Name: analyzing circuits with superposition
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 18 s
Channel: JoVE

叠加定理用于具有多个独立源的电路。
应用该定理时，每次只保留一个独立电源，同时将不作用的电压源用短路代替，将不作用的电流源用开路代替。
该定理指出，在线性电路中，元件两端的电压或通过元件的电流等于各个独立电源所贡献的代数和。
考虑一个包含电压源和电流源的电路，需要确定电阻两端的电压降。
电压降来自两个独立电源的贡献。
通过将电流源置零，可得到电压源的贡献。
通过应用基尔霍夫电压定律，确定回路电流。利用欧姆定律，计算电压降。
类似地，通过将电压源设为零，可获得当前的源贡献。
通过合并电阻，得到等效电阻。利用电流分流定律和欧姆定律，确定电压降。
最后，通过叠加各个独立源的贡献，得到电阻两端的总电压降。

叠加定理

叠加原理是一个基本概念，是指在线性电路中，元件两端的电压（或流过元件的电流）可以通过对每个具有隔离作用的独立源所产生的单独贡献进行求和来确定。当处理包含多个独立源的线性电路时，该原理是一个有价值的分析工具。为了能够有效地应用叠加原理，应当一次仅考虑一个独立源，同时停用所有的其他源，从而得到单个源所产生的输出（电压或电流）。 然后，可以将各个活动源的贡献进行代数相加，以此确定所有活动源的累积效应，从而简化电路分析过程。值得注意的是，相关源是不会受到影响的，因为它们会受到电路变量的控制。需要指出的是，利用叠加原理可能会增加分析的工作量。例如，在具有三个独立源的电路中，须分别分析三个独立的简化电路，每个电路都代表了单个源的贡献。尽管存在这一潜在缺点，叠加原理仍然是一种有价值的技术，可通过用短路代替电压源、用开路代替电流源来简化复杂电路。

叠加定理适用于具有多个独立电源的电路。  
应用该定理时，每次仅保留一个独立电源，而……

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

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 independent source in the circuit. The final voltage or current is found by algebraically adding the individual results. Dependent sources are not turned off because they depend on circuit variables.

This method can simplify complex circuits, but it may take more work. A circuit with three independent sources must be analyzed as three separate simplified circuits. Even so, superposition remains a useful tool for breaking down difficult linear circuit problems.

Analyzing Circuits with Superposition

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

Mesh currents give students a simpler way to analyze planar circuits. In mesh analysis, the unknowns are currents, not voltages. The method uses Kirchhoff's voltage law, or KVL, to build the equations needed to solve the circuit. A mesh is a closed loop in a circuit that does not contain any smaller loops inside it. Each independent mesh is assigned a mesh current, and this current is usually drawn in the clockwise direction. These mesh currents are used as the main circuit variables during...

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

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

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 superposition helps solve linear circuits by analyzing one independent source at a time, then adding the voltage or current contributions.

Analyzing Circuits with Superposition | 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

Analyzing Circuits with Superposition

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