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

중첩 정리는 여러 개의 독립적인 소스가 있는 회로에서 사용됩니다.
이 정리를 적용하려면 한 번에 하나의 독립적인 소스를 유지하면서 비활성 전압 소스를 각각 단락으로 교체하고 비활성 전류 소스를 개방 회로로 교체하십시오.
정리는 선형 회로의 요소를 통과하는 전압 또는 전류가 독립 소스의 기여도의 대수적 합이라고 말합니다.
전압과 전류 소스가 있는 회로를 생각해 보십시오., 여기서 저항기 양단의 전압 강하를 결정해야 합니다.
전압 강하는 두 개의 독립적인 소스로부터 영향을 받습니다.
전압 소스의 기여도는 전류 소스를 0으로 설정하여 얻습니다.
Kirchhoff의 전압 법칙을 적용하여 루프 전류를 결정합니다. 옴의 법칙을 사용하여 전압 강하가 계산됩니다.
마찬가지로, 전류 소스 기여도는 전압 소스를 0으로 설정하여 얻습니다.
저항을 결합하면 등가 저항을 얻을 수 있습니다. 전류 분할 규칙과 옴의 법칙을 사용하여 전압 강하가 결정됩니다.
마지막으로, 독립적인 소스의 기여도를 추가하여 저항기 전체의 총 전압 강하를 얻습니다.

중첩 정리

중첩 원리는 선형 회로에서 요소 전체의 전압(또는 통과하는 전류)이 분리되어 작동하는 각 독립 소스의 개별 기여를 합산하여 결정될 수 있다는 기본 개념입니다. 여러 개의 독립 소스가 포함된 선형 회로를 다룰 때 이 원리는 분석을 위한 귀중한 도구 역할을 합니다. 중첩 원리를 효과적으로 적용하려면 한 번에 하나의 독립 소스에만 집중하고 다른 모든 소스는 비활성화해야 합니다. 이 접근 방식은 활성 소스에서 발생하는 출력(전압 또는 전류)을 생성합니다.

모든 활성 소스의 누적 효과는 개별 기여를 대수적으로 추가하여 결정할 수 있습니다. 이는 회로 분석 과정을 단순화합니다. 특히, 종속 소스는 회로 변수에 의해 제어되므로 영향을 받지 않습니다. 중첩 원리를 활용하면 분석 노력이 증가할 수 있다는 점은 주목할 가치가 있습니다. 예를 들어, 3개의 독립적인 소스를 갖춘 회로를 다룰 때 각각 개별 소스의 기여도를 나타내는 3개의 개별적이고 단순화된 회로를 분석해야 합니다. 이러한 잠재적인 단점에도 불구하고 중첩 원리는 전압 소스를 단락 회로로, 전류 소스를 개방 회로로 대체하여 복잡한 회로를 단순화하는 귀중한 기술로 남아 있습니다.

중첩 정리는 여러 개의 독립적인 소스가 있는 회로에서 사용됩니다.
이 정리를 적용하려면 한 번에 하나의 독립적인 소스를 유지하는 동안 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

DC Circuit Analysis

DC 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Description

Transcript