Name: using node voltages in circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

节点分析是一种通过使用节点电压作为电路变量来简化电路分析的通用方法。
考虑一个包含三个节点和三个电阻的电路。
为了求解该电路中的节点电压，首先需要选择一个参考节点（或称基准节点），并将其电压设定为零。
其余的非参考节点相对于参考节点被赋予节点电压。
接下来，对非参考节点 1 和 2 应用基尔霍夫电流定律，可得到支路电流之间的关系。
此外，根据欧姆定律，流经三个电阻的支路电流可用节点电压表示。
现在，可以将支路电流的值代入根据基尔霍夫电流定律得到的方程中，从而得到两个联立方程。
对于一个电路 n 节点， n 得到1个独立方程。
如果已知电阻器的阻值和电源电流，则可将这些值代入这两个方程，然后求解以得到节点电压。

节点分析

节点分析是电气工程中用于简化电路分析过程的基本方法。该方法围绕了使用节点电压作为分析电路中主要变量的概念。其目的是为了能够确定电路中位于每个节点处的电压，然后可以使用该电压来寻找其他感兴趣的量，例如通过特定组件的电流。 例如，假设有一个由三个节点和三个电阻所组成的简单电路，如图1所示。节点分析的第一步会涉及到选择参考点或数据节点。该节点通常是根据其方便性来进行选择的，并且其中的电压值会被指定为零。 <img alt="Figure1" src="/files/ftp_upload/15047/15047_PT_Figure_1.svg" style="text-align: center; height: 136px;"> 图 1 随后的节点（称为非参考节点）会被分配到相对于该参考节点处的节点电压。在这个参考的示例中，有两个标记为1和2的非参考节点，其中的每个节点都有各自的节点电压。 为了能够建立起支路电流之间的关系，通常会将基尔霍夫电流定律 (KCL) 应用到非参考节点的位置。基尔霍夫电流定律指出了进入节点（或闭合边界）处其电流的代数和为零。由于该定律是基于电荷守恒原理，因此其中的电荷不能被创造或破坏。 当应用基尔霍夫电流定律后，可以通过欧姆定律将流过三个电阻的支路电流用节点电压来进行表示。欧姆定律假设了通过导体两端之间的电流与其两端之间的电压是成正比的。 支路电流能够以节点电压来进行表示，这些值被代入到由基尔霍夫电流定律所导出的方程中。这种替换能够产生两个联立方程组，因为对于具有“n”个节点的电路，可以得到“n-1”个独立的方程。 最后，如果电阻器和源电流的值是已知的，则可以将它们代入到两个方程中。对这些方程进行求解能够得出节点电压。这些信息是非常宝贵的，因为它能够帮助人们理解电路的行为、设计电路和排除电路故障。 总之，节点分析是电路分析方法中的强大工具之一，它提供了一种能够确定电路内部电压分布的系统方法，然后还能够用来计算电流和功率等其他参数。

节点分析是一种通过使用节点电压作为电路变量来简化电路分析的通用方法。  
考虑一个具有三个节点的电路以及……

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

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 example described, there are three nodes total, with two non-reference nodes labeled 1 and 2.

Next, Kirchhoff's Current Law, or KCL, is applied to the non-reference nodes. KCL states that the algebraic sum of currents entering a node is zero. This follows the idea that charge is conserved, so charge cannot be created or destroyed. After that, Ohm's Law is used to write the branch currents through the three resistors in terms of the node voltages.

Those current expressions are then substituted into the KCL equations. Because a circuit with n nodes gives n - 1 independent equations, the example produces two simultaneous equations. If the resistor values and source currents are known, they can be placed into these equations. Solving them gives the node voltages, which helps explain circuit behavior and can support circuit design or troubleshooting.

Using Node Voltages in Circuit Analysis

nodal 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 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 nodal analysis uses a reference node, KCL, and Ohm's Law to find node voltages and solve simple circuit equations in high school electronics.

Using Node Voltages in 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

Using Node Voltages in Circuit Analysis

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