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

Stellen Sie sich einen Widerstand vor, der an eine Quelle mit variabler Spannung angeschlossen ist. Wenn die Spannung erhöht wird, wird der entsprechende Stromwert aufgezeichnet.
Die grafische Darstellung zeigt einen linearen Zusammenhang zwischen Spannung und Strom.
Solche Schaltungen, bei denen die Schaltungsparameter trotz Änderungen der Spannung oder des Stroms konstant bleiben, werden als lineare Schaltungen bezeichnet.
Lineare Schaltungen bestehen aus linearen Elementen oder linearen unabhängigen Quellen und erfüllen die Eigenschaften von Homogenität und Additivität.
Dieses Prinzip kann bei der Schaltungsmodellierung hilfreich sein, um den Quellstrom vorherzusagen, wenn sich der Spannungsabfall an der Last ändert.
Zunächst werden der Strom durch den Lastwiderstand und der Spannungsabfall über dem oberen Widerstand bestimmt.
Als nächstes wird der Spannungsabfall über den zentralen Zweig ermittelt, der zur Berechnung des Stroms durch diesen Zweig verwendet wird. Durch das Anwenden von KCL erhält man den gesamten Quellenstrom.
Wenn sich die Lastspannung ändert, kann der neue Quellstrom gefunden werden, indem eine Konstante mit dem alten Strom multipliziert und die bekannten Werte ersetzt werden.
Das Linearitätsprinzip gilt jedoch nicht für die Leistungsberechnung, da die Leistung eine quadratische Abhängigkeit vom Strom hat.

lineare schaltkreise

Ein linearer Schaltkreis ist dadurch gekennzeichnet, dass sein Ausgang direkt proportional zu seinem Eingang ist, wobei er die Linearitätseigenschaft befolgt, die die Prinzipien der Homogenität (Skalierung) und Additivität umfasst. Homogenität besagt, dass, wenn der Eingang, auch als Anregung bezeichnet, mit einem konstanten Faktor multipliziert wird, der Ausgang, bekannt als Antwort, entsprechend mit demselben konstanten Faktor skaliert wird. Wenn beispielsweise der Strom mit einem konstanten 'k' multipliziert wird, erfährt die Spannung ebenfalls eine Zunahme um das 'k'-fache. Die Additivitätseigenschaft besagt, dass die Antwort auf eine Summe von Eingängen gleich der Summe der Antworten auf jeden einzelnen Eingang ist, der separat angelegt wird. Im Wesentlichen erzwingt diese Eigenschaft, dass das Verhalten des Schaltkreises auch dann konsistent bleibt, wenn mehrere Eingänge kombiniert werden. Bemerkenswert ist, dass ein Widerstand als lineares Element klassifiziert wird, weil er sowohl die Homogenität als auch die Additivitätseigenschaften innerhalb seiner Spannungs-Strom-Beziehung erfüllt. Allgemein wird ein Schaltkreis als linear angesehen, wenn und nur wenn er sowohl Additivitäts- als auch Homogenitätseigenschaften aufweist. Solche linearen Schaltkreise bestehen ausschließlich aus linearen Elementen, linearen abhängigen Quellen und unabhängigen Quellen. Im Gegensatz dazu stellt der Ausdruck für Leistung, der als das Verhältnis des Quadrats der Spannung zum Widerstand definiert ist, eine quadratische Funktion dar und fällt daher in die Kategorie der Nichtlinearität im Kontext der Schaltungsanalyse.

Lineare Schaltkreise

Stellen Sie sich einen Widerstand vor, der an eine Quelle mit variabler Spannung angeschlossen ist. Wenn die Spannung erhöht wird, wird der entsprechende Stromwert aufgezeichnet.
Die grafische ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

DC Circuit Analysis

DC-Schaltungsanalyse

KEY TERMS AND CONCEPTS

SCHLÜSSELBEGRIFFE UND KONZEPTE

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 Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Circuit Linearity and Resistor Behavior

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