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

网孔分析是一种便捷的方法，它采用网孔电流作为电路变量，可有效减少电路分析中所需联立的方程数量。
与节点分析不同，网孔分析仅适用于无交叉支路的平面电路。
确定任何平面电路中的网孔电流需遵循以下步骤。
首先，确定电路中所有独立网孔的总数，并为每个网孔分配网孔电流。
其次，将元件电压表示为网孔电流的函数，并对每个网孔应用基尔霍夫电压定律，从而得到一组线性方程。
最后，通过求解方程组得到网孔电流。
对于包含 &#34;i&#34; 个独立网孔的电路，网孔分析需要 &#34;i&#34; 个独立方程才能求得网孔电流。
假设所示双网孔电路中的电阻值和电源电压均为已知。
将这些值代入线性方程并求解，以得到网孔电流。
最后，可以利用计算得到的网孔电流值来确定支路电流 i1、i2 和 i3。

网格分析

网格分析是使用网格电流作为关键电路变量来简化电路分析的一种有价值的方法。与侧重于确定未知电压的节点分析不同，网格分析是应用基尔霍夫电压定律 (KVL) 来寻找电路内的未知电流。该方法对于减少需要求解联立方程组的数量非常有效。 

网格分析中的一个基本概念是网格和网格电流的定义。网格是位于电路内部的闭环，其中不包含任何其他环路。每个网格中都会分配一个网格电流，通常会假设它们在其各自的环路中沿着顺时针的方向流动。 

为了适用于网格分析，电路必须是平面的，这意味着可以在平坦的表面上绘制，而分支则不会发生相互交叉。另外，平面电路也非常适用于网格分析，因为它简化了过程。网格分析所涉及到的步骤如下：

<ul style="padding-left: 35px; list-style: disc;"> 

	<li>将网格电流分配给电路中的 “n”个独立网格。</li> 

	<li>对每 “n” 个网格应用基尔霍夫电压定律，同时使用欧姆定律以网格电流的形式来表示其中的元件电压。</li> 

	<li>求解所得的“n”个联立方程来得出网格电流的值。</li>

</ul> 

然后，这些网格电流可以确定电路内各个分支的电流。值得注意的是，除非网格是隔离的，否则网格电流与分支电流是不同的。

网孔分析是一种便捷的方法，采用网孔电流作为电路变量，可有效减少所需求解的联立方程数量……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

DC Circuit Analysis

直流电路分析

KEY TERMS AND CONCEPTS

关键术语与概念

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

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 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

Description

Transcript