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2016 15th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm)最新文献

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Transient modeling and validation of chilled water based cross flow heat exchangers for local on-demand cooling in data centers 数据中心就地按需冷却的基于冷冻水的横流换热器的瞬态建模与验证
M. del Valle, Carol Caceres, A. Ortega
Hybrid air/liquid cooling systems used in data centers enable localized, on-demand cooling, or “smart cooling” using various approaches such as rear door heat exchangers, overhead cooling systems and in row cooling systems. These systems offer the potential to achieve higher energy efficiency by providing local cooling only when it is needed, thereby reducing the overprovisioning that is endemic to traditional systems. At the heart of all hybrid cooling systems is an air to liquid cross flow heat exchanger which regulates the amount of cooling that the system provides by modulating the liquid or air flows or temperatures. Understanding the transient response of the heat exchanger is crucial for the precise control of the system. In this paper a 12 in. × 12 in water to air heat exchanger, with similar characteristics to the heat exchanger commonly found in data centers, is modeled using three partial differential equations solved by the use of a finite difference approach. The model is validated against experimental data obtained from an experimental rig designed to introduce controlled transient perturbations in temperature and flow on the inlet air and liquid flows to the heat exchanger. Experimental data were obtained for step change, ramp change, and sinusoidal variation in the inlet water temperature and mass flow rate. Steady state heat transfer coefficients are used in the air and liquid side of the heat exchanger. The heat transfer coefficient inside the tubes is calculated by the use of the Gnielinski correlation. A steady state technique is used to extract the air side heat transfer coefficient. With these parameters, it was found that the dynamic heat exchanger model agrees remarkably well with the transient experimental data. The modeling equations also provide insight into the characteristic response times of the heat exchanger in terms of the major independent non-dimensional parameters describing its design and operating conditions.
数据中心中使用的混合空气/液体冷却系统可以使用各种方法实现本地化,按需冷却或“智能冷却”,例如后门热交换器,顶部冷却系统和排冷却系统。这些系统仅在需要时提供局部冷却,从而提供了实现更高能源效率的潜力,从而减少了传统系统特有的过度供应。所有混合冷却系统的核心是一个空气-液体交叉流热交换器,它通过调节液体或空气的流动或温度来调节系统提供的冷却量。了解热交换器的瞬态响应对系统的精确控制至关重要。在这张纸上有一个12英寸。采用有限差分法求解的三个偏微分方程,对具有与数据中心中常见的换热器相似特性的x12水-空气换热器进行建模。该模型与实验数据进行了验证,实验数据来自一个实验装置,该实验装置设计用于引入受控的温度和流量的瞬态扰动,并对进入换热器的空气和液体流动进行了控制。得到了进口水温和质量流量的阶跃变化、斜坡变化和正弦变化的实验数据。换热器的空气侧和液体侧采用稳态传热系数。利用格涅林斯基关系计算了管内换热系数。采用稳态技术提取空气侧换热系数。利用这些参数,发现动态换热器模型与瞬态实验数据吻合得非常好。建模方程还可以根据描述其设计和运行条件的主要独立无量纲参数,深入了解热交换器的特征响应时间。
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引用次数: 10
Thermal optimization of embedded thermoelectric generators in refractory furnaces 难熔炉嵌入式热电发电机的热优化
K. Yazawa, A. Shakouri
Industrial energy consumption represents a large part of the energy flow in the United States and it would probably be similar in many other countries. Coal or gas fired furnaces are a major component of the energy consumption to supply high temperatures. Refractory wall is indispensable along the furnace pathway designed for melting or processing materials. Unfortunately, more than a fraction of the input energy diffuses across the refractory wall due to the high temperatures and the waste heat is dumped to the ambient. Thermoelectric power generator (TEG) has an ultra low profile and is widely scalable with arraying the modules. This configuration is matched very well with the requirement of harvesting energy from the waste heat through the refractory wall without any design change of the current furnaces. We propose a simple water-cooled TEG system replacing a fraction of the refractory wall thickness while maintaining the melt temperature and the heat flux would be the same as the current refractory wall with passive air cooling. Design optimization is conducted, trading-off the TEG module thickness and the furnace wall thickness maximizing the power output while maintaining the above heat flux. We will present a quantitative analysis based on an example of the conventional fire ports that produce furnace gases at a temperature of 1500 °C. The furnace is designed for melting glass pellets and maintaining the temperature of melt glass at 1000 °C in a pool. A facility with 500 ton/day capacity is modeled. There are four fire ports and 54 cm thick aluminum-zirconia-silica (AZS) refractory wall around the ports. The thermal optimization is conducted considering the design of TEG matched to desired heat flux of approximately 10 kW/m2. As shown in our earlier work, the TEG design with a smaller TE element fill factor down to 10% or below, will provide the most cost effective power generation. Interestingly, the additional material cost for the optimum TEG with 10% fill factor and a copper cold plate is much less expensive compared to the cost needed for the AZS refractory wall material that it is replacing. When the remaining thickness of the refractory wall is 25 cm, the power generation from TEG is 1.72 kW/m2 while maintaining the same heat flux. The total power output from the all four fire ports can be 66.1 kW and the cost for the TEG module is estimated to be $0.5 per Watt based on demonstrated robust high temperature TE material.
