Name: thevenin circuit equivalents
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 15 s
Channel: JoVE

戴维南定理指出，任何线性二端电路都可以用一个由单个电压源与电阻串联组成的等效电路来替代。
在无负载的情况下，开路端子间的电压即为戴维南电压。
在求戴维南电阻时，所有独立电源均被关闭，此时从端口看进去的电阻即为戴维南电阻。
如果电路包含受控源，则独立源仍需关闭，但在端口处需施加一个已知的测试源。
根据测得的端电压或电流，可以确定戴维南电阻。
最后，将负载连接到等效电路。利用电流分配公式计算通过负载的电流。根据欧姆定律，确定负载两端的戴维南电压。
电池可以用戴维南等效电路来表示。戴维南电压是电池的开路电压，电阻则是其内阻。
了解戴维南参数后，无需重新分析整个电路，即可轻松计算不同负载下的电流。

戴维宁定理

Thevinin's Theorem

戴维南定理在电路分析中发挥着至关重要的作用，同时还为电路中可变负载所带来的挑战提供了解决方案。在实际应用中，经常会遇到某些元件保持固定而其他元件发生波动的电路，并通常将其称为“负载”。典型的家用电源插座是可变负载的主要示例，因为它能够连接到各种电器，每种电器都有其独特的电气特性。每次插入或移除新设备时，整个电路都需要进行重新分析。戴维南定理提供了一种用等效电路来代替原有电路固定部分的技术，从而简化了分析和设计。 戴维南定理指出，线性两端电路可以用由电压源与电阻器串联所组成的等效电路来进行表示。该等效电路从外部角度有效地封装了原始电路的行为。两个关键的参数对戴维南等效电路进行了定义：戴维南等效电压 (VTh)，对应于端子处的开路电压；以及戴维南等效电阻 (RTh)，它代表了在所有条件下端子处的输入或等效电阻。从而使得独立来源被停用。 为了能够进一步说明这一概念，请观察图1和图2中所示的两个电路。当这些电路在其端子处共享相同的电压-电流关系时，它们会被视为是等效的。当端子变为开路时，则不会电流流动，开路端子上的电压将会变为戴维南电压。当所有独立的来源都关闭时。那么在端子上看到的电阻就是戴维宁电阻。 <img alt="Figure1" src="/files/ftp_upload/15053/15053_PT_Figure_1.svg" style="text-align: center; height: 128px;"> 图 1 <img alt="Equation1" src="/files/ftp_upload/15053/15053_PT_Equation_1.svg" style="text-align: center; height: 14px;"> <img alt="Figure2" src="/files/ftp_upload/15053/15053_PT_Figure_2.svg" style="text-align: center; height: 128px;"> 图 2 <img alt="Equation2" src="/files/ftp_upload/15053/15053_PT_Equation_2.svg" style="text-align: center; height: 14px;"> 为了能够在实际中应用这个想法并确定戴维南电阻，我们必须考虑以下两种情况： 情况1：在网络不包含依赖源的情况下，所有的独立源均会被停用，同时并以此来确定输入电阻，即位于端子a和b之间的电阻。 情况2：当网络中包含依赖源时，则需要继续停用所有的独立源。但是，不要停用相关源，因为它们是由电路变量来进行控制的。 值得注意的是，戴维宁电阻 (RTh) 的值有时可能为负，以此来表示电路是处于正在供电的状态而不是消耗电力的状态。这种情况在具有相关源的电路中是可行的。

戴维南定理指出，任何线性二端电路均可等效为一个由单个电压源与一个……串联组成的等效电路

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

DC Circuit Analysis

直流电路分析

KEY TERMS AND CONCEPTS

关键术语与概念

thevenin circuit equivalents

Thevenin circuit equivalents simplify linear two-terminal circuits by replacing the fixed part of a network with one equivalent source and one resistor. This method is useful when a circuit has a fixed section and a load that can change. A household electrical outlet is a familiar example, because different appliances can be plugged in or removed. Each change in load can require a new circuit analysis, so an equivalent circuit makes the work easier.

Thevenin's theorem states that a linear two-terminal circuit can be represented by a voltage source in series with a resistor. From the outside, this equivalent circuit has the same behavior as the original network. Two circuits are considered equivalent when they have the same voltage-current relationship at their terminals. The Thevenin equivalent voltage, VTh, is the open-circuit voltage at the terminals, and the Thevenin equivalent resistance, RTh, is the input resistance seen at the terminals when the independent sources are turned off.

