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## 物理代写|传感器代写Sensor代考|Deviations from Ideality: Errors

The deterministic model is advantageous when dealing with transduction chains, gains, and ranges. However, for a more significant degree of knowledge, this is not sufficient: real sensors (as anything of the real world) are affected by unpredictable errors/fluctuations arising from the physical nature of the environment and the interface.
We could roughly classify errors in two main categories:

Random errors: Unpredictable deviations of the output due to stochastic temporal variations. For stationary input and constant conditions of the sensing system, repeated readouts provide different results at any sample. They are realizations of random physical processes and are also referred to as noise. ${ }^8$

Systematic errors: Constant deviations of the sensor response from the ideal characteristic. For stationary input and constant conditions of the sensing system, repeated readouts provide the same error. This is given, for example, by nonlinear deviations of the real characteristic from the ideal one or by the output variation induced by influence parameters. Even if the error is fixed for repeated conditions, it should be pointed out that it has a degree of unpredictability so that stochastic models should describe it.

mode) in a real sensing system, it will be mapped into the output with some error added: $\Delta y_S+\Delta y_E$, as shown in Fig. 2.25A. In this case, the error could be precisely known and, by acquiring a large amount of data, we can characterize the error model using, for example, the associated probability distributions.

Conversely, if we know the error model and only observe the readout value (operating or prediction mode), we do not know the single error (outcome) entity even if we have characterized the error model. Therefore, since the errors have e stochastic behavior, the input could no longer be determined but estimated or predicted, as shown in Fig. 2.25B, under some degree of uncertainty.

## 物理代写|传感器代写Sensor代考|The Input−Output Duality of a Single Error

Following the previous discussion, the output variation $\Delta y$ of the readout could be dependent on both a signal $\Delta y_S$ or error $\Delta y_E$ (either systematic or random) of the system
$$\Delta y=\Delta y_S+\Delta y_E .$$
Owing to the linear behavior of the system, we can write
$$\Delta y=S \cdot \Delta x=S \cdot\left(\Delta x_S+\Delta x_E\right)$$
so that
$$\Delta x=\Delta x_S+\Delta x_E=\frac{\Delta y_S}{S}+\frac{\Delta y_E}{S},$$

where $\Delta x_E$ is referred to as the input-referred error. Therefore, the error could be modeled as something that is summed up to the input signal to give the same deviation of the output. We will see that if the error is ascribed to noise, it is referred to as input-referred noise (IRN) or equivalent input noise (EIN) or referred to input (RTI) noise.

We can graphically represent this relationship as in Fig. 2.26A, where we can see that the error $\Delta y_E$ (either systematic or random) of a real system is summed to the output signal $\Delta y_s$. Now, we can model the error as a contribution added to the output of an ideal system, as shown in Fig. 2.26B, which is also called output-referred error. Like the signal, we can model the same error by an additional fictitious input-referred contribution $\Delta x_E$ summed to the input of an ideal system in order to get the same output result. In other terms, we can map the output error into an input-referred error by dividing it by the gain of the system. Similarly, a source of errors placed at the input could be mapped to the output by multiplying it to the gain the system.

## 物理代写|传感器代写Sensor代考|The Input-Output Duality of a Single Error

$$\Delta y=\Delta y_S+\Delta y_E .$$

$$\Delta y=S \cdot \Delta x=S \cdot\left(\Delta x_S+\Delta x_E\right)$$

$$\Delta x=\Delta x_S+\Delta x_E=\frac{\Delta y_S}{S}+\frac{\Delta y_E}{S},$$

## 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。

Posted on Categories:Sensor, 传感器, 物理代写

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## 物理代写|传感器代写Sensor代考|Signal Characterization

Signals are functions describing the variation of states in physical or technology domains.

A first classification could be drawn between deterministic and random signals.

A deterministic signal is described by a mathematical function or rule that uniquely determines any past and any future state. The knowledge of a deterministic signal corresponds to the identification of the related function or rule model. An example is illustrated in Fig. 2.6A with a sinusoidal function.

A random signal is a signal in which future values are known only under the concept of probability. These signals can be described using the mathematical tool of random variables. The knowledge of stochastic signals corresponds to the identification of the random variable model characteristics, such as (among many others) its probability density function (PDF). An example is shown in Fig. 2.6C.
For a correct framework, it is better to focus on two distinct viewpoints in sensor design.

Characterization mode. We can characterize the system from a theoretical point of view, based on known physical models used in the design. Furthermore, from the experimental point of view, a known signal could be fed into the input, either deterministic (analytical function) or stochastic (by means of a known random variable), and the output is recorded. The experimental test could validate the theoretical model, if present, or be used to characterize an experimental model in the absence of a theoretical one.

Operating mode. The sensor, once characterized, monitors the environment to extract the information. In this case, the input is fed by an unknown signal whose knowledge will be determined on the basis of the sensor models.

## 物理代写|传感器代写Sensor代考|Limits of the Quasistatic Characteristic and Frequency Domain Representation

The input-output relationship determined by the static characteristic, as shown in Fig. 2.7, should be taken with great caution since it is valid when signal time variations are much lower than any time constant of the sensor system. If time constants of the sensor come into play, the input-output cross-point no longer follows the quasistatic characteristic due to the role of gain and phase shift operated by the system

If the system behaves as linear time-invariant (LTI), the gain and phase relationships between input and output are described by a complex function of the frequency $H(f)$ referred to as the transfer function. From now on, we will primarily refer to low-pass transfer functions so that the gain $S$, identified by the quasistatic characteristic, is equal to $H(0)$.

