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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|SUMMARY DESIGN EXAMPLE

In order to investigate the low-frequency volt-ampere (V-I) relationship of a two-terminal electronic device, it is often desirable to display the V-I relationship on the screen of an oscilloscope. A typical experimental circuit diagram for such a display is shown below: it consists of the series connection of a low-frequency function generator, a resistor, and the device under test (DUT).

The voltage across the DUT is given by $V_B$ and will serve as one of the inputs to the oscilloscope. The other input to the oscilloscope is the loop current. The most economical method for measuring this current is given by (current probes are quite expensive):
$$I=\frac{V_{A B}}{R} .$$
The location of the ground node in this circuit presents a problem. Safety regulations require that one terminal of the output of most function generators be at ground potential: similarly, one terminal of the input to most oscilloscopes is at ground potential. These ground connections do not prose a problem in measuring the voltage, $V_B$, hut measuring the voltage, $V_{A B}$, is difficult. The differential input mode to most oscilloscopes can solve this difficulty in measurement, but this mode cannot usually be invoked simultaneously with the required $x-y$ display mode.

The obvious solution to the measurement problem is an external differential amplifier with inputs at nodes A and B and an output to one of the oscilloscope channels. Design such a differential amplifier.
Solution:
A list of specifications is necessary for good design. The connection of the differential amplifier across the resistor, $R$, must not significantly disturb the measurements: It should have very high input resistance: $R_{i n}>1 \mathrm{M} \Omega$ matches the input resistance of most oscilloscopes. Similarly, the output of the differential amplifier should have low output resistance so that an accurate measurement can be made, $R_{\text {out }}<100 \Omega$ is adequate. The amplifier differential gain should be either unity or ten (10) so that a mix of oscilloscope probes can be utilized. CMRR should be high.
If a low-frequency function generator is used, $O_p A m p s$ can be used for the realization of the differential amplifier. The differential amplifier of Figure $1.20$ can easily be designed to meet all the specifications except input resistance. If the resistors are chosen to be sufficiently large to meet input resistance requirements, the ideal OpAmp approximations will fail. Therefore, it is necessary connect unity-gain buffers in series with each input. The circuit topology (next page) is therefore chosen.

The input and output resistance of this circuit automatically meets specifications using all common, commercial OpAmps. The requirement for two distinct values of the differential gain is accomplished with a double-pole, single-throw switch. When both indicated switches (each is a pole of the actual switch) are open, the differential gain is unity: when both are closed the differential gain is ten. After these topological design decisions, all that remains in the design is the choice of resistor values.

## 电气工程代写|数字电路代写digital circuit代考|OPERATIONAL AMPLIFIERS AND APPLICATIONS

1.22. A differential amplifier has a differential-mode gain of $92 \mathrm{~dB}$ and a CMRR of $80 \mathrm{~dB}$. Find the magnitude of the differential-mode output $v_{o(D M)}$ and the common-mode output $v_{o(C M)}$ if:
a) $v_1=1.6 \mu \mathrm{V}$ and $v_2=2 \mu \mathrm{V}$
b) $v_1–1.6 \mu \mathrm{V}$ and $v_2-2 \mu \mathrm{V}$
1.23. Design an OpAmp differential amplifier with:
a) A gain of 67 and a minimum input resistance of $22 \mathrm{k} \Omega$ for each input.
b) For an OpAmp with CMRR $=67 \mathrm{~dB}$ with a maximum common-mode input signal of $0.08 \mathrm{~V}$, find the differential input signal for which the differential-mode output is greater than 90 times the common-mode output.
1.24. A differential amplifier is constructed with an ideal $\mathrm{OpAmp}_{\mathrm{m}}$ and resistors of nominal values $1.0 \mathrm{k} \Omega$ and $4.7 \mathrm{k} \Omega$ (i.e., $R_A \approx R_C \approx 1.0 \mathrm{k} \Omega$ and $R_B \approx R_D \approx 4.7 \mathrm{k} \Omega$ ).
a) What is the worst case common-mode gain using resistors with $5 \%$ tolerance?
b) What is the CMRR for that case?
c) Repeat parts a) and b) for $0.5 \%$ tolerance resistors.

1.25. A differential amplifier shown has a differential-mode gain, $A_{D M}=5000$, and a CMRR of $56 \mathrm{~dB}$. Let $v_o=v_{o(C M)}+v_{o(D M)}=1.2 \mathrm{~V}$. Construct a graph of $v_2$ vs. $v_1$ showing the locus of all possible inputs that provide this output. Compare significant graph points to resistor ratios. Assume that $v_2 \geq v_1$ and the outputs add, and maintain $\left|v_2\right| \leq 5 \mathrm{~V}$.

# 数字电路代考

## 电气工程代写|数字电路代写digital circuit代考|SUMMARY DESIGN EXAMPLE

DUT 两端的电压由下式给出 $V_B$ 并将作为示波器的输入之一。示波器的另一个输入是回路电流。测量此电流的最经济的方法是 (电流探头非常昂 贵）:
$$I=\frac{V_{A B}}{R} .$$

## 电气工程代写|数字电路代写digital circuit代考|OPERATIONAL AMPLIFIERS AND APPLICATIONS

1.22。差分放大器的差模增益为 $92 \mathrm{~dB}$ 和一个 CMRR $80 \mathrm{~dB}$. 找出差模输出的幅度 $v_{o(D M)}$ 和共模输出 $v_{o(C M}$ 如果:
$-) v_1=1.6 \mu \mathrm{V}$ 和 $v_2=2 \mu \mathrm{V}$
b) $v_1-1.6 \mu \mathrm{V}$ 和 $v_2-2 \mu \mathrm{V}$
1.23。设计一个运算放大器差分放大器:
a) 增益为 67 ，最小输入电阻为 $22 \mathrm{k} \Omega$ 对于每个输入。
b) 对于具有 CMRR 的运算放大器 $=67 \mathrm{~dB}$ 最大共模输入信号为 $0.08 \mathrm{~V}$ ，找出差模输出大于共模输出 90 倍的差模输入信号。
1.24。差分放大器是用理想构造的 $\mathrm{OpAmp} \mathrm{p}{\mathrm{m}}$ 和标称值的电阻器 $1.0 \mathrm{k} \Omega$ 和 $4.7 \mathrm{k} \Omega$ (IE， $R_A \approx R_C \approx 1.0 \mathrm{k} \Omega$ 和 $R_B \approx R_D \approx 4.7 \mathrm{k} \Omega$ ) 。 a) 使用电阻器的最坏情况下共模增益是多少 $5 \%$ 宽容? b) 该案例的 CMRR 是多少? c) 重复 $a)$ 和 b) 部分 $0.5 \%$ 公差电阻。 1.25。所示的差分放大器具有差模增益， $A{D M}=5000$, 和 CMRR56 dB. 让 $v_o=v_{o(C M)}+v_{o(D M)}=1.2 \mathrm{~V}$. 构造一个图 $v_2$ 对比 $v_1$ 显示提供此输出的 所有可能输入的轨迹。将重要的图表点与电阻比进行比较。假使，假设 $v_2 \geq v_1$ 和输出添加，并保持 $\left|v_2\right| \leq 5 \mathrm{~V}$.

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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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