Linear Circuit Analysis

1. Introduction
2. Basic Concepts
3. Simple Circuits
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
6. AC Analysis
7. Magnetically Coupled Circuits
8. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
12. Two-Port Networks
Appendix

Nodes

A node is a collection of wires that are connected to each other. A circuit can have multiple nodes. For instance, the circuit shown in Fig. 1 has 5 nodes labeled $v_1$, $v_2$, $v_3$, $v_4$, and $v_5$.

V1 R1 R2 L1 I1 C1 v1 v2 v3 v4 v5
Fig. 1. Example of a circuit with 5 nodes.

Sometimes, one of the nodes is called the ground node. For instance, the circuits shown in Fig. 2 and Fig. 3 contain 4 nodes labeled $v_1$, $v_2$, $v_3$, and $v_4$, and the ground node (5 nodes in total). Notice that the two circuits have the same topology and the currents going through and the voltages across each component are the same.

V1 R1 R2 L1 I1 C1 v2 v3 v1 v4
Fig. 2. Example of a circuit with 5 nodes, one of which is the ground node. Notice that this circuit is equivalent to the one in Fig. 1.
V1 R1 R2 L1 I1 C1 v2 v3 v1 v4
Fig. 3. Example of a circuit with 5 nodes, one of which is the ground node. Notice that this circuit is equivalent to the ones in Fig. 1 and Fig. 2.

Any circuit should contain at least 2 nodes (see Fig. 4). When the circuit contains only 2 nodes, it is called a single node-pair circuit.

C1 R1 V1 v1 v2
Fig. 4. Example of a circuit with a single node-pair.

Nodal analysis is a method based on Kirchhoff's current law that can be used to analyze electric circuits.

See also