Name: current sources in mesh circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

メッシュ解析は、電流源を持つ回路では、解析に必要な方程式が少なくて済むため、より簡単になります。
1つのメッシュのみに電流源がある2メッシュ回路を考えてみましょう。
メッシュ電流が割り当てられ、電流ソースを含むブランチがメッシュ解析から除外されます。
キルヒホッフの電圧則を残りのメッシュに適用して、線形方程式を取得します。
2番目のメッシュの電流は大きさが等しいが、ソース電流と方向が逆であるため、簡略化された方程式により、最初のメッシュの電流を決定できます。
次に、両方のメッシュ間に電流源がある別の回路について考えてみます。
より大きなスーパーメッシュは、現在のソースとそれと直列に接続されている要素を除外することによって作成されます。
ここでも、キルヒホッフの電圧則をスーパーメッシュに適用すると、線形方程式が得られます。
さらに、キルヒホッフの電流法則は、電流源を持つ分岐が接続されているノードに適用され、2つの分岐電流をリンクする別の線形方程式が生成されます。
連立方程式の解は、メッシュ電流の値を提供します。

電流源を使用したメッシュ解析

独立または従属を問わず、電流源のある回路を解析すると、メッシュ解析が簡単になります。電流源があると、解析に必要な方程式の数が減ります。2 つの例でこれを示します。

1 つのメッシュ内の電流源: 回路内の 1 つのメッシュにのみ電流源がある場合、解析プロセスは簡単です。メッシュ電流は通常どおりに割り当てられ、電流源を含むメッシュは解析から除外されます。キルヒホッフの電圧法則 (KVL) が残りのメッシュに適用され、線形方程式が生成されます。電流源のあるメッシュ内の電流は、大きさは同じですが方向が反対であるため、最初のメッシュ内の電流を簡単に決定できます。

2 つのメッシュ間の電流源: 電流源が 2 つのメッシュ間にある場合、スーパーメッシュを作成することで解析を簡素化できます。これには、電流源と、それに直列に接続されているすべての要素を除外することが含まれます。スーパーメッシュに KVL を適用すると、線形方程式が生成されます。さらに、電流源のある分岐が接続されているノードにキルヒホッフの電流法則 (KCL) が適用され、2 つの分岐電流を結び付ける別の線形方程式が提供されます。これらの方程式を解くと、メッシュ電流の値が得られます。

スーパーメッシュの重要な特性は次のとおりです。

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
	<li>スーパーメッシュ内の電流源は、メッシュ電流を解くために必要な制約方程式を課します。</li>
	<li>スーパーメッシュには独自の電流はなく、囲んでいる個々のメッシュからの電流を包含します。</li>
	<li>KVL と KCL は、他のメッシュと同様にスーパーメッシュに適用されます。</li>
</ul>

メッシュ解析は、電流源を持つ回路では、解析に必要な方程式が少なくて済むため、より簡単になります。
電流が流れる2メッシュ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

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 a linear equation. The current in the mesh with the source is equal in magnitude but opposite in direction, so the first mesh current is easy to find.

A different case happens when a current source lies between two meshes. Here, the circuit can be handled with a supermesh, which is formed by excluding the current source and any elements in series with it. KVL is applied around the supermesh to create a linear equation. Then Kirchhoff's current law, or KCL, is used at a node connected to the current-source branch to link the two branch currents.

The current source inside a supermesh adds a needed constraint equation for solving the mesh currents. A supermesh has no current of its own. It combines the currents from the meshes it encloses. KVL and KCL are still applied to the supermesh like they are in any other mesh.

Current Sources in Mesh Circuit 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

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 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 current sources simplify mesh circuit analysis, including one-mesh cases and supermeshes, using KVL and KCL to solve for mesh currents.

Current Sources in Mesh 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

Current Sources in Mesh Circuit Analysis

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