Phase Change Switch Research Articles

Identification of low-voltage phase lines using IEC 61850 and K-means clustering

Accurate phase line topology identification of LV lines facilitates the handling of line faults, which is of great significance for the safe and stable operation of distribution networks. In this paper, we model and analyze the LV lines based on graph theory, and propose a phase line relationship identification scheme based on the combination of HPLC and k-means clustering for the problem of missing or dynamically changing phase line relationships of LV lines in the station area. Aiming at the known phase-line relationship in the station area such as distribution panel, two phase-line configuration schemes, Terminal extension and new phase-line description logical node PPLD, are proposed. The area is divided by combining the configuration information of IEC 61850 SCL and the information of metering automation system. If HPLC is configured in the unknown region, HPLC is used to identify the phase line relationship. If HPLC is not configured, k-means based algorithm is used for correlation analysis between voltage measurements. Example results from a place in Shandong show that the accuracy of the method proposed in this paper is 93.96 % on average, which is higher compared to the existing methods.Significance: Accurate identification of phase-line relationships in LV lines is essential for optimising load through phase-change switches. In this study, we propose a novel phase line relationship identification scheme that combines HPLC and k-means algorithm based on the existing equipment in the station area. Leveraging the known topology within the existing equipment (LTU, switchboard, etc.) in the station area, we introduce two phase line configuration schemes, Terminal extension (extending the known phase line relationship) and the new phase line description logical node PPLD (a novel approach for configuring known phase line relationships). Additionally, we suggest a method of regional division to recognise phase line relationships in unknown regions. If HPLC is configured, it is used for phase line identification; otherwise, a k-means based algorithm analyses voltage measurements. By tailoring identification schemes to the actual characteristics of the station area, we significantly reduce the amount of data to be identified, improving accuracy and resource efficiency.

The influence of thermo-electromechanical coupling on the performance of lead-free BNT-PDMS piezoelectric composites

In recent times, there have been notable advancements in haptic technology, particularly in screens found on mobile phones, laptops, light-emitting diode (LED) screens, and control panels. However, it is essential to note that the progress in high-temperature haptic applications is still in the developmental phase. Due to their complex phase and domain structures, lead-free piezoelectric materials such as Bi0.5Na0.5TiO3 (BNT)-based haptic technology behave differently at high temperatures than in ambient conditions. Therefore, it is essential to investigate the aspects of thermal management and thermal stability, as temperature plays a vital role in the phase and domain transition of BNT material. A two-dimensional thermo-electromechanical model has been proposed in this study to analyze the thermal stability of the BNT-PDMS composite by analyzing the impact of temperature on effective electromechanical properties and mechanical and electric field parameters. However, the thermo-electromechanical modelling of the BNT-PDMS composite examines the macroscopic effects of the applied thermal field on mechanical and electric field parameters, as phase change and microdomain dynamics are not considered in this model. This study analyzes the impact of thermo-electromechanical coupling on the performance of the BNT-PDMS composite compared to conventional electromechanical coupling. The results predicted a significant improvement in piezoelectric response compared to electromechanical coupling due to the increased thermoelectric effect in the absence of phase change and microdomain switching for temperature boundary conditions below depolarization temperature ( Td∼200∘ C for pure BNT material).

Effect of Deposition Pressure and Temperature on Tungsten Thin-Film Heater for Phase-Change Switch Applications.

Tungsten (W) film is increasingly utilized in various microheater applications due to its numerous advantages. These advantages include a high melting point, positive constant temperature coefficient of resistance (TCR), good mechanical stability, and compatibility with semiconductor processes. In this paper, deposition parameters for enhancing the properties of W film were investigated, and an optimized microheater was fabricated. It was found that the deposition temperature and pressure can modify the TCR to be negative or positive and the crystalline phase of W films to be alpha phases or mixed with beta phases. A W film deposited under 650 °C with a pressure of 1 pa has a positive TCR and pure alpha phase crystalline structure. We applied this optimized W film as a microheater in an RF phase-change switch (RFPCS), and the maximum voltage of the optimized W microheater increased by at least 48% in this work. By optimizing the microheater, the phase-change switch can be successfully actuated in both on and off states, demonstrated by the Raman results of the phase-change material. A voltage pulse of 20 V/200 ns was enough to turn the switch off with MΩ, and 11 V/3 μs could turn the switch on with 138 Ω. The optimized microheater and device can cycle 500 times without failure. The insertion loss and isolation of the device at 20 GHz was 1.0 dB and 22 dB.

