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

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 maximum power transfer occurs when $$\begin{equation}R_L=R_{Th}\end{equation}$$ This equation can be proved by expressing the power dissipated by the load resistor as a function of the load resistance $P=R_L I^2=R_L\cdot \left(\frac{V_{Th}}{R_{Th}+R_L}\right)^2$ and solving $P'(R_L)=0$ for $R_L$.

VTh RTh − + VL IL RL
Fig. 1. Maximum power dissipated by the load occurs when $R_L=R_{Th}$.

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.

Examples of Solved Problems
See also