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

노드 분석은 노드 전압을 회로 변수로 사용하여 회로 분석을 단순화하는 일반적인 방법입니다.
3개의 노드와 3개의 저항이 있는 회로를 고려하십시오.
이 회로에서 노드 전압을 찾기 위해 먼저 전압이 0으로 할당된 참조 또는 데이터 노드를 선택합니다.
나머지 비참조 노드에는 참조 노드에 상대적인 노드 전압이 할당됩니다.
다음으로, Kirchhoff의 현재 법칙을 비 참조 노드 1과 2에 적용하면 분기 전류 간의 관계를 제공합니다.
또한 옴의 법칙을 사용하여 세 개의 저항을 통과하는 분기 전류는 노드 전압으로 표현됩니다.
이제 분기 전류의 값을 Kirchhoff의 전류 법칙을 사용하여 얻은 방정식으로 대체하여 두 개의 동시 방정식을 얻을 수 있습니다.
n개의 노드가 있는 회로의 경우 n - 1개의 독립 방정식이 얻어집니다.
저항과 소스 전류의 값을 알고 있으면 두 방정식으로 대체할 수 있으며, 이를 해결하여 노드 전압을 얻을 수 있습니다.

노드 분석

노드 분석은 회로 분석 과정을 단순화하는 데 사용되는 전기 공학의 기본 방법입니다. 이 방법은 노드 전압을 회로 분석의 주요 변수로 사용하는 개념을 중심으로 진행됩니다. 목표는 회로의 각 노드에서 전압을 결정하는 것입니다. 이를 통해 특정 구성 요소를 통과하는 전류와 같은 다른 관심 수량을 찾는 데 사용할 수 있습니다.

예를 들어, Figure 1과 같이 3개의 노드와 3개의 저항기로 구성된 간단한 회로를 생각해 보십시오. 노드 분석의 첫 번째 단계에서는 기준 노드 또는 기준 노드를 선택합니다. 이 노드는 일반적으로 편의성에 따라 선택되며 해당 전압에는 0 값이 할당됩니다.

<img alt="Figure1" src="/files/ftp_upload/15047/15047_PT_Figure_1.svg" style="text-align: center; height: 136px;">
Figure 1

비기준 노드라고 하는 후속 노드에는 이 기준 노드를 기준으로 노드 전압이 할당됩니다. 여기에서 고려한 예에는 각각 해당 노드 전압이 있는 1과 2로 표시된 두 개의 비참조 노드가 있습니다.

분기 전류 간의 관계를 설정하기 위해 키르히호프의 전류 법칙(KCL)이 비참조 노드에 적용됩니다. KCL은 노드(또는 닫힌 경계)에 들어가는 전류의 대수적 합이 0이라고 명시합니다. 이 법칙은 전하보존의 원칙에 근거하고 있습니다. 즉, 전하는 생성되거나 소멸될 수 없습니다.

KCL을 적용한 후 옴의 법칙을 사용하여 세 개의 저항을 통과하는 분기 전류를 노드 전압으로 표현합니다. 옴의 법칙은 두 지점 사이의 도체를 통과하는 전류가 두 지점의 전압에 정비례한다고 가정합니다.

노드 전압으로 표현된 분기 전류를 사용하면 이러한 값이 KCL에서 파생된 방정식으로 대체됩니다. 이 대체 결과는 'n' 노드가 있는 회로의 경우 'n-1' 독립 방정식이 얻어지기 때문에 두 개의 연립 방정식이 생성됩니다.

마지막으로 저항과 소스 전류의 값을 알면 두 방정식으로 대체할 수 있습니다. 이 방정식을 풀면 노드 전압이 산출됩니다. 이 정보는 회로의 동작을 이해하고 전기 회로를 설계하거나 문제를 해결하는 데 도움이 될 수 있으므로 매우 중요합니다.

결론적으로, 노드 분석은 회로 분석의 강력한 도구로, 회로 내 전압 분포를 결정하는 체계적인 방법을 제공하며, 이를 통해 전류 및 전력과 같은 다른 매개변수를 계산하는 데 사용할 수 있습니다.

노드 분석은 노드 전압을 회로 변수로 사용하여 회로 분석을 단순화하는 일반적인 방법입니다.
세 개의 노드와 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

DC Circuit Analysis

DC 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

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...

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 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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