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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

## 电气工程代写|数字电路代写digital circuit代考|DIFFERENTIAL AMPLIFIERS

A differential amplifier is any two-input amplifier that has an output proportional to the difference of the inputs. The defining equation for a differential amplifier is then:
$$y_o=A\left(x_{i 1}-x_{i 2}\right),$$
where the output, $y_o$, and the inputs $\left{x_i\right}$ could be either voltages or currents. Previous discussions in this chapter have explored two differential amplifiers: the difference amplifier (shown in Figure 1.20) and the basic OpAmp itself. Each of these two examples has an output voltage that is proportional to the difference of two input voltages. In the case of the difference amplifier, the output expression was derived to be:
$$v_o=\frac{R_B}{R_A}\left(v_{i 2}-v_{i 1}\right),$$
if the resistor values were chosen so that
$$\frac{R_A}{R_B}=\frac{R_C}{R_D} .$$
Ideally this amplifier (or any differential amplifier) is sensirive only to the difference in the two input signals, and is completely insensitive to any common component of the two signals. That is, if the difference in inputs remains constant, the output should not vary if the average value of the two inputs changes. Unfortunatély, a diffëpential amplifiêr rareely meéts this goal, and the output has a slight dependence on the average of the input signals. The output for this type of imperfect differential amplifier is given by:
$$v_o=A_{D M} v_{i D M}+A_{C M} v_{i C M}=A_{D M}\left(v_{i 2}-v_{i 1}\right)+A_{C M}\left(\frac{v_{i 2}+v_{i 1}}{2}\right),$$
where
$A_{D M}=$ the amplification of the input signal difference, $v_2-v_1$,
and
$A_{C M}=$ the amplification of the input signal average, $\frac{\left(v_2+v_1\right)}{2}$.
The quality of a differential amplifier is displayed in its ability to amplify the differential signal while suppressing the common signal. A measure of this quality is the ratio of the differential gain to the amplification of the average (or common) part of the input signals. The measure of quality is named Common-mode rejection ratio (CMRR) and is usually expressed in decibels (dB). The defining equation for CMRR is:
$$\mathrm{CMRR}=20 \log {10}\left|\frac{A{D M}}{A_{C M}}\right|$$

## 电气工程代写|数字电路代写digital circuit代考|NON-IDEAL CHARACTERISTICS OF OPAMPS

In this section the most significant limitations of the non-ideal Operational Amplifier are discussed. A fundamental understanding of these non-ideal properties allows the electronics designer to choose circuit topologies and parameter values so that the performance of real, practical circuitry closely approximates the ideal case. The concept of an ideal OpAmp has allowed the use of simplified circuit analysis techniques to determine the performance of OpAmp circuits and concentration on the design philosophy behind the various OpAmp circuit topologies. The ideal OpAmp was defined with the following properties:

• Infinite Voltage Gain
• Infinite Input Resistance
• Zero Output Resistance
• Output Independent of Power Source Characteristics
• Properties Independent of Input Frequency
A number of non-ideal characteristics have been considered briefly in prior sections of this chapter:
• Output Saturation
• Finite Input Resistance
• Finite Voltage Gain
• Non-zero Output Resistance
These characteristics will be further discussed along with the following additional non-ideal characteristics:
• Input Parameter Variations
• Output Parameter Limitations
• Supply and Package Related Parameters
• In addition, the performance of an $\mathrm{OpAmp}$ is dependent on the frequency of the input signals. In many low-frequency applications this frequency dependence is not significant: $\mathrm{OpAmps}$ are commonly used in the audio frequency range and beyond without significant distortion. A discussion of frequency dependent behavior and its close relative, slew rate, is beyond the scope of this section: a discussion of the frequency dependence of OpAmp circuit performance can be found in Section $9.9$ (Book 3).

# 数字电路代考

## 电气工程代写|数字电路代写digital circuit代考|DIFFERENTIAL AMPLIFIERS

$$y_o=A\left(x_{i 1}-x_{i 2}\right),$$

$$v_o=\frac{R_B}{R_A}\left(v_{i 2}-v_{i 1}\right),$$

$$\frac{R_A}{R_B}=\frac{R_C}{R_D} .$$

$$v_o=A_{D M} v_{i D M}+A_{C M} v_{i C M}=A_{D M}\left(v_{i 2}-v_{i 1}\right)+A_{C M}\left(\frac{v_{i 2}+v_{i 1}}{2}\right),$$

$A_{D M}=$ 输入信号差的放大， $v_2-v_1$

$A_{C M}=$ 输入信号平均值的放大， $\frac{\left(v_2+v_1\right)}{2}$.

$$\mathrm{CMRR}=20 \log 10\left|\frac{A D M}{A_{C M}}\right|$$

## 电气工程代写|数字电路代写digital circuit代考|NON-IDEAL CHARACTERISTICS OF OPAMPS

• 无限电压增益
• 无限输入电阻
• 零输出电阻
• 输出与电源特性无关
• 与输入频率无关
的特性 在本章前面的章节中已经简要考虑了一些非理想特性：
• 输出饱和
• 有限输入电阻
• 有限电压增益
• 非零输出电阻
这些特性将与以下额外的非理想特性一起进一步讨论：
• 输入参数变化
• 输出参数限制
• 供应和包装相关参数
• 此外，一个性能运算放大器取决于输入信号的频率。在许多低频应用中，这种频率依赖性并不显着：运算放大器常用于音频范围及以上，无明显失真。频率相关行为及其密切相关的压摆率的讨论超出了本节的范围：关于运算放大器电路性能的频率相关性的讨论可以在第9.9（第 3 册）。

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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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