Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Currents and voltages
- Linear circuits
- Linear components
- Loops and nodes
- Series and parallel
- R, L & C combinations
- V & I combinations
- Power and energy
3. Simple Circuits
- Ohm's law
- Kirchhoff's current law
- Kirchhoff's voltage law
- Single loop circuits
- Single node-pair circuits
- Voltage division
- Current division
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
6. AC Analysis
7. Operational Amplifiers
8. Laplace Transforms
9. Time-Dependent Circuits
- Introduction
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
10. Two-port networks
Maximum Power Transfer in DC circuits
Maximum power transfer
Consider the circuit in Fig. 1. If $V_{Th}$ and $R_{Th}$ are specified and one can change the value of the load resistance, the maxium power transfer occurs when $$\begin{equation}R_L=R_{Th}\end{equation}$$
In general, if the $V_{Th} - R_{Th}$ series connection is replaced by a 2-port linear network containing multiple resistors, voltage sources and current sources, the 2-port network can always be replaced by its Thévenin equivalent circuit and we can use the above equation to calculate the load resistance for which the power transferred is maximum.