Methods for Analyzing Linear Circuits

Definition

• Network A set of sources and dipoles connected together by conductors with zero resistance.
• Linear network In a linear network, the voltage across a dipole is either constant or proportional to a current.

$$U = R I$$

• A branch consists of a circuit element between two nodes.

• A node is the junction of at least three conductors.

• A mesh is a set of branches forming a closed circuit.

• A loop in a circuit consists of a closed path without passing through the same mesh twice.

• In a linear circuit, the values of sources and elements are assumed to be known. The goal is to calculate voltages and currents in the circuit.

Which methods to use

• Then simplify to a 2-mesh circuit

  • Use Kirchhoff’s Method

• If it’s has multiple mesh circuit:

  • Use Thevenin or Norton to reduce the circuit to a 2-mesh circuit

• If it has multiples sources:

  • Use Superposition

Thévenin ↔ Norton Equivalence

$$\begin{cases} R_{Th} = R_N \\ E_{Th} = R_N \times I_N \end{cases}$$