A Review on Material Selection Benchmarking in GeTe-Based RF Phase-Change Switches for Each Layer.

The global demand for radio frequency (RF) modules and components has grown exponentially in recent decades. RF switches are the essential unit in RF front-end and reconfigurable systems leading to the rapid development of novel and advanced switch technology. Germanium telluride (GeTe), as one of the Chalcogenide phase-change materials, has been applied as an RF switch due to its low insertion loss, high isolation, fast switching speed, and low power consumption in recent years. In this review, an in-depth exploration of GeTe film characterization is presented, followed by a comparison of the device structure of directly heated and indirectly heated RF phase-change switches (RFPCSs). Focusing on the prototypical structure of indirectly heated RFPCSs as the reference, the intrinsic properties of each material layer and the rationale behind the material selection is analyzed. Furthermore, the design size of each material layer of the device and its subsequent RF performance are summarized. Finally, we cast our gaze toward the promising future prospects of RFPCS technology.

Structural phase transition and resistive switching properties of Cu x O films during post-thermal annealing

We studied the phase change and resistive switching characteristics of copper oxide (Cu x O) films through post-thermal annealing. This investigation aimed to assess the material’s potential for a variety of electrical devices, exploring its versatility in electronic applications. The Cu x O films deposited by RF magnetron sputtering were annealed at 300, 500, and 700 °C in ambient air for 4 min by rapid thermal annealing (RTA) method, and then it was confirmed that the structural phase change from Cu2O to CuO occurred with increasing annealing temperature. Resistive random-access memory (ReRAM) devices with Au/Cu x O/p+-Si structures were fabricated, and the ReRAM properties appeared in CuO-based devices, while Cu2O ReRAM devices did not exhibit resistive switching behavior. The CuO ReRAM device annealed at 500 °C showed the best properties, with a on/off ratio of 8 × 102, good switching endurance of ∼100 cycles, data retention for 104 s, and stable uniformity in the cumulative probability distribution. This characteristic change could be explained by the difference in the grain size and density of defects between the Cu2O and CuO films. These results demonstrate that superior and stable resistive switching properties of RF-sputtered Cu x O films can be obtained by low-temperature RTA.

Thermally processed phase change behavior on the stoichiometric efficacy of quaternary Se77.5-X Te20 Sn2.5 AgX (X = 2.5, 5, 7.5) thin films

Thin films of the quaternary metal chalcogenide have recently gained attention due to their improved electrical, optical, thermal, and structural properties. The structural, thermal, morphological, optical, and electrical properties of Ag-modified novel quaternary Se–Te–Sn–Ag thin film systems are investigated in this paper. Temperature-dependent structural, electrical, and thermoelectric properties are given special attention. From Differential Thermal Analysis/Thermogravimetric Analysis (DTA/TGA), the Ag content in this composition induces thermal stability and crystalline phase as well as glass phase transitions. High-temperature X-ray diffraction (HTXRD) patterns were used to investigate the temperature-dependent structural phase transition, grain size, lattice strain, and dislocation density. The morphological observations show that Ag concentration promotes the nucleation and growth processes of nanorod structures in as-deposited thin films. Optical characteristics reveal higher IR transparency in thin films and high refractive indexes in the range of 3.22–3.29. The as-deposited thin films resistivity decreases with increasing temperature and silver content. The Hall measurement corroborates the results obtained from the Seebeck measurements, indicating that the samples are n-type. The phase change switching mechanism of phase change devices is still unclear; there are two possible mechanisms: thermal and electronic models. This work proposes thermally processed phase transition behaviors in structural and electrical studies. The result of the above analyses shows that the quaternary Se–Te–Sn–Ag thin film will be a potential candidate for phase change device applications.

Multiwavelength camouflage metamaterials with adjustable emissivity.

