Name: thevenin circuit equivalents
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 15 s
Channel: JoVE

テブナンの定理は、任意の線形2端子回路は、抵抗器と直列に接続された単一の電圧源を持つ等価回路に置き換えることができると述べています。
負荷がない場合、開いている端子の両端の電圧はテブナン電圧になります。
テブナン耐性を見つけるために、すべての独立したソースはオフになっています。次に、端子間で見られる抵抗がテブナン抵抗です。
回路に従属ソースが含まれている場合、独立ソースはオフのままですが、既知のテストソースが端子に適用されます。
結果として得られる端子電圧または電流から、テブナン抵抗を決定できます。
最後に、負荷は等価回路に接続されます。負荷を流れる電流は、分周器の式を使用して計算されます。オームの法則を使用して、負荷の両端のテブナン電圧が決定されます。
バッテリーは、テブナンの等価回路として表すことができます。テブナン電圧はバッテリーの開回路電圧であり、抵抗はバッテリーの内部抵抗です。
テブナンのパラメータがわかれば、回路全体を再検討することなく、さまざまな負荷の電流を簡単に計算できます。

テビニンの定理

テブナンの定理は電気回路解析において極めて重要な役割を果たし、回路内の可変負荷によってもたらされる課題に対する解決策を提供します。実際のアプリケーションでは、特定の要素が固定されたままであり、他の要素が変動する回路 (「負荷」と呼ばれることがあります) がよく発生します。一般的な家庭用コンセントは、それぞれ独自の電気的特性を持つさまざまな機器に接続できるため、可変負荷の主な例として機能します。新しいアプライアンスを差し込んだり取り外したりするたびに、回路全体を新たに分析する必要があります。テブナンの定理は、回路の固定部分を等価回路に置き換える手法を提供し、それによって解析と設計を簡素化します。

テブナンの定理は、線形 2 端子回路は、抵抗と直列の電圧源からなる等価回路で表すことができると述べています。この等価回路は、外部の観点から見た元の回路の動作を効果的にカプセル化します。このテブナン等価回路は 2 つの重要なパラメータによって定義されます。テブナン等価電圧 (VTh) は端子の開路電圧に相当し、テブナン等価抵抗 (RTh) はすべての端子での入力抵抗または等価抵抗を表します。すべての独立した電源を除去した状態での端子間の入力抵抗、または等価抵抗を示します。

概念をさらに説明するために、Figure 1 と図 2 に示す 2 つの回路を考えてみましょう。これらの回路は、端子で同じ電圧と電流の関係を共有する場合、等価であるとみなされます。端子が開放状態のままで電流が流れない場合、開放端子間の電圧はテブナン電圧になります。すべての独立ソースがオフの場合。このとき、端子間に見られる抵抗がテブナン抵抗です。

<img alt="Figure1" src="/files/ftp_upload/15053/15053_PT_Figure_1.svg" style="text-align: center; height: 128px;">
Figure 1
<img alt="Equation1" src="/files/ftp_upload/15053/15053_PT_Equation_1.svg" style="text-align: center; height: 14px;">

<img alt="Figure2" src="/files/ftp_upload/15053/15053_PT_Figure_2.svg" style="text-align: center; height: 128px;">
Figure 2
<img alt="Equation2" src="/files/ftp_upload/15053/15053_PT_Equation_2.svg" style="text-align: center; height: 14px;">

このアイデアを実際に適用してテブナン抵抗を決定するには、2 つのシナリオを考慮する必要があります。

ケース 1: ネットワークに依存ソースが含まれていない状況では、すべての独立ソースが非アクティブになり、端子 a と b の間に見られる抵抗である入力抵抗が確認されます。

ケース 2: ネットワークに依存ソースが組み込まれている場合は、引き続きすべての独立ソースを非アクティブ化します。ただし、依存ソースは回路変数によって制御されるため、非アクティブ化しないでください。

テブナン抵抗 (RTh) の値が負の値になる場合があり、回路が電力を消費するのではなく供給していることを意味することに注意してください。このシナリオは、依存ソースのある回路で実現可能です。

テブナンの定理は、任意の線形2端子回路は、直列に単一の電圧源を持つ等価回路に置き換えることができると述べています...

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

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 two-terminal circuit can be represented by a voltage source in series with a resistor. From the outside, this equivalent circuit has the same behavior as the original network. Two circuits are considered equivalent when they have the same voltage-current relationship at their terminals. The Thevenin equivalent voltage, VTh, is the open-circuit voltage at the terminals, and the Thevenin equivalent resistance, RTh, is the input resistance seen at the terminals when the independent sources are turned off.

To find the Thevenin resistance, the method depends on the kind of sources in the network. If the circuit has no dependent sources, all independent sources are deactivated and the resistance between terminals a and b is found. If the network includes dependent sources, the independent sources are still turned off, but the dependent sources stay active because they are controlled by circuit variables. In some cases, RTh can be negative. That means the circuit is supplying power instead of consuming it, which can happen in circuits with dependent sources.

Thevenin Circuit Equivalents

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 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 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 Thevenin’s theorem replaces a linear two-terminal circuit with a voltage source and resistor, and how to find VTh and RTh in circuit analysis.

Thevenin Circuit Equivalents | 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

Thevenin Circuit Equivalents

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