2.2: Network Topology- Nodes, Branches and Loops
- Page ID
- 98398
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A planar circuit is a two-dimensional (2D) circuit with the characteristic feature of having no crossing branches, resulting in a flat and easily visualized configuration. Within the realm of planar circuits, several fundamental terms help describe and analyze the circuit's structure and behavior:
1. Node:
- A node in a planar circuit is a point where two or more circuit elements meet. It serves as a connection point for branches and allows current flow.
2. Essential Node:
- An essential node is a node where three or more branches meet. It is crucial for circuit analysis as the current flowing into and out of an essential node is considered.
3. Path:
- A path is a single continuous segment within the circuit that connects two nodes. It represents the route along which current can flow.
4. Branch:
- A branch is a single circuit element, such as a resistor, capacitor, or inductor, connecting two nodes in a planar circuit. Each branch contributes to the overall circuit configuration.
5. Loop:
- A loop is a closed path within the circuit, forming a closed circuit loop. It can be traversed without encountering the same node twice. Loops are essential for analyzing circuit behavior and identifying key relationships.
6. Mesh:
- A mesh is a specific type of loop that does not contain any other loops within it. In planar circuits, meshes play a significant role in circuit analysis and understanding the flow of currents.
Understanding these terms facilitates the analysis of planar circuits, enabling engineers and scientists to design and troubleshoot electronic systems effectively. The absence of crossing branches in planar circuits simplifies visualization and analysis, making it a practical and insightful approach in electronic circuitry.
Example: Identify nodes, essential node(s), loop(s), and mesh(es)
Figure 2.2.1 A resistive circuit.
A, B, C and D are nodes. Only B and D are essential nodes because there are interception points of three branches. A and C have only two branches, so they are not essential nodes. Path A-B-D-A, B-C-D-B, and A-B-C-D-A are loops. Only A-B-D-A and B-C-D-B are also mesh. A-B-C-D-A is not a mesh because it contains loops A-B-D-A and B-C-D-B.