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

ノード解析は、ノード電圧を回路変数として使用して回路解析を簡略化する一般的な方法です。
3つのノードと3つの抵抗を持つ回路を考えてみましょう。
この回路のノード電圧を見つけるには、まず、電圧がゼロに割り当てられている基準ノードまたはデータムノードを選択します。
残りの非参照ノードには、参照ノードに対して相対的な節点電圧が割り当てられます。
次に、キルヒホッフの電流法則を非参照ノード 1 と 2 に適用すると、分岐電流間の関係が得られます。
さらに、オームの法則を使用して、3つの抵抗器を通過する分岐電流はノード電圧で表されます。
これで、分岐電流の値をキルヒホッフの電流法則を使用して得られた方程式に代入して、2つの連立方程式を得ることができます。
n個のノードを持つ回路の場合、n-1個の独立した方程式が得られます。
抵抗とソース電流の値がわかっている場合は、それらを2つの方程式に代入し、方程式を解いてノード電圧を求めることができます。

ノード解析

ノード解析は、回路解析のプロセスを簡略化するために使用される電気工学の基本的な方法です。この方法は、回路解析の主な変数としてノード電圧を使用するという概念を中心に展開されています。目的は、回路内の各ノードの電圧を決定することであり、その電圧を使用して、特定のコンポーネントを流れる電流など、他の関心のある量を見つけることができます。

たとえば、Figure 1 に示すように、3 つのノードと 3 つの抵抗で構成される単純な回路を考えてみましょう。ノード解析の最初のステップには、基準ノードまたは基準ノードの選択が含まれます。このノードは通常、利便性に基づいて選択され、その電圧には値 0 が割り当てられます。

<img alt="Figure1" src="/files/ftp_upload/15047/15047_PT_Figure_1.svg" style="text-align: center; height: 136px;">

Figure 1

ノードと呼ばれる後続のノードには、この基準ノードを基準としたノード電圧が割り当てられます。ここで検討する例では、1 および 2 というラベルが付けられた 2 つのノードがあり、それぞれにそれぞれのノード電圧があります。

分岐電流間の関係を確立するために、キルヒホッフの電流則 (KCL) がノードに適用されます。 KCL は、ノード (または閉じた境界) に入る電流の代数和はゼロであると述べています。この法則は、電荷保存の原則に基づいています。つまり、電荷は生成または破壊されません。

KCL を適用した後、オームの法則を使用して、3 つの抵抗を通過する分岐電流をノード電圧で表します。オームの法則は、2 点間の導体を流れる電流が 2 点間の電圧に正比例すると仮定します。

分岐電流がノード電圧で表されるため、これらの値は KCL から導出された式に代入されます。 「n」個のノードを持つ回路の場合、「n-1」個の独立したFigureが得られるため、この置換により 2 つの連立Figureが生成されます。

最後に、抵抗とソース電流の値がわかっている場合は、それらを 2 つの式に代入できます。これらのFigureを解くと、ノード電圧が得られます。この情報は、回路の動作を理解したり、電気回路の設計やトラブルシューティングを行うのに役立つため、非常に貴重です。

結論として、ノード解析は回路解析における強力なツールであり、回路内の電圧の分布を決定する系統的な方法を提供し、それを使用して電流や電力などの他のパラメータを計算できます。

ノード解析は、ノード電圧を回路変数として使用して回路解析を簡略化する一般的な方法です。
3つのノードを持つ回路を考えてみましょう...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

DC Circuit Analysis

直流回路解析

KEY TERMS AND CONCEPTS

主要用語および概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Using Node Voltages in Circuit Analysis

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