Metamaterials-based multispectral camouflage has attracted growing interest in most fields of military and aerospace due to its unprecedented emission adjustability covering an ultra-broadband spectral range. Conventional camouflage mainly concentrates on an individual spectral range, e. g. either of visible, mid-wavelength-infrared (MWIR) or long-wavelength-infrared (LWIR), which is especially incapable of self-adaptive thermal camouflage to the changing ambient environment. Here, we theoretically demonstrate a multispectral camouflage metamaterial consisting of a four-layer titanium/silicon/vanadium dioxide/ titanium (Ti/Si/VO2/Ti) nanostructure, where the background temperature-adaptive thermal camouflage is implemented by exploiting the switchable metal/dielectric state of the phase-changing material VO2 for regulating the infrared emissivity of the designed metamaterial, whilst visible color camouflage is also achieved by tuning thickness of middle Si layer to match the background's appearance. It has been shown that the designed metamaterial with the dielectric state of VO2 enables thermal camouflage of high background temperature by increasing the thermal emission (average emissivity of 0.69/0.83 for MWIR/LWIR range), meanwhile, the metamaterial of the metallic state of VO2 for low background temperature thermal camouflage stemming from low emission (average emissivity of 0.29 for both MWIR/LWIR range) due to high infrared reflection. Furthermore, the designed metamaterial structural color is robust for a phase change switching. This proposed adaptive camouflage provides a potential strategy to broaden dynamical camouflage technology for further practical application in the fields of military and civilian.

Novel four-port RF phase change switches based on GeTe thin film

An indirect-heated phase-change switch (PCS) using germanium telluride (GeTe) has been fabricated using thermal actuation driven by thin film heater on the model. Switches require a low ON-state resistance and a high OFF-state resistance with OFF/ON resistance ratio of 105. The finite element analysis simulation is applied to simulate the temperature of individual node GeTe with different microwave heating pulses. Finally, in order to reduce the phase-change time and increase the switching speed of indirectly heated switching structures, a new four-port indirectly heated phase change switching structure is proposed. In this paper, the heat dissipation of the switch is increased by etching deep grooves on the back of the switch. This structure obviously reduces the phase change time compared to conventional indirectly heated phase change switches the time between ON-state and OFF-state is reduced by more than 19% and the total process is reduced by more than 47%. The GeTe PCSs with etched grooves not only significantly increases the switching speed, but also reduces the risk of recrystallization of the phase change material.

Electrode area dependent switching behavior of Ge2Sb2Se4Te1 phase change material driven by narrow voltage pulse

As a recently studied phase change material, Ge2Sb2Se4Te1 (GSST) shows excellent potential in the application of optical devices, because it presents very low loss in the amorphous state within the optical communication wavelength of 1550 nm and exhibits significant differences in optical properties before and after phase change. However, it is still challenging that, in real GSST devices, phase change switching is driven by narrow voltage pulse. In this study, the sandwich structures of GSST film with different electrode areas were prepared to analyze the phase change switching performance between crystalline and amorphous states. The results show that the endurance cycling of phase change switching increases with decreasing electrode area. When the electrode radius is 1 μm, the phase change switching number can reach 10 000. The improvement of this phase change switching can be attributed to the temperature uniformity, which was verified by the simulation of electrical pulse heating.

Resistance Ratio Enhancement in Phase-Change RF Switches at Cryogenic Temperatures

This letter reports the dc and radio frequency (RF) performance of the phase-change RF switches (PCRS) as a function of temperature. Resistance change behavior of the germanium telluride (GeTe) material is experimentally investigated over 77 to 335 K. The device shows metallic behavior in the crystalline state which exhibits consistent low resistivity over a wide temperature range, while in the amorphous state, resistance increases to more than eleven orders of magnitude as a function of decreasing temperature from 300 to 77 K. Device current–voltage (IV) characteristics and the RF performance are investigated for multiple device cycles. The RF performance of the PCRS is reported with and without microheater are examined to confirm the performance variation of the phase-change switches at cryogenic temperatures.

Advantages of Ta-Doped Sb3Te1 Materials for Phase Change Memory Applications.

Phase change memory (PCM), a typical representative of new storage technologies, offers significant advantages in terms of capacity and endurance. However, among the research on phase change materials, thermal stability and switching speed performance have always been the direction where breakthroughs are needed. In this research, as a high-speed and good thermal stability material, Ta was proposed to be doped in Sb3Te1 alloy to improve the phase transition performance and electrical properties. The characterization shows that Ta-doped Sb3Te1 can crystallize at temperatures up to 232 °C and devices can operate at speeds of 6 ns and 8 × 104 operation cycles. The reduction of grain size and the density change rate (3.39%) show excellent performances, which are both smaller than that of Ge2Sb2Te5 (GST) and Sb3Te1. These properties conclusively demonstrate that Ta incorporation of Sb3Te1 alloy is a material with better thermal stability and faster crystallization rates for PCM applications.

