Name: mesh currents for circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 20 s
Channel: JoVE

Die Netzanalyse ist eine praktische Methode, bei der Netzströme als Schaltungsvariablen verwendet werden, wodurch die Anzahl der gleichzeitigen Gleichungen bei der Schaltungsanalyse effektiv reduziert wird.
Im Gegensatz zur Knotenanalyse gilt die Netzanalyse nur für planare Schaltkreise ohne sich kreuzende Abzweigungen.
Die Bestimmung der Eingriffsströme in einem planaren Stromkreis umfasst die folgenden Schritte.
Zuerst wird die Gesamtzahl der unabhängigen Netze in der Schaltung identifiziert, und jedem Netz werden Netzströme zugewiesen.
Zweitens werden die Elementspannungen als Funktionen der Geflechtströme ausgedrückt, und das Kirchhoffsche Spannungsgesetz wird auf jedes Netz angewendet, um einen Satz linearer Gleichungen zu erhalten.
Schließlich werden die Netzströme durch Lösen des Gleichungssatzes erhalten.
Für eine Schaltung mit "i"-unabhängigen Netzen erfordert die Netzanalyse "i"-unabhängige Gleichungen, um die Netzströme zu erhalten.
Angenommen, die Werte der Widerstände und Quellspannungen für die vorgestellte Zwei-Mesh-Schaltung sind bekannt.
Diese Werte werden in die linearen Gleichungen eingesetzt und gelöst, um die Netzströme zu erhalten.
Abschließend können die berechneten Werte der Eingriffsströme verwendet werden, um die Abzweigströme i1, i2 und i3 zu bestimmen.

maschenanalyse

Die Maschenanalyse ist eine wertvolle Methode zur Vereinfachung der Schaltungsanalyse, bei der Maschenströme als Schlüsselvariablen des Schaltkreises verwendet werden. Im Gegensatz zur Knotenanalyse, die darauf abzielt, unbekannte Spannungen zu bestimmen, wendet die Maschenanalyse das Kirchhoffsche Spannungsgesetz (KVL) an, um unbekannte Ströme innerhalb eines Schaltkreises zu finden. Diese Methode ist besonders praktisch, um die Anzahl der gleichzeitig zu lösenden Gleichungen zu reduzieren. 
 Ein grundlegendes Konzept in der Maschenanalyse ist die Definition von Maschen und Maschenströmen. Eine Masche ist eine geschlossene Schleife innerhalb eines Schaltkreises, die keine anderen Schleifen in sich enthält. Jeder Masche wird ein Maschenstrom zugewiesen, der in der Regel angenommen wird, in Uhrzeigerrichtung innerhalb ihrer jeweiligen Schleife zu fließen. Damit die Maschenanalyse anwendbar ist, muss der Schaltkreis planar sein, d.h., er kann auf einer flachen Oberfläche gezeichnet werden, ohne dass sich Zweige kreuzen. Planare Schaltkreise sind ideal für die Maschenanalyse, da sie den Prozess vereinfacht. Die Schritte der Maschenanalyse sind wie folgt: 
<ul style="padding-left: 35px; list-style-type: disc;"> 
 	<li>Weisen Sie jeder der „n“ unabhängigen Maschen im Schaltkreis Maschenströme zu.</li> 
 	<li>Wenden Sie KVL auf jede der „n“ Maschen an und drücken Sie die Elementspannungen in Bezug auf die Maschenströme unter Verwendung des Ohmschen Gesetzes aus.</li> 
 	<li>Lösen Sie die resultierenden „n“ simultanen Gleichungen, um die Werte der Maschenströme zu erhalten.</li> 
 </ul> 
 Diese Maschenströme können dann verwendet werden, um verschiedene Zweigströme innerhalb des Schaltkreises zu bestimmen. Es ist wichtig zu beachten, dass Maschenströme von Zweigströmen unterschieden sind, es sei denn, eine Masche ist isoliert.

Maschenanalyse

Die Netzanalyse ist eine praktische Methode, bei der Netzströme als Schaltungsvariablen verwendet werden, wodurch die Anzahl der gleichzeitigen Gleichungen effektiv reduziert wird ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

DC Circuit Analysis

DC-Schaltungsanalyse

KEY TERMS AND CONCEPTS

SCHLÜSSELBEGRIFFE UND KONZEPTE

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 analysis.

Mesh analysis works only for planar circuits. A planar circuit is one that can be drawn on a flat surface without any branches crossing. This shape makes the method easier to apply because the loops are clear and separate.

The process starts by assigning mesh currents to the n independent meshes in the circuit. Next, KVL is applied to each mesh, and element voltages are written in terms of mesh currents using Ohm's law. The resulting n simultaneous equations are then solved to find the mesh currents, which can be used to determine branch currents. Mesh currents and branch currents are not the same unless a mesh is isolated.

Mesh Currents for Circuit 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 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

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

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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 mesh currents and Kirchhoff's voltage law simplify planar circuit analysis by turning loops into solvable current equations for high school students.

Mesh Currents for Circuit Analysis | 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

Mesh Currents for Circuit Analysis

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