Basic Characteristics of Sensors

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foreword

This article mainly explains the general content of the sensor,
the concept of the sensor, the classification of the sensor, the basic characteristics of the sensor, the calibration of the sensor, the current status of the sensor technology

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1. The concept of sensor

1. Basic concepts

(1) Definition 1:

A sensor is a device or device that can sense a specified measured value and convert it into a usable output signal according to certain rules

Note:
In some disciplines, sensors are also called sensitive elements, detectors, converters, etc.

(2) Definition 2:

A device or device that can sense (or respond) to a specified measured value and convert it into a usable signal output according to certain rules. The sensor is usually composed of a sensitive element that directly responds to the measured element, a conversion element that produces a usable signal output, and a corresponding electronic circuit.

(3) Definition 3:

A sensor is a measuring device that converts the measured object into a certain physical quantity that
has a definite corresponding relationship with a certain accuracy and is easy to apply.

(4) Definition 4:

In a broad sense, a sensor is a type of transducer, and a transducer is a device that converts energy from one form to another. Transducers include both sensors and actuators.

2. Basic composition of the sensor

Second, the classification of sensors

Sensors are knowledge-intensive and technology-intensive products, and their types are very diverse. The main classification methods are:

1. According to the mechanism of physical laws

结构型传感器
物性型传感器
复合型传感器

2. According to the power supply mode of the circuit

无源传感器
有源传感器

3. Classification by principle

电参量式传感器；
磁电式传感器；
压电式传感器；
光电式传感器；
气电式传感器；
热电式传感器；
波式传感器；
射线式传感器；
半导体式传感器；
其他原理的传感器；

4. Classified by purpose

温度传感器；
光敏传感器；
力敏传感器；
磁敏传感器；
气体传感器；
湿度传感器；
声敏传感器；
流量传感器；
生物传感器；

5. According to the signal output mode

Analog sensor
Digital sensor

Three, the basic characteristics of the sensor

1. Static features

(1) Linearity

If factors such as hysteresis and creep are not considered , the relationship between the output and input of the sensor can be expressed as the following polynomial:
$$y=a_0+a_{1}x+a_2{x}^2+a_3{x}^3+...+a_n{x}^{}$$
The deviation between the actual sensor characteristic curve and the fitting straight line is called the nonlinear error:δ = ± Δ L max YFS × 100 % (non-linear error) Δ L max : the maximum deviation between the actual curve and the fitting curve YFS :$${}^{full}$$
$$\begin{gathered} d=\pm \frac{LOST{\_}_{max}}{Y_{FS}}\times 100\%(non-linear\; error) \\ LOST{\_}_{max}:Maximum\; deviation\; between\; actual\; curve\; and\; fitted\; curve \\ {Y}_{FS}:full\; scale\; output \end{gathered}$$

(2) Sensitivity

Sensitivity can be measured by the derivative of each point of the input-output curve

(3) Hysteresis

$$\begin{gathered} d_H=\pm \frac{\Delta H_{max}}{Y_{FS}}\times 100\%(non-linear\; error) \\ \Delta H_{max}:Maximum\; output\; deviation\; of\; positive\; and\; negative\; range \\ {Y}_{FS}:full\; scale\; output \end{gathered}$$

(4) Repeatability

$$\begin{gathered} d_K=\pm \frac{\Delta R_{max}}{Y_{FS}}\times 100\%(non-linear\; error) \\ \Delta R_{max}:Maximum\; output\; deviation\; for\; repeated\; same\; measurement\; of\; uniform\; sensor \\ {Y}_{FS}:full\; scale\; output \end{gathered}$$

(5) Resolution

$$\begin{gathered} d_X=\frac{\Delta X{\_}_{max}}{Y_{FS}}\times 100\%(non-linear\; error) \\ \Delta X{\_}_{max}:Maximum\; measurement\; change\; required\; per\; unit\; output \\ {Y}_{FS}:full\; scale\; output \end{gathered}$$

(6) Temperature stability

$$\begin{gathered} a_T=\frac{Y_2-Y_1}{Y_{FS}\Delta T}\times 100\%(non-linear\; error) \\ {Y}_1,Y_{2}are\; the\; temperature{T}_1,T_{2}output\; value\; when \\ {Y}_{FS}:full\; scale\; output \\ \Delta T=T_2-T_1 \end{gathered}$$

2. Dynamic characteristics

(1) (Step) Transient Response Characteristics

(2) Unit (step) transient response of a first-order sensor

$$t\frac{dy(t}{\mathrm{d}t}+y(t)=x(t)$$

(3) Unit (step) transient response of a second-order sensor

(4) Characteristic parameters in the step response transition process

	 时间常数τ
	 上升时间tr
	 响应时间ts
	 振荡次数N
	 稳态误差e

Fourth, the frequency domain analysis method of the sensor

1. Mathematical model of the sensor

Mathematical Model of n-order Sensor System

If the input signal is a sine wave $X(t)=Asin\left(\omega t\right)$ , after Fourier transform

2. Frequency response of the first-order sensor

(1) Transfer function

$$H(jw)=\frac{1}{t\left(jw\right)+1}$$

(2) Amplitude-frequency characteristics

$$A(w)=\frac{1}{\sqrt{1+(w\tau {)}^2}}$$

(3) Phase-frequency characteristics

$$\Theta \left(w\right)=-arctan(w\tau )$$

3. Frequency response of the second-order sensor

(1) Transfer function

$$H(jw)=\frac{1}{1-(\frac{w}{w_0}{)}^2+2je\frac{w}{w_0}}$$

(2) Amplitude-frequency characteristics

$$A(w)=\frac{1}{\sqrt{[1-(\frac{w}{w_0}{)}^2{]}^2+(2e\frac{w}{w_0}{)}^2}}$$

(3) Phase-frequency characteristics

$$\Theta \left(w\right)=-arctan\left(\frac{2e\frac{w}{w_0}}{1-(\frac{w}{w_0}{)}^2}\right)$$

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Summarize

Readers are welcome to correct me if the article is inappropriate