Reconfigurable Metalens with Phase-Change Switching between Beam Acceleration and Rotation for 3D Depth Imaging.

Depth imaging is very important for many emerging technologies, such as artificial intelligence, driverless vehicles and facial recognition. However, all these applications demand compact and low-power systems that are beyond the capabilities of most state-of-art depth cameras. Recently, metasurface-based depth imaging that exploits point spread function (PSF) engineering has been demonstrated to be miniaturized and single shot without requiring active illumination or multiple viewpoint exposures. A pair of spatially adjacent metalenses with an extended depth-of-field (EDOF) PSF and a depth-sensitive double-helix PSF (DH-PSF) were used, using the former metalens to reconstruct clear images of each depth and the latter to accurately estimate depth. However, due to these two metalenses being non-coaxial, parallax in capturing scenes is inevitable, which would limit the depth precision and field of view. In this work, a bifunctional reconfigurable metalens for 3D depth imaging was proposed by dynamically switching between EDOF-PSF and DH-PSF. Specifically, a polarization-independent metalens working at 1550 nm with a compact 1 mm2 aperture was realized, which can generate a focused accelerating beam and a focused rotating beam at the phase transition of crystalline and amorphous Ge2Sb2Te5 (GST), respectively. Combined with the deconvolution algorithm, we demonstrated the good capabilities of scene reconstruction and depth imaging using a theoretical simulation and achieved a depth measurement error of only 3.42%.

The study of NiCr/GeTe ohmic contacts in the GeTe film based directly heated phase change switch

NiCr can be used as a heating electrode to effectively reduce the insertion loss and switching power of the phase change switch. Therefore, the specific contact resistivity (ρc) between NiCr and GeTe was obtained, which is 7.45 × 10−7 (CTLM) or 3.66 × 10−7 (TLM). EDS shows that annealing at 300 °C induces NiCr diffusion to the GeTe films surface, which reduces the number of dangling bonds and facilitates the reduction of ρc(GeTe/NiCr). XPS indicates that the GeTe films surface treated with NH4OH solution is enriched in Ge2+ leading to a decrease in ρc(GeTe/NiCr). In contrast, the GeTe films surface treated with HCl solution is enriched in Te0, and the removal of oxides is obvious, while the ρc(NiCr/GeTe) increases. Finally, a direct heating phase change switch base on GeTe films was realized using NiCr film as the heating electrode with resistance window of over 105.

High-speed four-port indirect-heating phase-change switch with a top microheater based on GeTe

针对传统加热器中置间接加热型相变开关的固有切换速度缓慢难题，本文提出一种加热器顶置的射频开关新结构FIPCS-T，通过热传导过程自上而下的定向性，建立了更加有效的焦耳热能量利用方法。根据新结构中不同射频参数的仿真，表明FIPCS-T结构对升温过程和淬火过程均能缩短相变材料达到临界温度的时间，升温过程比淬火过程的缩短更加显著，相比于传统中置间接加热相变开关的升温-淬火环节时间缩短20%以上，这不仅可以有效提高间接加热相变开关的切换速度，同时还能够有效降低重结晶风险，并可在微波、毫米波、太赫兹等超大范围频段保持低反射、低插损和端口高隔离性能。虽然GeTe相变材料在存储等方面开展了多年研究，但其特殊相变特征能否解决射频开关面临的挑战，前所未有，本文探索研究结果表明：GeTe热相变机理与PIN、MEMS等其他原理相比，新射频开关的速度更快、工作频率更高、插入损耗更低。在射频开关特性验证的基础上，我们构建了由5个FIPCS-T单元组成的DGS可重构滤波器，实现了滤波器频率和带宽的重构，证明了开关状态组合对于滤波器媒质特性的调控能力；再通过5单元FIPCS-T开关状态的组合与电致热控制，实现了低通、带通滤波特征的可重构，为未来大规模天线、大规模电路等先进可重构无线电系统的智慧调控提供了全新的射频开关机理和方法。同时，引入类似相变存储器多值方案的控制方法，可有效提升相变开关的调控和选择维度，增加可调控的性能范围和参数，实现其他类型开关不能实现的更深层次调控优势。

