Name: circuit linearity and resistor behavior
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 17 s
Channel: JoVE

可変電圧源に接続された抵抗について考えてみましょう。電圧が増加すると、対応する電流値が記録されます。
グラフ表現は、電圧と電流の間の線形関係を明らかにします。
電圧や電流が変化しても回路パラメータが一貫しているこのような回路は、線形回路と呼ばれます。
線形回路は、線形要素または線形独立ソースで構成され、均質性と加法性の特性を満たします。
この原理は、負荷の両端の電圧降下が変化したときのソース電流を予測する回路モデリングに役立ちます。
最初に、負荷抵抗を流れる電流と上部抵抗の両端の電圧降下が決定されます。
次に、中央分岐の両端の電圧降下が得られ、それを使用してその分岐を流れる電流が計算されます。KCLを適用すると、合計ソース電流が得られます。
負荷電圧が変化すると、古い電流に定数を掛けて既知の値を代入することにより、新しいソース電流を見つけることができます。
ただし、電力は電流に二乗依存性があるため、線形性の原理は電力の計算には適用されません。

線形回路

線形回路は、出力が入力に直接比例し、均一性 (スケーリング) と加法性の原理を含む線形特性に従うという特徴があります。均一性は、励起とも呼ばれる入力が定数係数で乗算されると、応答として知られる出力が同じ定数係数で対応してスケーリングされることを示します。たとえば、電流が定数「k」倍になると、電圧も同様に「k」倍増加します。

加法性プロパティは、入力の合計に対する応答が、個別に適用された個々の入力に対する応答の合計と等しいことを規定します。本質的に、この特性により、複数の入力が結合された場合でも回路の動作が一貫したままになることが強制されます。

特に、抵抗器は電圧と電流の関係内で均一性と加成性の両方の特性を満たしているため、線形要素として分類されます。一般に、回路が加法性と均一性の両方の特性を示す場合にのみ、回路は線形であると見なされます。このような線形回路は、線形要素、線形依存ソース、および独立ソースのみで構成されます。

逆に、電圧と抵抗の二乗の比として定義される電力の式は二次関数を構成するため、回路解析の文脈では非線形のカテゴリに分類されます。

可変電圧源に接続された抵抗について考えてみましょう。電圧が増加すると、対応する電流値が記録されます。
グラフィカルな...

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

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 equals the sum of the responses to each input applied separately.

A resistor is a linear element because its voltage-current relationship follows both homogeneity and additivity. A circuit is considered linear only when it has both properties. Linear circuits contain linear elements, linear dependent sources, and independent sources.

Power does not follow the same pattern. Its expression uses the square of voltage divided by resistance, so it is a quadratic function. That makes power a nonlinearity in circuit analysis.

Circuit Linearity and Resistor Behavior

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 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 circuit linearity depends on homogeneity and additivity, why resistors are linear elements, and why power is treated as nonlinear in circuit analysis.

Circuit Linearity and Resistor Behavior | 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

Circuit Linearity and Resistor Behavior

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