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# 物理代写|模拟电路代写Analog Circuit代考|ECE511 From Netlist to Pathfinding

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## 物理代写|模拟电路代写Analog Circuit代考|From Netlist to Pathfinding

While the netlist is available for any circuit, it does not provide any information on how the devices’ terminals should be connect, that is, the terminal-to-terminal connectivity is also needed. Starting from the netlist, if the terminal-to-terminal connectivity of each net is unknown, the routing of single-port multiterminal signal nets is usually addressed as the classical Steiner minimal tree (SMT) problem. Where, a set of Steiner points must be found in order to minimize the SMT total interconnect length that contains all the terminals of the net. This problem is often generalized as the rectilinear Steiner minimal tree (RSMT), when only edges defined by vertical or horizontal segments are considered, however, the problem is still NP-complete [50].

A RSMT global router is used in [51] for wiring length estimation, and, when the terminal-to-terminal connectivity is found, the traditional pathfinding algorithm is used. These deterministic pathfinding algorithms developed in the late $1980 \mathrm{~s}$, are variations of the classic maze algorithm [51-53], which is the most common approach, but line-expansion techniques [4] can also be found. Each instance of those approaches is used to generate a wire that connects two different terminals in the presence of obstacles (e.g., devices placed on the floorplan or other wires), usually by means of a grid-based or tile-based representation to ensure no overlaps or design rule violations, where the routing of all nets is done by iterating the different wires. The design rule validations are usually forced in the path-finding algorithms, e.g., by expanding the grids or routing channels with the minimum space requirements. Since an analog cell has a considerable number of conflicting nets, each one containing multiple wires, heuristics for net (re)ordering, backtracking and re-routing must be used to obtain valid solutions [1].

A different approach to automatic routing is the template adjustment techniques $[54,55]$, these have the highest setup times, but outperform the remaining by its fast and user-defined generation. A detailed state-of-the-art on the pathfinding algorithms and analog layout routing difficulties can be found in the Chapter Routing Analog Circuits by Dündar and Unutulmaz of [1].

## 物理代写|模拟电路代写Analog Circuit代考|Electromigration and IR-Drop

AMS ICs suffer from diverse non-idealities that became increasingly more relevant with the reduction of the circuit sizes in the last years, and may cause catastrophic circuit failures. These non-idealities must be taken into account during the circuit design in order to mitigate their effect on the product reliability [56]. Two of these non-idealities are: electromigration, which refers to the material migration in the power networks and signal wires that are stressed with high current-densities, deteriorating the interconnect lifetime; and IR-Drop, that consists of a fluctuation of the net voltage due to the interconnect resistances, affecting circuit behavior and performance $[57,58]$.

Analyzing the electromigration physical phenomenon, J. R. Black, in 1969 , was the first to developed a theoretical model to estimate the median time to failure (MTF) in hours of an interconnect in an IC [59], as presented in Eq. (2.5). The model was developed for the aluminum conductors used during the early years of integration industry.
$$M T F=\frac{A}{J^n} \exp \left(-\frac{\Phi}{k \cdot T}\right)$$
where, $A$ is a constant that contains a factor involving the cross-sectional area of the interconnect, $J$ the current-density in amperes per square centimeter, $\Phi$ the activation energy in electron volts for the interconnect material, $k$ the Boltzmann constant, $T$ the working temperature of the interconnect, and $n$ is used as a scaling factor. By observing Eq. (2.5) it is notorious that only two parameters can be changed by the designer: the current-density, which can be controlled by designing the proper interconnects for the current imposed on them, i.e., the wider the interconnect is assigned, the smaller is the current-density and subsequently electromigration resistance [58]; and the temperature, which may be indirectly controlled by assigning power and thermally-sensitive devices and interconnects in different areas of the chip, and by considering worst-case conditions in the determination of the current-densities.
While the accuracy of the model of Eq. (2.5) is outdated for today’s integration technologies, the principles that the combined effects of current-density and temperature are responsible for the gradual degradation of the interconnect is still valid.

## 物理代写|模拟电路代写Analog Circuit代考|From Netlist to Pathfinding

[51]中使用 RSMT 全局路由楍进行布线长度估计，并且当发现終端到終煓的连接时，使用传统的寻路算法。这些确定性寻路算法 是在后期开发的 $1980 \mathrm{~s}$ ，是经典迷宆算法 [51-53] 的变体，这是最常见的方法，但也可以找到线扩展技术 [4]。这些方法的每个实 例都用于在存在障碍物（例如，放置在平面图上的设备或其他电线）的情况下生成连接两个不同終端的电线，通常通过基于网格或 基于图块的表示来确保不会重叕或违反设计规则，其中所有网絡的布线都是通过迭代不同的电线来完成的。设计规则验证通常在寻 路算法中强制执行，例如，通过扩展网格或以最小空间要求布线通道。由于一个模拟单元有相当数量的冲突网絡，每个网络包含多 条线，网络 (重新) 排序的试探去，

## 物理代写|模拟电路代写Analog Circuit代考|Electromigration and IR-Drop

AMS IC 存在各种非理想性，这些非理想性在过去几年随着电路尺寸的缩小而变得越来越重要，并且可能导致灾难性的电路故障。 在电路设计过程中必须考虑这些非理想因羏，以减轻它们对产品可靠性的影响 [56]。其中两个非理想情况是：电迁移，指在高电 流密度下受力的电源网络和信号线中的材料迁移，会摍短互连寿命；和 IR-Drop，它由互连电阻引起的净电压波动组成，影响电 路行为和性能 $[57,58]$.
1969 年，JR Black 分析了电迁移物理现象，率先开发了一个理论模型来估计 IC [59] 互连的中位故障时间 (MTF)，如等式 1 所 示。(2.5)。该模型是为集成行业早期使用的铝导体开发的。
$$M T F=\frac{A}{J^n} \exp \left(-\frac{\Phi}{k \cdot T}\right)$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。