BeginnerTopic 26 of 106Electrical Engineering
Node-voltage analysis
Apply KCL at nodes to solve for node potentials.
In depth
Choose a reference node, write KCL at each other node in terms of node voltages, and solve the linear equations. Voltage sources between nodes form supernodes. Suited to circuits with many parallel branches; yields a matrix G·v=i.
Key points
- N-1 equations for N nodes
- Conductance matrix
- Basis of SPICE
ExampleA three-node circuit gives two equations in two unknown voltages.
What is Node-voltage analysis?
Apply KCL at nodes to solve for node potentials.
Why is it important to understand node-voltage analysis?
Node analysis is the most systematic way to solve circuits with several branches, and it scales well to large networks.
How do I choose the reference node?
Choose the node with the most connections to ground or the one common to the most branches, which reduces the number of unknowns.
What do I do with voltage sources between nodes?
Treat the source as a supernode, combining the two nodes and using the source voltage as an extra constraint.
How is Node-voltage analysis used in practice?
Typical applications include solving the node voltages of a resistor network for a sensor interface, finding the output voltage of an op-amp circuit with feedback and analysing a bridge circuit with several sources.
What should I learn before Node-voltage analysis?
Study "Measuring instruments" first (topic 25 of 106 in Electrical Engineering). It covers the groundwork this topic builds on.
What are the key points of Node-voltage analysis?
N-1 equations for N nodes. Conductance matrix. Basis of SPICE.
Can you give an example of Node-voltage analysis?
A three-node circuit gives two equations in two unknown voltages.
What comes after Node-voltage analysis?
The next topic is "Mesh-current analysis", which builds directly on this one.
How difficult is Node-voltage analysis?
It is classed as Beginner in Electrical Engineering (topic 26 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.