Synthesis mechanism and magnetoresistance effect of millimeter-sized GeTe faceted crystals

GeTe materials have a wide range of applications in the fields of thermoelectrics, phase-change switching or storage, ferroelectrics, spintronics, and so on. In this paper, millimeter-sized GeTe faceted crystals are synthesized through heterogeneous chemical reactions without metal catalysts or transport agents. Most of the crystals have hexagonal surfaces, while a few crystals have rectangular surfaces, which are dominated by the closest packed (111) planes and the low-energy (100) planes, respectively. The 180° and 141°/39° ferroelectric domain walls are found on the (111) plane of hexagonal GeTe crystals by the chemical etching. By studying the products under different conditions, it's inferred that the GeTe faceted crystals are grown below the melting point by the reactions of preferentially deposited Ge motes and Te2/GeTe2 vapor phase, which are caused by the partial dissociation of polycrystalline GeTe. Hexagonal GeTe crystals with (111) plane exhibit non-saturating linear magnetoresistance (MR) of ∼25.9% under 9 T at 4.2 K, but the MR of rectangular crystals with (100) plane is just ∼9.5%. The MR effect of GeTe is likely related to the spin splitting on band structure due to the Rashba effect and the intrinsic inhomogeneity of telluride because of the heavily self-doped characteristic.

Electrodeposition of GeSbTe-Based Resistive Switching Memory in Crossbar Arrays

In this work, we report on the fabrication of resistive random-access memory cells based on electrodeposited GeSbTe material between TiN top and bottom electrodes in a crossbar architecture. The cells exhibit asymmetric bipolar resistive switching characteristics under the same SET and RESET compliance current (CC), showing highly uniform and reproducible switching properties. A multi-state switching behavior can be also achieved by varying the sweeping voltage and CC. Unlike phase-change switching, the switching between the high-resistance state and the low-resistance state in these cells can be attributed to the formation and rupture of conductive Te bridge(s) within the Te-rich GeSbTe matrix upon application of a high electric field. The results point toward the usage of the electrodeposition method to fabricate advanced functional device structures for application in non-volatile memory.

Indirectly Heated Switch as a Platform for Nanosecond Probing of Phase Transition Properties in Chalcogenides

Although phase-change materials (PCMs) have been studied for more than 50 years, temperature-dependent characterization of the phase transition dynamics remains challenging due to the lack of nanosecond-nanoscale thermometry. In this article, we utilize the four-terminal, indirectly heated phase-change switch (IPCS), which was originally designed for nonvolatile radio frequency (RF) applications, as an ultrafast electrothermal platform to study PCM. We propose a novel experimental setup that allows nanosecond probing of the transient resistance of the PCM, beyond the melting temperature (>1100 K), due to the built-in electrical isolation between the PCM path and the thermal actuation path of the IPCS. The embedded metallic heater can induce reversible phase transitions between the crystalline and amorphous phases of the PCM. Our platform enables simultaneous measurements of the dynamics of PCM resistance (as a probe for the phase of the material) and heater temperature, during the application of heating pulses. Furthermore, we map the surface temperature of the IPCS at steady state by scanning thermal microscopy (SThM) and show the effect of cooling by electrodes in devices with overlap between the heater and PCM contacts. Our method can be used to study chalcogenides and other amorphous semiconductors for reconfigurable electronics and neuromorphic hardware.

(Invited) ALD of Phase Change and Threshold Switching Materials for Next-Generation Nonvolatile Memory Devices

