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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|电动力学代写electromagnetism代考|MiCROSTRIP LiNes

Let us now consider microstrip. This was first introduced in Section $2.9$ when we considered the capacitance of a printed circuit track over a ground-plane. To find the inductance of this arrangement, we would have to plot the magnetic field surrounding the track. This involves a considerable amount of work, which we can avoid by using the rule introduced at the end of the last section.

When we considered coaxial cable and twin feeder, we found that $L^{\prime} C^{\prime}=\mu \varepsilon$. So, if we can determine the capacitance, we can find the inductance per unit length. In Section 2.9, we found that we could approximate the capacitance to that of a parallel plate capacitor (Equation (2.48))
$$C^{\prime}=\frac{\varepsilon_0 \varepsilon_r w}{h} \mathrm{Fm}^{-1}$$
Or, if the track width is much less than the thickness of the board, the capacitance of a cylindrical wire over a ground-plane (Equation (2.49))
$$C^{\prime}=\frac{2 \pi \varepsilon_0 \dot{\varepsilon}_r}{\ln \left(\frac{h}{w}\right)} \mathrm{Fm}^{-1}$$
Thus, the inductance lies between
$$L^{\prime}=\frac{\mu_0 h}{w} \mathrm{H} \mathrm{m}^{-1}$$

for the parallel plate approximation, and
$$L^{\prime}=\frac{\mu_0}{2 \pi} \ln \left(\frac{h}{w}\right) \mathrm{Hm}^{-1}$$
for the wire above ground approximation.

## 物理代写|电动力学代写electromagnetism代考|ENERGY StORAGE

In the same way that energy is stored in an electric field, energy can also be stored in a magnetic field. This is useful in switch-mode power supplies. To find the stored energy, let us take an inductor connected to a d.c. source. This inductor will take a certain amount of current, limited by the resistance of the coil. If we increase the current by a small amount $\mathrm{d} l$ in time $\mathrm{d} t$, the flux causes a back-emf given by
$$\mathrm{d} V=L \frac{\mathrm{d} I}{\mathrm{~d} t}$$

As the current flowing through the coil is $I$, the instantaneous power supplied is
$$I \mathrm{~d} V=L I \frac{\mathrm{d} I}{\mathrm{~d} t}$$
This power is supplied in time $\mathrm{d} t$, and so the energy supplied in raising the current from $I$ to $I+\mathrm{d} l$ is
\begin{aligned} \mathrm{d} E &=I \mathrm{~d} V \mathrm{~d} t \ &=L I_{\mathrm{d} t}^{\mathrm{d} I} \mathrm{~d} t \ &=L I \mathrm{~d} I \end{aligned}
Thus, we can find the energy supplied in raising the current from zero to $I$ by integrating Equation (3.65). So,
\begin{aligned} \text { stored energy } &=\int_0^1 L I \mathrm{~d} I \ &=\frac{1}{2} L I^2 \mathrm{~J} \end{aligned}
It is interesting to compare this equation with that obtained for the energy stored in a capacitor, Equation $(2.51)$, stored energy $=1 / 2 C V^2$ joule.

# 电动力学代考

## 物理代写|电动力学代写electromagnetism代考|MiCROSTRIP LiNes

$$C^{\prime}=\frac{\varepsilon_0 \varepsilon_r w}{h} \mathrm{Fm}^{-1}$$

$$C^{\prime}=\frac{2 \pi \varepsilon_0 \dot{\varepsilon}_r}{\ln \left(\frac{h}{w}\right)} \mathrm{Fm}^{-1}$$

$$L^{\prime}=\frac{\mu_0 h}{w} \mathrm{Hm}^{-1}$$

$$L^{\prime}=\frac{\mu_0}{2 \pi} \ln \left(\frac{h}{w}\right) \mathrm{Hm}^{-1}$$

## 物理代写|电动力学代写electromagnetism代考|ENERGY StORAGE

$$\mathrm{d} V=L \frac{\mathrm{d} I}{\mathrm{~d} t}$$

$$I \mathrm{~d} V=L I \frac{\mathrm{d} I}{\mathrm{~d} t}$$

$$\mathrm{d} E=I \mathrm{~d} V \mathrm{~d} t \quad=L I_{\mathrm{d} t}^{\mathrm{d} I} \mathrm{~d} t=L I \mathrm{~d} I$$

$$\text { stored energy }=\int_0^1 L I \mathrm{~d} I \quad=\frac{1}{2} L I^2 \mathrm{~J}$$

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## 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。

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