To find the Thevenin resistance, the method depends on the kind of sources in the network. If the circuit has no dependent sources, all independent sources are deactivated and the resistance between terminals a and b is found. If the network includes dependent sources, the independent sources are still turned off, but the dependent sources stay active because they are controlled by circuit variables. In some cases, RTh can be negative. That means the circuit is supplying power instead of consuming it, which can happen in circuits with dependent sources.

Thevenin Circuit Equivalents

nodal analysis

Using Node Voltages in Circuit Analysis

Nodal analysis uses node voltages to simplify circuit analysis. In this method, the voltage at each node becomes the main variable. Once those voltages are known, they can be used to find other values, such as the current through specific circuit parts. The process begins by choosing a reference node, also called a datum node. This node is selected for convenience and assigned a voltage of zero. The other nodes, called non-reference nodes, are then measured relative to that point. In the...

nodal analysis with voltage sources

Supernode Equations in Nodal Analysis

Nodal analysis uses node voltages and Kirchhoff’s laws to solve circuits with voltage sources. It is a systematic method for breaking a complex circuit into smaller parts that are easier to analyze. In this example, the circuit includes four resistors and two voltage sources. One voltage source is connected between a non-reference node and the reference node. In that case, the non-reference node voltage can be written directly as the source voltage. This removes one unknown and makes the...

mesh analysis

Mesh Currents for Circuit Analysis

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mesh analysis with current sources

Current Sources in Mesh Circuit Analysis

Current sources make mesh circuit analysis easier because they can reduce the number of equations needed. This applies to both independent and dependent current sources. The method depends on where the current source is placed in the circuit. When a current source appears in only one mesh, the setup is simple. Assign mesh currents as usual, but leave out the mesh that contains the current source from the equation process. Then apply Kirchhoff's voltage law, or KVL, to the remaining mesh to get...

source transformation

Circuit Source Equivalents

Circuit source equivalents make it easier to simplify electrical circuits in circuit analysis. A source transformation replaces a voltage source in series with a resistor by a current source in parallel with a resistor, or it replaces a current source in parallel with a resistor by a voltage source in series with a resistor. The key idea is that the equivalent resistance at the circuit terminals stays the same when the original sources are turned off. When making the change, the current source...

linear circuits

Circuit Linearity and Resistor Behavior

Circuit linearity describes how a circuit responds when its input changes. A linear circuit has an output that is directly proportional to its input. This behavior follows two rules: homogeneity and additivity. Homogeneity means that if the input, or excitation, is multiplied by a constant factor, the response is multiplied by the same factor. For example, if the current is increased by a constant k, the voltage also increases by k times. Additivity means that the response to a sum of inputs...

superposition theorem

Analyzing Circuits with Superposition

Superposition is a circuit analysis method for linear circuits with more than one independent source. It lets you find the voltage across or current through an element by adding the separate effects of each source acting alone. To use superposition, keep one independent source active and turn off the others. A voltage source is replaced by a short circuit, and a current source is replaced by an open circuit. Then calculate the output from the single active source. Repeat the process for each...

thevinin's theorem

Thevenin circuit equivalents simplify linear two-terminal circuits by replacing the fixed part of a network with one equivalent source and one resistor. This method is useful when a circuit has a fixed section and a load that can change. A household electrical outlet is a familiar example, because different appliances can be plugged in or removed. Each change in load can require a new circuit analysis, so an equivalent circuit makes the work easier. Thevenin's theorem states that a linear...

norton's theorem

Norton Equivalent Circuit in DC Analysis

Norton equivalent circuit in DC analysis shows how a linear two-terminal circuit can be replaced by a simpler network. The replacement uses a current source, called I_N, in parallel with a resistor, called R_N. I_N is the short-circuit current through the terminals, and R_N is the input or equivalent resistance seen at the terminals when the independent sources are turned off. To find Norton's resistance, all independent sources in the circuit are set to zero. The resistance measured at the...

maximum power transfer

Load Matching in Thevenin Circuits

Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load. The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load...

design example: strain gauge bridge or wheatstone bridge

design-example-strain-gauge-bridge-or-wheatstone-bridge

Wheatstone Bridge Output for Strain Gauge Design

A strain gauge and Wheatstone bridge work together to turn mechanical strain into an electrical signal. In engineering, this setup is often used to measure force or pressure. Each part of the bridge has a resistance that changes slightly when strain is applied. The main goal is to turn a very small voltage output into a larger, easier-to-read signal. A voltmeter can then measure that output more clearly. To do this, an engineer designs the strain gauge circuit and figures out how much...

key terms and concepts

Learn how Thevenin’s theorem replaces a linear two-terminal circuit with a voltage source and resistor, and how to find VTh and RTh in circuit analysis.

Thevenin Circuit Equivalents | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Thevenin Circuit Equivalents

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