工业能源消耗占美国能源流动的很大一部分,在许多其他国家可能也是如此。燃煤或燃气炉是提供高温能源消耗的主要组成部分。耐火壁是为熔化或加工材料而设计的炉道上不可缺少的部分。不幸的是,由于高温,超过一部分的输入能量扩散穿过耐火墙,余热被倾倒到环境中。热电发电机(TEG)具有超低的外形和广泛的可扩展的模块阵列。这种结构非常符合在不改变现有炉体设计的情况下,通过耐火壁从废热中收集能量的要求。我们提出了一种简单的水冷TEG系统,在保持熔体温度和热流密度与目前采用被动空气冷却的耐火壁相同的情况下,替换部分耐火壁厚度。进行设计优化,在保持上述热流密度的同时,权衡TEG模块厚度和炉壁厚度,使输出功率最大化。我们将根据一个在1500°C温度下产生炉气的传统火口的例子进行定量分析。该炉设计用于熔化玻璃球团,并在池中保持熔融玻璃的温度在1000°C。以500吨/天的生产能力为模型。有4个火口,火口周围有54 cm厚的AZS耐火墙。考虑热流密度约为10 kW/m2的TEG设计,进行了热优化。正如我们之前的工作所示,TEG设计具有较小的TE元件填充系数,可降至10%或以下,将提供最具成本效益的发电。有趣的是,具有10%填充系数的最佳TEG和铜冷板的额外材料成本,与它所取代的AZS耐火壁材料所需的成本相比要便宜得多。当耐火壁剩余厚度为25cm时,在保持相同热流密度的情况下,TEG发电量为1.72 kW/m2。所有四个消防端口的总输出功率可达66.1 kW,基于已演示的坚固的高温TE材料,TEG模块的成本估计为每瓦0.5美元。
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引用次数: 3
Experimental investigation of CRAH bypass for enclosed aisle data centers 封闭通道数据中心CRAH旁路的实验研究
H. Erden, M. Yildirim, M. Koz, H. Khalifa
Aisle containments in data centers help provide uniform server inlet air temperatures. This allows the cooling system to run at a higher evaporator temperature and more efficiently. On the other hand, CRAH units run at higher speeds to ascertain that racks receive sufficient air flow. Since CRAH fan power already constitutes an important component of data center power use, such increases in the fan power can overshadow the energy savings due to more efficient chiller operation. CRAH bypass configuration is proposed to achieve optimum operating condition for enclosed aisle data centers. This configuration utilizes fan-assisted perforated floor tiles to induce a fraction of tile flow from the room through bypass ports or leakage paths and help decreasing the amount of air flow passing through the large flow resistances of CRAH units. Experimental results show that there is an optimum operating condition for the specific data center test cell that is designed to represent an enclosed aisle data center utilizing the proposed CRAH bypass configuration. Here, the flow characteristics of major system components and experimental measurements have been used to calibrate a flow network model (FNM) for the design optimization and trade-off analysis of the proposed system. Calibrated FNM along with a thermodynamic model (TM) of the cooling infrastructure provides an estimate of the energy use at various fractions of CRAH bypass air and chilled water temperatures. This study introduces the design of the experimental setup for testing CRAH bypass configuration for enclosed aisles and for calibrating models to predict the cooling infrastructure energy saving potential of the proposed technique.
