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# 电气工程代写|射频电路代写RF Circuit代考|EE505 Passive Modeling

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## 电气工程代写|射频电路代写RF Circuit代考|Passive Modeling

Lumped or surface-mount elements are attractive due to their small size, broad bandwidth, and commercial availability compared with distributed elements. At low frequencies, component size is very small compared to the wavelength. Therefore, they can be used with minimal concern. However, at higher frequen- cies (UHF and above), this is not the case. Lumped elements exhibit spurious resonances, fringing fields (radiation leakage), loss, and other parasitic (undesired) effects (discussed in Chapter 6) [1].

## 电气工程代写|射频电路代写RF Circuit代考|Capacitor

The equivalent circuit model of a lumped-element capacitor is shown in Figure $3.1$ where $C_{n o m}$ is the nominal capacitance, $L_s$ is the series parasitic inductance, ESR is the equivalent series resistance, and $C_p$ is the parallel parasitic capacitance.

Fortunately, data sheets often include one or more of these parameters to aid designers. If not, S-parameters are usually available so that values can be tuned to match the frequency response. Figure $3.2$ shows the effect $L_s$ has on the capacitor frequency response. The $L_s=0.000$ curve has no parasitic effect. As $L_s$ increases, the high-frequency response degrades quickly.

Some components are marketed as having “low ESR.” They are designed for high-frequency applications. Having a low ESR will reduce the loss, especially at high frequency.

Sometimes data sheets quantify the loss of capacitor by its quality factor $(Q)$, which is defined as:
$$Q=\frac{1}{2 \pi f C_{\text {nom }} \cdot E S R}$$

where $f$ is the frequency (hertz), $C_{\text {nom }}$ is the nominal capacitance (farads), and ESR is the series resistance $(\Omega)$. This equation can be used to calculate ESR.
Data sheets may also specify the series-resonant frequency (SRF) of a capacitor. This is the frequency where $C_{n o m}$ and $L_s$ are equal, but opposite in magnitude. At that frequency, the capacitor behaves like a parallel RC circuit with $E S R$ and $C_p$. To calculate $L_s$ from $S R F$, the following equation can be used:
$$L_s(\mathrm{nH})=\frac{1000}{4 \pi^2 C(\mathrm{pF}) \cdot \mathrm{SRF}(\mathrm{GHz})^2}$$
$C_p$ accounts for any deviation from the frequency response that cannot be predicted. It is determined by trial and error until the measured frequency response matched the equivalent circuit model.

## 电气工程代写射频电路代写RF Circuit代考|Capacitor

$$Q=\frac{1}{2 \pi f C_{\text {nom }} \cdot E S R}$$

$$L_s(\mathrm{nH})=\frac{1000}{4 \pi^2 C(\mathrm{pF}) \cdot \mathrm{SRF}(\mathrm{GHz})^2}$$
$C_p$ 解释无法预则的频率响应的任何偏差。它是通过反复试验确定的，直到测得的频率响应与等效电路模型相匹配。

## 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。