Name: current sources in mesh circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

Die Netzanalyse ist in Schaltkreisen mit Stromquellen einfacher, da weniger Gleichungen für die Analyse erforderlich sind.
Stellen Sie sich eine Schaltung mit zwei Netzen vor, bei der sich eine Stromquelle in nur einem Netz befindet.
Die Netzströme werden zugewiesen, und der Zweig mit der Stromquelle wird von der Netzanalyse ausgeschlossen.
Das Kirchhoffsche Spannungsgesetz wird auf das verbleibende Netz angewendet, um eine lineare Gleichung zu erhalten.
Da der Strom im zweiten Netz gleich groß ist, aber in entgegengesetzter Richtung zum Quellstrom, ermöglicht die vereinfachte Gleichung die Bestimmung des Stroms im ersten Netz.
Betrachten Sie nun eine andere Schaltung mit einer Stromquelle zwischen beiden Netzen.
Ein größeres Supernetz wird erstellt, indem die Stromquelle und die mit ihr in Reihe geschalteten Elemente ausgeschlossen werden.
Auch hier ergibt sich bei Anwendung des Kirchhoffschen Spannungsgesetzes auf das Supernetz eine lineare Gleichung.
Zusätzlich wird das Kirchhoffsche Stromgesetz auf einen Knoten angewendet, an dem der Zweig mit der Stromquelle verbunden ist, was eine weitere lineare Gleichung ergibt, die die beiden Zweigströme verbindet.
Die Lösungen der simultanen Gleichungen liefern die Werte der Eingriffsströme.

maschenanalyse mit stromquellen

Die Maschenanalyse vereinfacht sich bei der Analyse von Schaltungen mit Stromquellen, unabhängig davon, ob sie unabhängig oder abhängig sind. Das Vorhandensein von Stromquellen reduziert die Anzahl der für die Analyse erforderlichen Gleichungen. Zwei Fälle veranschaulichen dies: Stromquelle in einer Masche: Der Analyseprozess ist unkompliziert, wenn sich eine Stromquelle nur in einer Masche der Schaltung befindet. Die Maschenströme werden wie gewohnt zugewiesen, wobei die Masche mit der Stromquelle von der Analyse ausgeschlossen wird. Das Kirchhoffsche Spannungsgesetz (KVL) wird auf die verbleibende Masche angewendet, wodurch eine lineare Gleichung entsteht. Da der Strom in der Masche mit der Quelle betragsmäßig gleich, aber entgegengesetzt gerichtet ist, kann der Strom in der ersten Masche leicht bestimmt werden. Stromquelle zwischen zwei Maschen: Liegt eine Stromquelle zwischen zwei Maschen, kann die Analyse durch die Erstellung einer Supermasche vereinfacht werden. Dabei wird die Stromquelle sowie alle in Reihe mit ihr verbundenen Elemente aus der Maschenanalyse ausgeschlossen. Die Anwendung des KVL auf die Supermasche ergibt eine lineare Gleichung. Zusätzlich wird das Kirchhoffsche Stromgesetz (KCL) auf einen Knoten angewendet, an dem die Verzweigung mit der Stromquelle verbunden ist. Dies liefert eine weitere lineare Gleichung, die die beiden Zweigströme verknüpft. Das Lösen dieser Gleichungen liefert die Werte der Maschenströme. Zu den entscheidenden Eigenschaften einer Supermasche gehören:
<ul style="padding-left: 35px; list-style-type: disc;"> 
 	<li>Die Stromquelle innerhalb der Supermasche stellt eine Nebenbedingung auf, die zur Lösung der Maschenströme erforderlich ist.</li> 
 	<li>Eine Supermasche hat keinen eigenen Strom; sie umfasst die Ströme der einzelnen Maschen, die sie umschließt.</li> 
 	<li>KVL und KCL werden auf eine Supermasche angewendet wie auf jede andere Masche.</li> 
 </ul>

Maschenanalyse mit Stromquellen

Die Netzanalyse ist in Schaltkreisen mit Stromquellen einfacher, da weniger Gleichungen für die Analyse erforderlich sind.
Stellen Sie sich eine Zwei-Mesh-Schaltung mit einem Strom ...

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 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 a linear equation. The current in the mesh with the source is equal in magnitude but opposite in direction, so the first mesh current is easy to find.

A different case happens when a current source lies between two meshes. Here, the circuit can be handled with a supermesh, which is formed by excluding the current source and any elements in series with it. KVL is applied around the supermesh to create a linear equation. Then Kirchhoff's current law, or KCL, is used at a node connected to the current-source branch to link the two branch currents.

The current source inside a supermesh adds a needed constraint equation for solving the mesh currents. A supermesh has no current of its own. It combines the currents from the meshes it encloses. KVL and KCL are still applied to the supermesh like they are in any other mesh.

Current Sources in Mesh Circuit Analysis

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Mesh Currents for Circuit Analysis

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mesh analysis with current sources

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...

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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...

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norton's theorem

Norton Equivalent Circuit in DC Analysis

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key terms and concepts

Learn how current sources simplify mesh circuit analysis, including one-mesh cases and supermeshes, using KVL and KCL to solve for mesh currents.

Current Sources in Mesh 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

Current Sources in Mesh Circuit Analysis

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