数据中心的通道密封有助于提供统一的服务器入口空气温度。这使得冷却系统在更高的蒸发器温度下运行,效率更高。另一方面,CRAH单元以更高的速度运行,以确保机架获得足够的气流。由于CRAH风扇功率已经构成了数据中心电力使用的重要组成部分,因此风扇功率的增加可能会掩盖由于更高效的冷却器运行而节省的能源。为了实现封闭通道数据中心的最佳运行状态,提出了CRAH旁路配置。这种配置利用风扇辅助穿孔地板砖,诱导一小部分地板砖通过旁路端口或泄漏路径从房间流出,并有助于减少通过CRAH单元的大气流阻力的空气流量。实验结果表明,对于特定的数据中心测试单元,存在一个最佳的运行条件,该测试单元被设计为利用所提出的CRAH旁路配置来代表封闭通道数据中心。在这里,主要系统组件的流动特性和实验测量已被用来校准流量网络模型(FNM),用于设计优化和折衷分析所提出的系统。经过校准的FNM以及冷却基础设施的热力学模型(TM)提供了在CRAH旁通空气和冷冻水温度的不同部分下的能源使用估计。本研究介绍了实验装置的设计,用于测试封闭通道的CRAH旁路配置和校准模型,以预测所提出技术的冷却基础设施节能潜力。
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引用次数: 9
A computational study of PCB layer orientation of WCSP assembly under temperature dependent drop impact loading 温度相关跌落冲击载荷下WCSP组件PCB层取向的计算研究
A. Mahmood, Trina Barua, Saylalee Sabne, A. R. Nazmus Sakib, D. Agonafer
Chip Scale Packages (CSP) are used more and more in the portable electronic devices with its growing popularity due to small form factor. Electrical, Thermomechanical and Mechanical loadings act simultaneously on the electronic products during their daily usage. Due to the market demand, new high-performance functions are continuously being integrated with these devices despite the decreasing from factor and generation of more thermal stresses inside. These smaller devices are more prone to accidental drop and experience impact load, causing board interconnect failure by the repeatability of the drop occurrences. Therefore, the reliability of these products due to various loadings are being researched by taking multi-dimensional approach. A computational study has been carried out in this paper to investigate the effect of impact loading on the solder joints of WLCSP component boards. Here, a more thorough understanding of the solder joint behavior is examined by carrying out drop test with respect to elevated temperature and using PCBs of varying thickness and layer stack-ups. The same WLCSP is used for different boards and subjected to drop test according to the JEDEC specifications [1]. Two different types of boards are used and to simulate the actual drop test modified Input G method, that is Direct Acceleration Input method, was followed. The comparison of the boards has been made to understand the effect of temperature on the reliability of solder interconnects and on the strain generation induced in the PCBs during the drop test. It has been found that due to decreasing elastic modulus at higher temperature the behavior of both the boards are similar except the fact that thin board experiences relatively more stress in its interconnects after crossing a threshold temperature.
芯片级封装(CSP)由于其小巧的外形尺寸,在便携式电子设备中得到越来越多的应用。在电子产品的日常使用过程中,电气、热力和机械负荷同时作用于电子产品。由于市场需求,新的高性能功能不断被集成到这些设备中,尽管这些设备内部的热应力越来越大。这些较小的设备更容易发生意外跌落和冲击负载,由于跌落事件的重复性导致电路板互连故障。因此,采用多维度的方法研究这些产品在各种载荷作用下的可靠性。本文对冲击载荷对WLCSP组件板焊点的影响进行了计算研究。在这里,通过对高温和使用不同厚度和层堆叠的pcb进行跌落测试,对焊点行为进行更彻底的了解。相同的WLCSP用于不同的板,并根据JEDEC规范[1]进行跌落测试。采用了两种不同类型的板,并采用了改进的G输入法,即直接加速度输入法来模拟实际的跌落试验。对两种电路板进行了比较,以了解温度对焊料互连可靠性的影响以及在跌落试验中pcb中产生的应变。研究发现,在较高的温度下,由于弹性模量的降低,两种板的行为是相似的,除了薄板在超过阈值温度后在其互连处经历相对更大的应力。
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引用次数: 0
Thermal behavior of water-copper and water-stainless steel heat pipes operating in cycles 循环运行的水-铜和水-不锈钢热管的热行为
Debora de O. Silva, R. Riehl
Heat pipes are a closed tube or chamber of different shapes whose inner surfaces are lined with a porous capillary wick, containing a saturated working fluid. It is a technology not restricted to aerospace applications, which is frequently used as thermal control devices of satellites and space vehicles. Some other sectors are finding interest on applying heat pipes to promote the thermal control of electronic equipment and heat exchangers performance augmentation. The use of heat pipes in such equipment allows the development of more compact and efficient heat exchangers compared to traditional designs, which increases the interest on applying them for industrial purposes. Heat pipes operating at mid-level temperatures have found several applications on both aerospace and industry segments. This work has the objective to present experimental results of heat pipes operation designed and manufactured in stainless steel and copper, using water as working fluid, operating on cycles at temperatures up to 200°C focusing on industrial applications. Test results showed reliable operation during the cycles, with fast start-ups and transients, achieving thermal conductances of up to 21.9 W/°C. Even though water-copper heat pipes present a better thermal performance when compared to the water-stainless steel heat pipes, there is a wide application not only for industry but also for aerospace.
