Name: using node voltages in circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

A análise nodal é um método geral para simplificar a análise de circuitos usando tensões de nós como variáveis de circuito.
Considere um circuito com três nós e três resistores.
Para encontrar as tensões do nó neste circuito, primeiro é selecionado um nó de referência ou datum, cuja tensão é atribuída a zero.
Os restantes nós não de referência são atribuídos a tensões nodais relativas ao nó de referência.
Em seguida, aplicando a lei atual de Kirchhoff aos nós não referenciais 1 e 2, obtém-se a relação entre as correntes de ramificação.
Além disso, usando a lei de Ohm, as correntes de ramificação que passam pelos três resistores são expressas em termos das tensões do nó.
Agora, os valores das correntes de ramificação podem ser substituídos nas equações obtidas usando a lei de corrente de Kirchhoff para obter duas equações simultâneas.
Para um circuito com n nós, n - 1 equações independentes são obtidas.
Se os valores dos resistores e correntes da fonte forem conhecidos, eles podem ser substituídos nas duas equações, que podem então ser resolvidas para obter as tensões do nó.

análise nodal

A análise nodal é um método fundamental em engenharia elétrica usado para simplificar o processo de análise de circuitos. Este método gira em torno do conceito de usar tensões de nós como variáveis ​​primárias para análise de circuitos. O objetivo é determinar a tensão em cada nó de um circuito, que pode então ser usada para encontrar outras grandezas de interesse, como correntes através de componentes específicos.

Considere, por exemplo, um circuito simples composto por três nós e três resistores, conforme mostrado na Figura 1. O primeiro passo na análise nodal envolve a seleção de um nó de referência ou de referência. Este nó é normalmente escolhido com base na conveniência e sua tensão recebe um valor zero.

<img alt="Figure1" src="/files/ftp_upload/15047/15047_PT_Figure_1.svg" style="text-align: center; height: 136px;" />

Os nós subsequentes, chamados de nós não de referência, recebem tensões nodais relativas a este nó de referência. No exemplo aqui considerado, existem dois nós sem referência rotulados como 1 e 2, cada um com suas respectivas tensões de nó.

Para estabelecer uma relação entre as correntes dos ramos, a Lei das Correntes de Kirchhoff (LCK) é aplicada aos nós não-referência. LCK afirma que a soma algébrica das correntes que entram em um nó (ou em uma fronteira fechada) é zero. Esta lei baseia-se no princípio da conservação da carga – ou seja, uma carga não pode ser criada ou destruída.

Seguindo a aplicação do LCK, a Lei de Ohm é usada para expressar as correntes dos ramos que passam pelos três resistores em termos das tensões dos nós. A Lei de Ohm postula que a corrente que passa por um condutor entre dois pontos é diretamente proporcional à tensão entre os dois pontos.

Com as correntes de ramo expressas em termos de tensões de nó, esses valores são substituídos nas equações derivadas de LCK. Essa substituição resulta em duas equações simultâneas, pois, para um circuito com 'n' nós, são obtidas 'n-1' equações independentes.

Por último, se os valores dos resistores e das correntes da fonte forem conhecidos, eles podem ser substituídos nas duas equações. Resolver essas equações produzirá as tensões dos nós. Esta informação é inestimável, pois pode ajudar na compreensão do comportamento do circuito e no projeto ou solução de problemas de circuitos elétricos.

Concluindo, a análise nodal é uma ferramenta poderosa na análise de circuitos, fornecendo um método sistemático para determinar a distribuição de tensões dentro de um circuito, que pode então ser usado para calcular outros parâmetros como correntes e potência.

Análise Nodal

A análise nodal é um método geral para simplificar a análise de circuitos usando tensões de nós como variáveis de circuito.
Considere um circuito com três nós e ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

DC Circuit Analysis

Análise de Circuitos CC

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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 example described, there are three nodes total, with two non-reference nodes labeled 1 and 2.

Next, Kirchhoff's Current Law, or KCL, is applied to the non-reference nodes. KCL states that the algebraic sum of currents entering a node is zero. This follows the idea that charge is conserved, so charge cannot be created or destroyed. After that, Ohm's Law is used to write the branch currents through the three resistors in terms of the node voltages.

Those current expressions are then substituted into the KCL equations. Because a circuit with n nodes gives n - 1 independent equations, the example produces two simultaneous equations. If the resistor values and source currents are known, they can be placed into these equations. Solving them gives the node voltages, which helps explain circuit behavior and can support circuit design or troubleshooting.

Using Node Voltages in Circuit Analysis

nodal 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

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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...

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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

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...

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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 nodal analysis uses a reference node, KCL, and Ohm's Law to find node voltages and solve simple circuit equations in high school electronics.

Using Node Voltages in Circuit Analysis | 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

Using Node Voltages in Circuit Analysis

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