Name: mesh currents for circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 20 s
Channel: JoVE

メッシュ解析は、メッシュ電流を回路変数として使用する便利な方法であり、回路解析に関与する連立方程式の数を効果的に削減します。
節点解析とは異なり、メッシュ解析は分岐を交差しない平面回路にのみ適用されます。
平面回路のメッシュ電流を決定するには、次の手順が必要です。
まず、回路内の独立したメッシュの総数が特定され、各メッシュにメッシュ電流が割り当てられます。
次に、要素電圧はメッシュ電流の関数として表され、キルヒホッフの電圧則が各メッシュに適用されて一連の線形方程式が得られます。
最後に、メッシュ電流は一連の方程式を解くことによって得られます。
「i」個の独立したメッシュを持つ回路の場合、メッシュ解析では、メッシュ電流を得るために「i」個の独立した方程式が必要です。
提示された2メッシュ回路の抵抗とソース電圧の値がわかっていると仮定します。
これらの値は線形方程式に代入され、解かれてメッシュ電流が得られます。
最後に、メッシュ電流の計算値を使用して、分岐電流i1、i2、およびi3を決定できます。

メッシュ解析

メッシュ解析は、回路解析を効率化する有用な手法であり、その際にはメッシュ電流を主要な回路変数として使用します。節点解析が未知の電圧の決定に焦点を当てているのに対し、メッシュ解析ではキルヒホッフの電圧則 (KVL) を適用して回路内の未知の電流を求めます。この方法は、解く必要がある連立方程式の数を減らす場合に特に便利です。

メッシュ解析の基本概念は、メッシュとメッシュ電流の定義です。メッシュは、回路内に他のループを含まない閉じた経路を指します。各メッシュにはメッシュ電流が割り当てられ、通常、それぞれのループ内で時計回りに流れると想定されます。

メッシュ解析を適用するには、回路が平面的である必要があります。つまり、分岐が互いに交差することなく平面上に回路を描画できることを意味します。平面回路はプロセスを簡素化するため、メッシュ解析に最適です。メッシュ解析に必要な手順は次のとおりです。

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
	<li>回路内の「n」個の独立したメッシュのそれぞれにメッシュ電流を割り当てます。</li>
	<li>KVL を「n」個のメッシュのそれぞれに適用し、オームの法則を使用して要素電圧をメッシュ電流で表します。</li>
	<li>得られた n 個の連立方程式を解き、メッシュ電流の値を取得します。</li>
</ul>

メッシュ電流を用いて、回路内の各分岐電流を求めることができます。メッシュ電流が分岐電流と異なる場合があるため、メッシュが分離されているかどうかを注意深く考慮することが重要です。

メッシュ解析は、メッシュ電流を回路変数として採用する便利な方法であり、関連する連立方程式の数を効果的に削減します...

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

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 analysis.

Mesh analysis works only for planar circuits. A planar circuit is one that can be drawn on a flat surface without any branches crossing. This shape makes the method easier to apply because the loops are clear and separate.

The process starts by assigning mesh currents to the n independent meshes in the circuit. Next, KVL is applied to each mesh, and element voltages are written in terms of mesh currents using Ohm's law. The resulting n simultaneous equations are then solved to find the mesh currents, which can be used to determine branch currents. Mesh currents and branch currents are not the same unless a mesh is isolated.

Mesh Currents for Circuit Analysis

nodal analysis

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Supernode Equations in Nodal Analysis

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mesh 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...

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Circuit Source Equivalents

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Circuit Linearity and Resistor Behavior

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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...

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Thevenin Circuit Equivalents

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norton's theorem

Norton Equivalent Circuit in DC Analysis

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Load Matching in Thevenin Circuits

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key terms and concepts

Learn how mesh currents and Kirchhoff's voltage law simplify planar circuit analysis by turning loops into solvable current equations for high school students.

Mesh Currents for 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

Mesh Currents for Circuit Analysis

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