Name: norton equivalent circuit in dc analysis
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 14 s
Channel: JoVE

ノートンの定理では、線形の2端子回路は、抵抗器と並列に接続された単一の電流源で構成される等価回路に置き換えることができると述べています。
ノートンの定理を実装するには、2つの負荷端子から負荷抵抗を取り外します:残りのネットワークは、これらの端子から見たノートン等価回路で置き換えられます。
ノートンの抵抗は、すべての独立したソースを 0 に設定することで決定できます。端子間の等価抵抗または入力抵抗はノートンの抵抗です。
ノートンの電流を見つけるには、すべてのソースを元の位置に戻します。次に、マークされた端子間の短絡電流を見つけて、ノートンの電流を計算します。
最後に、ネットワークをノートンの等価回路に交換し、負荷抵抗を再度接続します。
ソース変換手法は、ノートンとテブナンの等価回路間の変換に使用できます。
開回路電圧、短絡電流、および入力抵抗または等価抵抗が、テブナンまたはノートンの等価回路を決定するために知っていなければなりません。
ノートンとテブナンの定理とオームの法則との密接な関係は、複雑な電気回路を解くのに役立ちます。

ノートンの定理

ノートンの定理は、線形 2 端子回路を、電流源 (ⅠN) と抵抗 (RN) を並列に接続した等価回路で置き換えることができるという基本原理です。ここで、ⅠN は端子を流れる短絡電流を表し、(RN) はすべての独立した電源を除去した状態での端子の入力抵抗または等価抵抗を表します。これは、図 (a) に示されている回路を図 (b) に示されている回路と交換できることを意味します。

<img alt="Figure1" src="/files/ftp_upload/15054/15054_PT_Figure_1.svg" style="text-align: center; height: 132px;">
図(a)

<img alt="Figure1" src="/files/ftp_upload/15054/15054_PT_Figure_2.svg" style="text-align: center; height: 132px;">
 図(b)

ノートン抵抗の決定には、回路内のすべての独立電源をショート（電圧源）またはオープン（電流源）にするプロセスが含まれます。結果として得られる値は、定理の適用に不可欠なノートンの抵抗を表します。ノートンの電流を計算するには、すべてのソースを元の構成に戻してから、マークされた端子間の短絡電流を確認する必要があります。変換を完了するには、ネットワークをノートンの等価回路に置き換え、負荷抵抗を再接続する必要があります。テブナンまたはノートンの等価回路を確立するには、開路電圧、短絡電流、入力抵抗または等価抵抗についての知識が必要です。これらのパラメータは、回路変換の重要な入力として機能します。ノートンの定理とテブナンの定理の間の密接な関係は、次の関係によって与えられます。

<img alt="Equation1" src="/files/ftp_upload/15054/15054_PT_Equation_1.svg" style="text-align: center; height: 14px;">
<img alt="Equation1" src="/files/ftp_upload/15054/15054_PT_Equation_2.svg" style="text-align: center; height: 34px;">

オームの法則の原理と組み合わせることで、複雑な電気回路を解決するための貴重なツールが提供されます。

ノートンの定理は、任意の線形2端子回路を、単一の電流源で構成される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

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 marked terminals is then taken as R_N. To find Norton's current, the sources are restored to their original values and the short-circuit current between the terminals is found.

After the Norton equivalent is built, the load resistor is connected again to complete the transformation. This method gives a compact way to study how the circuit behaves at its terminals. It is closely linked to Thevenin's theorem, since both use the open-circuit voltage, short-circuit current, and equivalent resistance.

These relationships, together with Ohm's law, help solve more complex electrical circuits. By converting a network into its Norton form, students can compare terminal behavior more easily. The theorem is a useful tool for circuit analysis when a two-terminal linear network must be simplified.

Norton Equivalent Circuit in DC 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 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 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 Norton equivalent circuits simplify a linear two-terminal network using a current source, parallel resistance, and short-circuit current.

Norton Equivalent Circuit in DC 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

Norton Equivalent Circuit in DC Analysis

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