Maximum Power Transfer
Pmax = Vth² / (4 · Rth)
Quick answer
This calculator solves Pmax = Vth² / (4 × Rth) (when Rload = Rth) for Maximum Power. With Thévenin Voltage 12 V, Thévenin Resistance 0.47 kΩ, the result is 76.6 mW. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The maximum power a source can deliver to a load occurs when the load resistance equals the source’s internal (Thévenin) resistance. At that matched point the load receives one quarter of the open-circuit voltage squared divided by the source resistance, and exactly half the total power (the other half is lost in the source). This sets the ceiling on deliverable power and underlies impedance matching.
Variables
- Pmax — Maximum power into the load (W)
- Vth — Thévenin (open-circuit) voltage (V)
- Rth — Thévenin (source) resistance (Ω)
Practical Notes
Matching maximizes power but caps efficiency at 50%; for power delivery (not signal) systems prefer Rload ≫ Rsource for efficiency. Matching matters most in RF and small-signal work.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Pmax | Maximum Power | W | µW, mW, W, kW |
| Vth | Thévenin Voltage | V | pV, nV, µV, mV, V, kV |
| Rth | Thévenin Resistance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Thévenin Voltage 12 V, Thévenin Resistance 0.47 kΩ
- 2. The relation: Pmax = Vth² / (4 × Rth) (when Rload = Rth)
- 3. Substitute: Vth = 12 V, Rth = 0.47 kΩ
- 4. Result: Maximum Power = 76.6 mW
Related quantities from the same inputs
- P = V² / R = 0.3064 W
- I = V / R = 25.53 mA
Worked examples
Minimum range
Given: Thévenin Voltage 0.33 V, Thévenin Resistance 1 Ω
Result: Maximum Power = 27.23 mW
Low range
Given: Thévenin Voltage 3.3 V, Thévenin Resistance 10 Ω
Result: Maximum Power = 0.2723 W
Typical
Given: Thévenin Voltage 12 V, Thévenin Resistance 0.47 kΩ
Result: Maximum Power = 76.6 mW
High range
Given: Thévenin Voltage 0.23 kV, Thévenin Resistance 4.7 kΩ
Result: Maximum Power = 2.814 W
Maximum range
Given: Thévenin Voltage 2.3 kV, Thévenin Resistance 47 kΩ
Result: Maximum Power = 28.14 W
Solving for each variable
Solve for Maximum Power
Thévenin Voltage 0.33 V, Thévenin Resistance 1 Ω → 27.23 mW
Solve for Thévenin Voltage
Maximum Power 10 mW, Thévenin Resistance 1 Ω → 0.2 V
Solve for Thévenin Resistance
Maximum Power 10 mW, Thévenin Voltage 0.33 V → 2.723 Ω
How Maximum Power changes with Thévenin Voltage
| Thévenin Voltage (input) | Maximum Power (result) |
|---|---|
| 1.2 V | 0.766 mW |
| 3 V | 4.787 mW |
| 6 V | 19.15 mW |
| 9 V | 43.09 mW |
| 12 V | 76.6 mW |
| 18 V | 0.1723 W |
| 24 V | 0.3064 W |
| 48 V | 1.226 W |
| 84 V | 3.753 W |
| 120 V | 7.66 W |
The same result in other units
| Unit | Value |
|---|---|
| µW | 76600 |
| mW | 76.6 |
| W | 0.0766 |
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<p><a href="https://vbatpower.com/formulas/max-power-transfer/">Maximum Power Transfer</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Maximum Power Transfer?
Use Pmax = Vth² / (4 × Rth) (when Rload = Rth). With Thévenin Voltage 12 V, Thévenin Resistance 0.47 kΩ, Maximum Power works out to 76.6 mW.
What is the formula for Maximum Power Transfer?
The formula is Pmax = Vth² / (4 × Rth) (when Rload = Rth). The maximum power a source can deliver to a load occurs when the load resistance equals the source’s internal (Thévenin) resistance.
How do you find Thévenin Voltage when you know the other values?
Rearrange for Thévenin Voltage: with Maximum Power 10 mW, Thévenin Resistance 1 Ω, Thévenin Voltage is 0.2 V.
How do you find Thévenin Resistance when you know the other values?
Rearrange for Thévenin Resistance: with Maximum Power 10 mW, Thévenin Voltage 0.33 V, Thévenin Resistance is 2.723 Ω.
What units does Maximum Power Transfer use?
Maximum Power is shown in µW, mW, W. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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