Under a given set of boundary conditions (BCs), the thermal performance of an electronic system is generally evaluated based on its steady-state response to constant power loads and thermal BCs that are time-averaged values of the actual transient or cyclic loads and BCs. Such analysis may produce accurate results if the time dependence of the power cycles and thermal BCs is small. Ideally, transient thermal analyses with actual time-dependent BCs and power cycles should be performed to determine the steady-state behavior. While being less overwhelming compared to laboratory experiments, fully time-dependent computational fluid dynamics (CFD) analysis still requires a large amount of CPU time. In order to overcome this large computational cost, several approximate models, such as resistor-capacitor ( R- C) thermal network approaches, have been developed. Although reasonably accurate, these models require rigorous curve-fitting effort followed by an optimization process, which only makes them practical for relatively simple systems. The present study builds a state-space model applicable to heat transfer problems and makes comparisons with the R- C networks. The state-space model is later applied to determine the transient thermal behavior of a complex system, namely, a multidie SOIC chip over a printed circuit board (PCB), with a significant reduction in CPU time and no compromise on the accuracy. Finally, as a demonstration of systemic thermal design, an optimization exercise is performed on the above state-space model, in which the power cycles on individual die elements are controlled to limit the maximum temperature on the package die.

中文翻译：

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使用状态空间建模技术进行跨尺度电子系统的热分析和设计


在一组给定的边界条件 (BC) 下，电子系统的热性能通常根据其对恒定功率负载和热 BC 的稳态响应来评估，热 BC 是实际瞬态或循环负载和 BC 的时间平均值。如果功率循环和热 BC 的时间依赖性很小，则此类分析可以产生准确的结果。理想情况下，应使用实际的时间相关 BC 和功率循环进行瞬态热分析，以确定稳态行为。虽然与实验室实验相比，完全依赖时间的计算流体动力学 (CFD) 分析的难度较小，但仍然需要大量的 CPU 时间。为了克服这种巨大的计算成本，已经开发了几种近似模型，例如电阻电容（RC）热网络方法。尽管相当准确，但这些模型需要严格的曲线拟合工作以及随后的优化过程，这仅使它们对于相对简单的系统来说实用。本研究建立了一个适用于传热问题的状态空间模型，并与 R-C 网络进行了比较。随后，状态空间模型被应用于确定复杂系统（即印刷电路板 (PCB) 上的多芯片 SOIC 芯片）的瞬态热行为，从而显着减少 CPU 时间且不影响精度。最后，作为系统热设计的演示，对上述状态空间模型进行了优化练习，其中控制各个芯片元件上的功率周期以限制封装芯片上的最高温度。