热管是一种不同形状的封闭管或室,其内表面内衬有多孔毛细管芯,其中含有饱和的工作流体。它是一种不局限于航空航天应用的技术,经常被用作卫星和空间飞行器的热控制装置。其他一些部门也对应用热管来促进电子设备的热控制和热交换器性能的提高感兴趣。与传统设计相比,在此类设备中使用热管可以开发更紧凑和高效的热交换器,这增加了将其应用于工业目的的兴趣。在中等温度下工作的热管在航空航天和工业领域都有很多应用。这项工作的目的是展示用不锈钢和铜设计和制造的热管操作的实验结果,以水为工作流体,在高达200°C的温度下循环操作,重点是工业应用。测试结果表明,在循环期间运行可靠,启动和瞬态速度快,热导率高达21.9 W/°C。尽管水-铜热管比水-不锈钢热管表现出更好的热性能,但它不仅在工业上有广泛的应用,而且在航空航天领域也有广泛的应用。
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引用次数: 1
On energy efficiency of liquid cooled HPC datacenters 液冷HPC数据中心的能源效率研究
M. Patterson, S. Krishnan, John M. Walters
HPC Data Center's performance and growth are now being limited by both cost and power. A cost-efficient data center and an energy-efficient data center are all too often mutually exclusive, but they do not have to be. Liquid cooling is one area that, when done right, can improve both costs and energy efficiency. The design for liquid cooling systems generally begins with the ASHRAE liquid cooling datacenter classes. These provide guidance to both datacenter facility cooling system designers and electronic equipment manufacturers by providing a common baseline and understanding of the interface conditions between the cooling and the IT equipment. Further, the liquid cooling classes also suggest possible cooling equipment for a given datacenter class. Due to the aforementioned cooling equipment prescription, perception exists that moving from W1/W2 class environments to W3 or W4 classes represent increased energy efficiency during IT equipment operation. In this paper we show this not to be the case universally and explore a more detailed, technical approach to optimizing both cost and energy efficiency. The range of parameters includes geographical and climate conditions, state of the existing data center cooling infrastructure (greenfield, retrofit, cluster change-out, expansion), and IT level liquid cooling architecture. Through this analysis we show that for energy efficient operation of the IT equipment there exists an optimum liquid operating temperature that can also provide the lowest TCO. This temperature can drive the right capital investment as well as reduce facility operational expense and IT operational expense. We also explore the impact on reliability, the controls architecture, use of efficiency metrics, cluster compute performance, and opportunities for energy re-use.
