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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|INPUT PARAMETER VARIATIONS

When an ideal OpAmp has zero output, one expects that the input will have the following properties:

• the voltage difference at the input will be zero, and
• each input current will be zero.
Real OpAmps have input voltage differences and currents that vary from the ideal. These differences are described by the quantities Input Offset Voltage, Input Bias Current, and Input Offset Current.

The input offset voltage, $V_{O S}$, is defined as the difference in voltage between the OpAmp input terminals when the output voltage is zero. ${ }^{18}$ This voltage difference is due to slightly different propertics of the input circuitry at cach of the input terminals.

For typical OpAmps the offset voltage is a few millivolts or less, and can often be nulled with an external three-terminal potentiometer connected between the offset null terminals of the OpAmp with the middle terminal of the potentiometer connected either to ground or one of the supply voltage terminals (the connections vary with $\mathrm{OpAmp}$ type and manufacturer). If the offset voltage is not nulled, it appears as an additional input voltage in series with the true inputs to the $\mathrm{OpAmp}{\mathrm{p}}$ (See Figure 1.26). The input offset voltage is also a function of temperature: the nulling circuitry may need to be adjusted as $\mathrm{OpAmp}$ temperature varies. The offset voltage and its variation with temperature place a lower limit on the magnitude of DC voltages that can act as inputs tô an $\mathrm{O}{\bar{p}} \Lambda \mathrm{mp}$ without crrōncous circuit operation.

There are several other limitations on the operation of $\mathrm{OpAmps}_{\mathrm{p}}$ that relate to the manufacturer’s package and the power supply to which the OpAmp is connected. The limitations can be found in $\mathrm{OpAmp}$ data sheets. The primary limitations are:

• Power Dissipation
• Operating Temperature Range
• Supply Voltage Range
• Supply Current
• Power Supply Rejection Ratio
All OpAmps have a limitation on the maximum amount of power that can be dissipated safely on a continuous basis. Power dissipation is package dependent with ceramic packages having the

highest rating. Metal and plastic packages have lower ratings with plastic the lowest. Typical values are in the 100-500 $\mathrm{mW}$ range.

OpAmps are guaranteed to operate within specifications provided the temperature of the package is within the operating temperature range specification. Commercial grade devices have a temperature range of $0^{\circ} \mathrm{C}$ to $+70^{\circ} \mathrm{C}$, the range for industrial grade devices is $-25^{\circ} \mathrm{C}$ to $+85^{\circ} \mathrm{C}$, and military grade devices operate from $-55^{\circ} \mathrm{C}$ to $+125^{\circ} \mathrm{C}$.

The supply voltages $V_{C C}$ have maximum and minimum values for proper operation of the OpAmp. Typical maxima are in the range of $\pm 18 \mathrm{~V}$ to $\pm 22 \mathrm{~V}$, but specialized units may operate at much higher levels. Minima are typically about $\pm 5 \mathrm{~V}$ but may range as low as $\pm 2 \mathrm{~V}$. As has been mentioned before, the output voltage swing must lie within the rails set by the supply voltage. Specialized OpAmps can operate with a one-sided supply: typically the negative power supply terminal is grounded and the other power supply terminal is connected to $+V_{C C}$.

The supply current is defined as the current that an $\mathrm{O}{\mathrm{P}} \mathrm{Amp}{\mathrm{m}} \mathrm{d}$ traws from the power supply when the OpAmp output is zero. This is a particularly important parameter in battery-operated applications.

Variations in the supply voltage, $\pm V_{C C}$, can feed through to the output-typically through offset voltage variation. The ratio of the change in offset voltage to the change in power supply voltage is defined as the power-supply rejection ratio (PSRR):
$$P S R R=\frac{\Delta V_{O S}}{\Delta V_{C C}}$$
PSRR can be expressed in V/V or in decibels, where
$$\left.P S R R\right|{d \bar{B}}=20 \log \frac{\Delta V{O S}}{\Delta V_{\Gamma \Gamma}} .$$
If $O p A m p s$ are used with a high-performance voltage regulator, the error due to PSRR can essentially be eliminated in OpAmp applications.

While the list of non-ideal OpAmp properties may seem large, each property contributes but a small error that, with careful choices of circuit topology and circuit element value, can be nearly eliminated. There is insufficient space in a text of this nature to investigate all effects in all possible circuits. While the demonstrations have been kept to a minimum, it is hoped that the reader has developed a “feel” for the most important effects and a sense of how to compensate for them. The goood circuit Designeer should keeep all of thesses sécond-ordér éfeects in mind and act appropriately.

# 数字电路代考

## 电气工程代写|数字电路代写digital circuit代考|INPUT PARAMETER VARIATIONS

• 输入端的电压差为零，并且
• 每个输入电流将为零。
真正的运算放大器的输入电压差和电流与理想值不同。这些差异由输入失调电压、输入偏置电流和输入失调电流量来描述。

• 功耗
• 工作温度范围
• 电源电压范围
• 电源电流
• 电源抑制比
所有运算放大器都对可连续安全耗散的最大功率有限制。功耗取决于封装，陶瓷封装具有
最高评价。金属和塑料封装的额定值较低，塑料封装的最低。典型值在 100-500mW范围。
如果封装温度在工作温度范围规范内，则运算放大器保证在规范内工作。商业级设备的温度范围为 $0^{\circ} \mathrm{C}$ 至 $+70^{\circ} \mathrm{C}$ ，工业级设备的范围是 $-25^{\circ} \mathrm{C}$ 至 $+85^{\circ} \mathrm{C}$ 和军用级设备从 $-55^{\circ} \mathrm{C}$ 至 $+125^{\circ} \mathrm{C}$.
电源电压 $V_{C C}$ 具有正确操作运算放大器的最大值和最小值。典型的最大值在 $\pm 18 \mathrm{~V}$ 至 $\pm 22 \mathrm{~V}$ ，但专业单位可能在更高的水平上运作。最小值通常约 为 $\pm 5 \mathrm{~V}$ 但可能范围低至 $\pm 2 \mathrm{~V}$. 如前所述，输出电压摆幅必须位于电源电压设定的轨内。专用运算放大器可以使用单侧电源运行：通常负电源端子接 地，另一个电源端子连接到 $+V_{C C}$.
电源电流被定义为电流，一个OPAmpmd当运算放大器输出为零时，从电源中吸取。这是电池供电应用中一个特别重要的参数。
电源电压的变化， $\pm V_{C C}$ ，可以通过偏移电压变化馈送到输出端。失调电压变化与电源电压变化之比定义为电源抑制比 (PSRR):
$$P S R R=\frac{\Delta V_{O S}}{\Delta V_{C C}}$$
PSRR 可以用 V/ 或分贝表示，其中
$$P S R R \mid d \bar{B}=20 \log \frac{\Delta V O S}{\Delta V_{\Gamma \Gamma}} .$$
如果 $O p A m p s$ 与高性能稳压器一起使用时，由于 PSRR 引起的误差在 OpAmp 应用中基本上可以消除。
虽然非理想运算放大器属性的列表可能看起来很大，但每个属性都只是一个小错误，通过仔细选择电路拓扑和电路元件值，几乎可以消除该错误。这 种性质的文本中没有足够的空间来研究所有可能电路中的所有影响。虽然演示已保持在最低限度，但希望读者已经对最重要的影响产生了一种”感 觉”，并了解了如何补偿它们。优秀的电路设计师应该牢记所有的第二顺序影响并采取适当的行动。

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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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