Memory technology continues to be at a crossroads. Established devices such as DRAM, Flash, and SRAM remain dominant, but each are facing increasingly formidable challenges in scaling, cost, and performance. Emerging memory technologies are attempting to displace these three or to find application spaces between those they traditionally support. However, no emerging memory has been able to demonstrate significant advantages over the incumbents, resulting in a proliferation of options such as phase change memory (PCM), filamentary resistive memory (ReRAM), ferroelectric memory (FERAM), magnetic memory (e.g. STT-MRAM and SOT-MRAM), and several others. Of these, the most successful has been PCM as evidenced by the commercial introduction of PCM based crosspoint memory in 2017. PCM based crosspoint memory has had limited market penetration in part due to the high manufacturing cost; the current layer-by-layer approach to PCM fabrication makes scaling difficult. In order to be cost competitive, crosspoint arrays will need to be manufactured in a style similar to that of 3D V-NAND where the active layers are deposited conformally inside deep features simultaneously forming hundreds of junctions. Chemical Vapor Deposition or Atomic Layer Deposition of these films is likely required to make this a reality. Some progress in materials for the PCM memory element has been reported; however, a remaining concern for crosspoint memory is the selector device, used in suppressing the sneak path current, consisting of a non-linear two-terminal device to properly select each memory element. In addition to high non-linearity, a selector device also requires high on-state current density JON, fast switching time, high endurance, stability, high scalability and back-end-of-line (BEOL) integration. Several selector devices have been proposed to date, e.g., mixed-ionic-electronic-conduction (MIEC), field-assisted superlinear threshold (FAST), and amorphous silicon (a-Si) selectors, but Ovonic Threshold Switch (OTS) composed of chalcogenide multinary materials clearly appears as the best candidate to cover all the mentioned requirements for high-density crosspoint applications.Currently, chalcogenide materials are deposited by using physical vapor deposition (PVD) that allows for fine tuning of the film stoichiometry, but at the same time limits its conformality and homogeneity on a large scale. To address this challenge, atomic layer deposition (ALD) is desirable; unfortunately, only ALD OTS As-free compositions with high leakage and limited endurance have been developed so far. In this report we describe the process and materials for GeSbTe PCM and a novel quaternary GeAsSeTe ALD OTS composition. We show a physical characterization of the ALD films and provide a comprehensive electrical characterization of integrated devices in DC and pulsed regimes. The OTS selector performance, in particular, shows excellent results (See Figure 1) - good selectivity (> 104), low threshold voltage (Vth) drift (< 40 mV/dec), fast switching (< 10 ns), excellent endurance (> 109 cycles) and robust stability. These results pave the way for future development of ALD chalcogenide-based selectors as a leading technology for multiple-stack integration of crosspoint memory arrays. To provide a physical understanding of the devices under study, we propose an analytical model for the subthreshold conduction mechanism, allowing for future development and optimization of the composition for 3D crosspoint memory applications.Figure 1. Electrical performance of an OTS selector over one billion cycles a) Pulsed-IV taken at each decade of the 1e9 endurance cycles. b) Sub-threshold current measured at each decade of the 1e9 endurance cycles. c) Evolution of the threshold voltage throughout the endurance test. Each point is measured three times, and all three measurements are reported d) Selector window at each decade of the endurance test. Figure 1

Compact Modeling and Electrothermal Measurements of Indirectly Heated Phase-Change RF Switches

Four-terminal, inline, indirectly heated phase-change switches (IPCS) have emerged as great contenders for reconfigurable radio frequency (RF) integrated circuits, providing state-of-the-art cutoff frequency thanks to their built-in dc-RF decoupling. However, the switching of IPCS devices is determined by their temperature which is challenging to predict. In this article, we present a physics-based compact model of the IPCS, validated by finite-element method simulations and measurements of IPCS devices. The model accurately predicts the thermal and electrical dynamics of the device by considering the changes in heater resistance, contact resistance, and parasitic capacitance. The complete model is implemented in Verilog-A, and a downloadable version is freely available at the nanoHUB.org. We show how the compact model can be used for rapid device evaluation and optimization between RF performance and energy efficiency. Nanosecond electrical thermometry of the heater for varying pulses during IPCS device operation and RF measurements is used to experimentally validate the model.

Research on Three-phase Unbalance Control of Distribution Area Based on Intelligent Fusion Terminal

As the three-phase four-wire system is used in power transmission and distribution in our country, the single-phase load is the most part of power consumption. The three-phase imbalance of voltage and current on the outlet side of transformers may occur due to the unexpectedly increase or decrease of the load in a certain phase of the low-voltage distribution network. This phenomenon will reduce the service time of the equipment and the power quality of the power supply. A multiple population genetic algorithm (MPGA) is proposed in this paper to treat this problem. Intelligent fusion terminal (IFT) is used as the hardware application platform to communicate with phase-change switch in order to execute the optimal strategy, the three-phase current of the load side would be balanced after the strategy is executed. An example is simulated with MATLAB to show the effectiveness of MPGA.