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Maximum Power Transfer Theorem: Load Matching and Efficiency

A Thevenin equivalent source drives a variable load \(R_L\) | Power versus load resistance | Maximum-power condition \(R_L = R_{th}\)

Circuit Parameters

12 V
1 V50 V
50 Ω
10 Ω1000 Ω
50 Ω
1 Ω2000 Ω

Power and Efficiency

Current Load Power \(P_L\) 0.00 W
Maximum Power \(P_{max}\) 0.00 W
Efficiency \(\eta\) 0.0 %
Match Status —
\(R_L\) for Max Power —

Current Operating Point

Load Current: 0.00 A
Load Voltage: 0.00 V
Power Curve \(P_L(R_L)\)
\(R_{th}\) Reference Line
Power-Load Curve | Red dot = Maximum power point | Orange dot = Current operating point | Green dashed line = R_th

Circuit Diagram

Maximum power transfer circuit diagram

DC Maximum Power Transfer

The load receives maximum power when \(R_L\) equals \(R_{th}\):
\(P_{max} = \frac{U_{th}^2}{4 R_{th}}\)
At this point, efficiency \(\eta = 50\%\) (source internal resistance and load each consume half the power).
\(P_L = \frac{U_{th}^2 R_L}{(R_{th} + R_L)^2}\)

Matching Properties

When \(R_L\) deviates from \(R_{th}\), power decreases (parabolic shape).
As \(R_L\) increases, the power rises to a maximum and then falls.
At the maximum power point, \(R_L = R_{th}\), and the power curve reaches its peak.
Switch to AC mode to observe the complex conjugate matching condition.