高性能计算数据中心的性能和增长现在受到成本和功率的限制。一个经济高效的数据中心和一个高能效的数据中心常常是相互排斥的,但它们并不一定要如此。液体冷却是一个领域,如果做得好,可以提高成本和能源效率。液体冷却系统的设计通常从ASHRAE液体冷却数据中心课程开始。这些标准为数据中心设施冷却系统设计人员和电子设备制造商提供了一个共同的基线,并了解了冷却设备和IT设备之间的接口条件。此外,液冷类还建议为给定的数据中心类提供可能的冷却设备。由于前面提到的冷却设备处方,人们认为从W1/W2类环境转移到W3或W4类环境意味着在IT设备运行期间提高了能源效率。在本文中,我们表明这种情况并非普遍存在,并探索了一种更详细的技术方法来优化成本和能源效率。参数范围包括地理和气候条件、现有数据中心冷却基础设施的状态(新建、改造、集群变更、扩展)以及IT级液冷架构。通过这一分析,我们表明,对于IT设备的节能运行,存在一个最佳的液体工作温度,也可以提供最低的TCO。这种温度可以推动正确的资本投资,并减少设施运营费用和IT运营费用。我们还探讨了对可靠性的影响、控制体系结构、效率指标的使用、集群计算性能以及能源再利用的机会。
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引用次数: 10
CFD study of flow boiling in silicon microgaps with staggered pin fins for the 3D-stacking of ICs 交错针翅硅微隙内流动沸腾的CFD研究
D. Lorenzini, Y. Joshi
Flow boiling in surface-enhanced microgaps represents a promising thermal control method for the removal of relatively high heat fluxes in applications such as three-dimensional (3D) integration of microelectronics. Although a few experimental investigations have reported encouraging results for these types of cooling layers, the computational fluid dynamics (CFD) analysis of the involved physics has lagged behind due to a number of challenges. In the present study, a phase-change model is used with the Volume of Fluid (VOF) method for interface tracking to analyze the transient flow regime evolution due to boiling in a microgap with circular pin fins for area enhancement, where the simultaneous heat conduction is solved in the silicon medium. High-Performance Computing (HPC) is used for investigating two-phase flow and heat transfer in a relatively dense array of pin fins of 150 μm diameter populating a 175 μm height microgap, which is 10 mm long. The dielectric refrigerant R245fa is used as the coolant due to its negligible electrical conductivity, desirable for inter-tier cooling. Results provide useful insight on how the vapor phase is generated and distributed as a function of the axial direction, as well as the implication on heat transfer and resulting surface temperatures to identify trends and required conditions for the reliable operation in potential microelectronic applications.
在三维(3D)微电子集成等应用中,表面增强微隙中的流动沸腾代表了一种有前途的热控制方法,用于去除相对高的热流通量。尽管一些实验研究报告了这些类型的冷却层令人鼓舞的结果,但由于许多挑战,所涉及的物理计算流体动力学(CFD)分析滞后。在本研究中,采用相变模型和流体体积法(VOF)进行界面跟踪,分析了在硅介质中同时热传导的圆形针翅微隙中沸腾引起的瞬态流态演变。采用高性能计算(HPC)研究了直径为150 μm、高175 μm、长10 mm的微间隙内相对密集的引脚鳍阵列中的两相流动和传热。采用介电制冷剂R245fa作为冷却剂,因为其导电性可忽略不计,适合层间冷却。结果提供了关于气相如何产生和分布作为轴向的函数的有用见解,以及对传热和由此产生的表面温度的含义,以确定在潜在的微电子应用中可靠运行的趋势和所需条件。
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引用次数: 6
Two-phase jet impingement heat sink integrated with a compact vapor compression system for electronics cooling 两相射流冲击散热器集成了一个紧凑的蒸汽压缩系统的电子冷却
Pablo A. de Oliveira, J. Barbosa
This paper introduces a compact vapor compression cooling system equipped with a small-scale oil-free linear motor R-134a compressor and a novel heat sink that integrates the evaporator and the expansion device into a single unit. At the present stage of the development, a single orifice was used to generate the high-speed two-phase impinging jet on the heated surface. The effects of the applied thermal load, orifice diameter, orifice-to-heater distance, hot reservoir temperature and compressor stroke on the system performance were quantified. The system performance was evaluated in terms of the temperature of the heated surface, heat transfer coefficient, coefficient of performance and second-law efficiency. The operating conditions that maximized the system performance for specific operating conditions have been identified.
