Name: analyzing circuits with superposition
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 18 s
Channel: JoVE

重ね合わせ定理は、複数の独立したソースを持つ回路で使用されます。
この定理を適用するには、一度に1つの独立したソースを維持しながら、非アクティブな電圧ソースを短絡に、非アクティブな電流ソースを開回路にそれぞれ置き換えます。
この定理は、線形回路の要素間の電圧または電流が、独立したソースからの寄与の代数的合計であると述べています。
電圧源と電流源を持つ回路では、抵抗器の両端の電圧降下を決定する必要があります。
電圧降下には、両方の独立したソースからの寄与があります。
電圧源の寄与は、電流源をゼロに設定することによって得られます。
キルヒホッフの電圧則を適用することにより、ループ電流が決定されます。オームの法則を使用して、電圧降下が計算されます。
同様に、電流源の寄与分は、電圧源をゼロに設定することによって得られます。
抵抗を組み合わせると、等価抵抗が得られます。電流分周則とオームの法則を使用して、電圧降下が決定されます。
最後に、独立したソースからの寄与分を加算することにより、抵抗器両端の合計電圧降下が得られます。

重ね合わせの理

重ね合わせの理は、線形回路において、素子の電圧 (または電流) が、分離して動作する各独立した電源の個々の寄与を合計することによって決定できるという基本的な概念です。複数の独立電源を含む線形回路を扱う場合、この原理は解析のための貴重なツールとして機能します。重ね合わせの理を効果的に適用するには、一度に 1 つの独立電源に焦点を当て、他のすべてのソースを無効にする必要があります。このアプローチでは、有効な電源からの出力 (電圧または電流) が得られます。

すべてのアクティブなソースの累積効果は、それらの個々の寄与を代数的に加算することによって決定できます。これにより、回路解析プロセスが簡素化されます。特に、従属電源は回路変数によって制御されるため、影響を受けません。重ね合わせの理を利用すると、分析作業が増加する可能性があることに注意してください。たとえば、3 つの独立電源を特徴とする回路を扱う場合、それぞれが個別のソースの寄与を表す 3 つの別個の単純化された回路を解析する必要があります。このように分析手順が増えるものの、重ね合わせの理は複雑な回路を単純化する有効な手法である。この方法により、電圧源は短絡、電流源は開放され、回路解析が容易になります。

重ね合わせ定理は、複数の独立したソースを持つ回路で使用されます。
この定理を適用するには、一度に 1 つの独立したソースを保持しながら...

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

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 independent source in the circuit. The final voltage or current is found by algebraically adding the individual results. Dependent sources are not turned off because they depend on circuit variables.

This method can simplify complex circuits, but it may take more work. A circuit with three independent sources must be analyzed as three separate simplified circuits. Even so, superposition remains a useful tool for breaking down difficult linear circuit problems.

Analyzing Circuits with Superposition

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

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 superposition helps solve linear circuits by analyzing one independent source at a time, then adding the voltage or current contributions.

Analyzing Circuits with Superposition | 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

Analyzing Circuits with Superposition

Description

Transcript