Name: supernode equations in nodal analysis
Uploaded: 2025-05-22T09:06:13.000Z
Duration: 1 min 11 s
Channel: JoVE

노드 분석은 종속 또는 독립 전압 소스를 갖는 회로의 분석을 효과적으로 단순화할 수 있습니다.
하나의 전압 소스가 비참조 노드와 참조 노드 사이에 연결되도록 구성된 4개의 저항과 2개의 전압 소스가 있는 회로를 고려하십시오.
여기서, non-reference node의 전압은 소스의 전압과 동일하게 기록될 수 있습니다.
다른 전압 소스는 두 개의 비참조 노드 사이에 연결됩니다. 이들은 슈퍼노드 또는 일반화된 노드를 형성합니다.
슈퍼 노드가 있는 회로를 분석하려면 Kirchhoff의 전류 및 전압 법칙을 모두 적용하여 노드 전압을 결정해야 합니다.
첫째, Kirchhoff의 현재 법칙은 각 요소를 통과하는 전류를 고려하여 슈퍼노드에 적용됩니다. 얻어진 방정식은 노드 전압으로 작성할 수 있습니다.
그런 다음 Kirchhoff의 전압 법칙을 슈퍼 노드에 적용하기 위해 회로를 다시 그립니다.
슈퍼노드를 포함하는 루프를 시계 방향으로 돌면 제약 조건 방정식이 제공됩니다.
결과 세 개의 방정식을 풀어 이제 노드 전압을 결정할 수 있습니다.

전압 소스를 사용한 노드 분석

노드 분석은 종속 또는 독립 전압 소스가 있는 회로를 포함하여 복잡한 회로의 분석을 단순화하기 위해 전기 공학에서 사용되는 매우 효과적인 방법입니다. 그 강점은 회로를 관리 가능한 구성 요소로 분해하여 엔지니어가 더 쉽게 이해하고 해결할 수 있도록 하는 체계적인 접근 방식에 있습니다.

Figure 1과 같이 4개의 저항기와 2개의 전압 소스를 포함하는 회로를 생각해 보십시오. 이러한 전압 소스 중 하나는 비기준 노드와 기준 노드 사이에 연결됩니다. 이 구성에서 비기준 노드의 전압은 소스의 전압과 동일하게 직접 기록될 수 있습니다. 이는 알려지지 않은 항목의 수를 줄여 문제를 단순화합니다.

<img alt="Figure1" src="/files/ftp_upload/15048/15048_PT_Figure_1.svg" style="text-align: center; height: 140px;">

다른 전압 소스는 두 개의 비기준 노드 사이에 연결됩니다. 이 구성은 슈퍼노드 또는 일반화된 노드로 알려진 것을 형성합니다. 슈퍼노드는 노드 분석의 독특한 개념으로, 비참조 노드 사이에 전압 소스가 연결된 상황을 처리하는 데 도움이 됩니다.

슈퍼노드가 있는 회로를 분석하려면 키르히호프의 전류 법칙(KCL)과 키르히호프의 전압 법칙(KVL)을 모두 적용해야 합니다. 먼저 슈퍼노드에 KCL을 적용합니다. 이 법칙에 따르면 노드에 들어가는 전류의 합은 노드에서 나가는 전류의 합과 같습니다. 슈퍼노드 내의 각 요소를 통과하는 전류를 고려함으로써 방정식을 얻고 노드 전압으로 작성할 수 있습니다.

다음으로 KVL을 적용하기 위해 회로를 다시 그려 슈퍼노드가 포함된 루프를 강조 표시합니다. KVL은 폐쇄 루프 또는 네트워크의 메쉬에서 기전력의 합은 해당 루프의 전위 강하의 합과 동일하다고 명시합니다. 이 루프를 시계 방향으로 돌면 제약 방정식이 생성됩니다.

이러한 단계를 통해 회로의 동작을 나타내는 세 가지 방정식이 얻어집니다. 이러한 방정식을 동시에 풀어 노드 전압을 결정할 수 있습니다.

노드 분석은 종속 또는 독립 전압 소스를 갖는 회로의 분석을 효과적으로 단순화할 수 있습니다.
4개의 저항이 있는 회로를 고려하십시오 ...

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 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 circuit easier to solve.

The other voltage source is connected between two non-reference nodes. That connection creates a supernode, also called a generalized node. A supernode is a special case in nodal analysis that helps when a voltage source sits between two nodes that are not the reference node.

To analyze the supernode, Kirchhoff’s Current Law (KCL) is used first. KCL says the total current entering a node equals the total current leaving it. The currents through the elements in the supernode are written in terms of the node voltages to form one equation.

Next, Kirchhoff’s Voltage Law (KVL) is applied. The circuit is redrawn to show the loop that includes the supernode, and the loop is traced in a clockwise direction. KVL states that the sum of the electromotive forces in a closed loop equals the sum of the voltage drops in that loop, which gives a second constraint equation.

These steps produce three equations for the circuit. The equations can then be solved together to find the node voltages. This approach shows how nodal analysis handles voltage sources connected to both the reference node and other nodes.

Supernode Equations in Nodal Analysis

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

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 supernodes, KCL, and KVL to solve circuits with voltage sources and find unknown node voltages.

Supernode Equations in Nodal 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

Supernode Equations in Nodal Analysis

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