As shown in Fig. 2.8A, if we excite a first-order low-pass system with a sinusoidal signal having frequency components greater than the reciprocal of its characteristic time constant, we have that the static characteristic could not determine the phase shift and the amplitude of the output signal components. The input-output relationship might be described by a closed trajectory or limit cycle or orbit in the input-output space whose shape is determined by the system time-response description (e.g., poles and zeros) transfer function for small signals) in the bias point. In the case of a linear system, single time-constant and low-pass behavior with respect to a small sinusoidal excitation, as shown in Fig. 2.8B, the phase and amplitude scale could be described by an ellipse trajectory. ${ }^2$ For very low frequency, the ellipse is squeezed on the ideal static curve; then, for increasing frequency, the phase lag increases the ellipse’s minor axis. Finally, the amplitude scale is the determinant effect for very high frequency by squeezing the ellipse on a horizontal line. The previous observation on the static characteristic’s role points out that a frequency-domain representation is necessary when time variations come into play.

.

## 物理代写|传感器代写传感器代考|准静态特性和频域表示的极限

. 如图2.7所示，由静态特性决定的输入输出关系应该非常谨慎，因为当信号时变化远远低于传感器系统的任何时间常数时，它是有效的。当传感器的时间常数起作用时，由于系统操作的增益和相移的作用，输入输出交叉点不再遵循准静态特性 如果系统表现为线性时不变(LTI)，则输入和输出之间的增益和相位关系用频率$H(f)$的复函数描述，称为传递函数。从现在开始，我们将主要参考低通传递函数，使由准静态特性识别的增益$S$等于$H(0)$ .

## 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。

Posted on Categories:Sensor, 传感器, 物理代写

## avatest™帮您通过考试

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## 物理代写|传感器代写Sensor代考|At the Origin of Uncertainty: Thermal Agitation

Errors are differences from observed results from what we expect. One of the primary sources of error is noise, arising from random physical processes (Chapter 6), so that it is one of the main limiting factors of the sensing process. As discussed, noise limits the resolution of the electronic interfaces (Chapter 7); thus, the amount of information conveyed into the sensor.

If we look at Fig. 1.10, we can see a simple mechanical force transducer (Chapter 11). One end of a cantilever is anchored to a firm reference while a variable force is exerted on the other free end. On the cantilever’s upper side, a laser beam is reflected toward a surface or a position-sensitive optical sensor (Chapter 9). Therefore, the position of the cantilever beam is proportional to the input force, realizing a force meter.

What is the limit of discrimination of this “sensor”? In principle, we can sense any slight variation of the input. If it is hard to distinguish variations on the screen, we can move the screen to a greater distance than the original one to look at variations clearer. In principle, this sensor has an “infinite” capability of discrimination (down to fundamental physical limits).

Unfortunately, nature made things a more complex way, and we know that any mechanical system is at a microscopic level subject to molecular agitation. In thermal equilibrium, any atom of the cantilever and any molecule of the surrounding gas is subject to a natural thermal agitation where the mean kinetic energy of any particle of the system is a microscopic expression of the temperature.

## 物理代写|传感器代写Sensor代考|Basic Constraints of Electronic Sensor Design

Looking back to all the examples of this chapter, we can devise several basic interdependences and constraints to be taken into account in sensor design.

• Resolution-bandwidth tradeoff. We can increase the resolution (i.e., reduce the uncertainty) by averaging the readouts by following the law of large numbers, as in the force sensor example. However, we must assume that the input force shall be stable during the averaging. This means that averaging is limited by signal bandwidth, and we cannot follow input signals that are faster than the averaging time. Therefore, the higher the resolution, the lower the bandwidth.
• Resolution-power consumption tradeoff. Depending on the complexity of the information to be extracted, we need to use higher amounts of power due to the larger computation requirements to gain higher information (resolution).
• Bandwidth-power consumption tradeoff. Since the computation requires energy consumption in real systems, the elaboration of higher information in a shorter time implies higher power consumption.

A block diagram of the foregoing relationships is shown in Fig. 1.11. The diagram shows the basic constraints of the sensor design divided into three main areas (Chapters 2 and 3). The first is related to the information constraint related to the amount of information conveyed by the sensing system, which is represented by the dynamic range. The dynamic range is in turn determined by the operating range and the input-referred resolution of the system. A second area is related to the system’s time constraint, that is, the bandwidth. A third area is related to the energy constraint, which is represented by the power consumed by the sensing system.

A given electronic technology or architecture allows us to determine figures of merit (Chapter 3) relating and trading off the three areas mentioned above. Therefore, once we have two out of the three constraints set, we can determine the remaining. For example, once we have the required bandwidth and dynamic range for a given figure of merit, we can determine the minimum required power consumption for a given technology. Alternatively, we can determine the dynamic range for a given power budget and bandwidth, that is, its maximum achievable resolution.

## 物理代写|传感器代写Sensor代考|电子传感器设计的基本约束

• 分辨率-带宽折衷。我们可以增加分辨率(即，减少不确定性)，通过遵循大数定律平均读数，就像在力传感器的例子中一样。但是，我们必须假设在求平均过程中输入的力是稳定的。这意味着平均受到信号带宽的限制，我们不能跟踪比平均时间快的输入信号。因此，分辨率越高，带宽越低。
• 分辨率-功耗权衡。根据要提取的信息的复杂性，我们需要使用更高的功率，因为计算需求更大，以获得更高的信息(分辨率)。
• 带宽-功耗权衡。由于在实际系统中计算需要消耗能量，在更短时间内细化更高的信息意味着更高的功耗。

## 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。