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When the branch constitutive relations of all circuit elements have an admittance representation, nodal analysis is possible. Nodal analysis generates a small set of network equations that can be solved by hand if the network is small or quickly solved by computer using linear algebra. The branch current method, also known as nodal analysis, node-voltage analysis or the branch current method, is a method of calculating the voltage (potential difference) between “nodes” (points where elements or branches link) in an electrical circuit using branch currents. Nodal analysis is a way of analysing circuits in terms of voltage dips between nodes in a circuit diagram.
Nodal analysis can be done in the time or frequency domains, but it is only applicable to LTI systems. Nonlinear systems can be approximated around an operational point and employed in nodal analysis, despite the fact that the solution algorithm used in nodal analysis is only defined for linear systems.
What is Nodal analysis?
Nodal analysis is a method for estimating the voltage distribution between nodes in a circuit using mathematics. This procedure, also known as the node-voltage method, employs Ohm’s law, Kirchhoff’s voltage law and Kirchhoff’s current law to create an equation that relates the voltage measured between each circuit node and a reference voltage (usually ground). The voltage drops between nearby nodes are used as variables in a set of linear equations, which may be solved with a typical technique (e.g., Gauss-Jordan elimination).
Features of Nodal analysis
- Kirchhoff’s current law is used to do nodal analysis.
- There will be n-1 simultaneous equations to solve when there are n nodes in a particular electrical circuit.
- ‘n-1’ must be solved to obtain all of the node voltages.
- The number of non-reference nodes and nodal equations to be obtained are both the same.
- Nodal Voltage Analysis is a powerful complement to the preceding mesh analysis because it uses the same matrix analysis ideas.
- As a result, the net outcome of summing all of these nodal voltages is zero. Then, if the circuit has “n” nodes, there will be “n-1” independent nodal equations, which are enough to describe and solve the circuit.
Procedure of Nodal Analysis
The general method for developing a matrix equation for nodal analysis is to write out a set of equations linking the voltage drop across different components to the currents flowing into each node using Kirchoff’s laws between each node in a circuit diagram. The procedure is as follows:
- Create a circuit diagram with each node’s currents defined.
- Choose a reference node (typically ground) and create a variable to represent the voltage at each node in relation to the reference node.
- In terms of the circuit impedances and voltages at surrounding nodes, write down Kirchoff’s current law for each node.
- In matrix form, rewrite the node voltages system of equations.
- Using an inverse matrix, solve the matrix equation.
Types of nodes in Nodal Analysis
- A non-reference node is one that has a fixed Node Voltage. Non Reference nodes are, for example, Node 1 and Node 2.
- A reference node is a node that serves as a point of reference for all other nodes. The Datum Node is another name for it.
There are several different types of reference nodes: –
- Chassis Ground — This type of reference node serves as a shared ground for multiple circuits.
- Earth Ground — This type of reference node is utilised when the earth potential is employed as a reference in any circuit.
Super Node
When two non-reference nodes are joined by a voltage source (independent or dependent), a generalised node called the Super node is formed. As a result, a Super node can be thought of as a surface that encloses the voltage source as well as its two nodes.
Properties
- At the Super node, the voltage differential between two non-reference nodes is always known.
- A super node does not produce its own voltage.
- To solve a super node, you’ll need to use both KCL and KVL.
- The super node can be formed by connecting any element in parallel with the voltage source.
- A Super node, like a simple node, satisfies the KCL.
CONCLUSION
Analysing electrical circuits is essential for ensuring that current equipment functions properly. Most modern electronics go through some type of simulation and evaluation procedure to ensure that designs work as intended and to offer a set of reference calculations for in-circuit tests to compare to. SPICE simulations are the workhorses for circuit design and analysis, with numerous built-in simulations in today’s commercial solutions.
Nodal analysis is a fundamental approach for examining voltage and current distribution in a circuit and it is one of the simulations available in SPICE simulators. Kirchhoff’s laws and Ohm’s law are efficiently combined in a single matrix equation using this technique. Continue reading to discover more about nodal analysis and its applications in circuit design and analysis.