本文介绍了一种紧凑的蒸汽压缩冷却系统,该系统配备了一台小型无油直线电机R-134a压缩机和一种将蒸发器和膨胀装置集成为一体的新型散热器。在目前的发展阶段,采用单孔在受热表面产生高速两相冲击射流。量化了外加热负荷、节流孔直径、节流孔到加热器的距离、储热器温度和压缩机行程对系统性能的影响。从受热面温度、传热系数、性能系数和第二定律效率等方面评价了系统的性能。已经确定了在特定工作条件下使系统性能最大化的工作条件。
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引用次数: 3
Evaporative intrachip hotspot cooling with a hierarchical manifold microchannel heat sink array 蒸发芯片热点冷却与分层流形微通道散热器阵列
Kevin P. Drummond, J. Weibel, S. Garimella, Doosan Back, D. Janes, M. Sinanis, D. Peroulis
A hierarchical manifold microchannel heat sink is used to dissipate heat from a small hotspot region superposed on a larger region of uniform background heat flux. A 5 mm × 5 mm overall chip footprint area is cooled using a 3 × 3 array of intrachip silicon microchannel heat sinks fed in parallel using a manifold distributor. Each heat sink consists of a bank of 25 high-aspect-ratio microchannels that are nominally 30 μm wide and 300 μm deep. The uniform background heat flux is generated with a 3 × 3 array of thin-film heaters fabricated on the chip; temperature sensors placed in each of these nine heating zones provide spatially resolved chip surface temperature measurements. An individually powered 200 μm × 200 μm hotspot heater is centered on the chip. The heat sink thermal and hydraulic performance is evaluated using HFE-7100 as the working fluid and for mass fluxes ranging from 600 kg/m2s to 2070 kg/m2s at a constant inlet temperature of 60°C and outlet pressure of 122 kPa. Background heat fluxes up to 450 W/cm2 and hotspot fluxes of greater than 2500 W/cm2 are simultaneously dissipated. The chip temperature uniformity and maximum temperature rise during hotspot heating are assessed. For the case with the highest simultaneous background and hotspot heat fluxes, the measured heat sink pressure drop is ~75 kPa and the average chip temperature is ~30°C above the fluid inlet temperature.
采用分层流形微通道散热器,将小热点区域的热量分散到较大的均匀背景热流区域上。一个5毫米× 5毫米的整体芯片占地面积是使用一个3 × 3阵列的芯片内硅微通道散热片,并联使用一个流形分布器。每个散热器由一组25个高纵横比的微通道组成,这些微通道的名义宽度为30 μm,深度为300 μm。均匀的本底热流由在芯片上制作的3 × 3薄膜加热器阵列产生;放置在这九个加热区的温度传感器提供空间分辨芯片表面温度测量。单独供电的200 μm × 200 μm热点加热器位于芯片中央。在进口温度为60℃,出口压力为122 kPa的恒定条件下,以HFE-7100作为工作流体,质量通量为600 kg/m2s至2070 kg/m2s,对散热器的热性能和水力性能进行了评估。高达450 W/cm2的背景热通量和大于2500 W/cm2的热点通量同时消散。评估了芯片在热点加热过程中的温度均匀性和最大温升。在背景热流和热点热流同时最高的情况下,测得的散热器压降为~75 kPa,芯片平均温度比流体入口温度高~30℃。
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引用次数: 34
Investigation of internal package structure based on the analysis of dynamic temperature response 基于动态温度响应分析的内部封装结构研究
M. Janicki, T. Torzewicz, A. Napieralski
This paper presents the investigations of internal package structure based on the analyses of device dynamic thermal responses to power step excitation recorded in various cooling conditions. The analyses are carried out for two theoretically identical power devices representing different technological generations. As demonstrated in the paper, both thermal and electrical behaviors of these devices differ substantially. The time constant spectra and the cumulative structure functions calculated from the recorded thermal responses revealed deep internal differences between the devices. These results were confirmed also by measurements of device geometries taken after the disassembly of their packages. Owing to the proposed approach it was possible also to generate compact thermal models of both devices in the form RC Cauer ladders whose elements could be attributed some physical meaning. These models were finally validated with the measurements showing excellent accuracy of thermal simulation.
本文在分析不同冷却条件下功率阶跃激励下器件动态热响应的基础上,对内部封装结构进行了研究。对代表不同技术时代的两个理论上相同的功率器件进行了分析。如本文所示,这些器件的热学和电学行为都有很大的不同。根据记录的热响应计算的时间常数光谱和累积结构函数揭示了器件之间的深层内部差异。这些结果也证实了测量设备的几何形状后,他们的包装拆卸。由于所建议的方法,也有可能以RC Cauer梯的形式生成这两种装置的紧凑热模型,其元素可以赋予某些物理意义。最后用实测数据对模型进行了验证,显示出较好的热模拟精度。
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引用次数: 0
期刊
2016 15th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm)
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