (which are a generalization of the modulation of wavetrains) leading to a vector two‐way Boussinesq equation. The derived PDE adheres to the previous results (such as [1]) in the sense that all but one of its coefficients is related to the conservation laws along the relative equilibrium solution, which are then projected to form a corresponding scalar system. The theory is applied to two examples to highlight how both the criticality can be assessed and the two‐way Boussinesq equation's coefficients are obtained. The first is the coupled Nonlinear Schrodinger (NLS) system and is the first time the two‐way Boussinesq equation has been shown to arise in such a context, and the second is a stratified shallow water model which validates the theory against existing results.