Inductor AC Winding Loss
Pac = Iac² · Rac
Quick answer
This calculator solves Pac = Iac(rms)² × Rac for AC Loss. With AC RMS Current 20 mA, AC Resistance 0.47 kΩ, the result is 0.188 W. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
At the switching frequency a winding’s effective resistance rises far above its DC value because of skin and proximity effects that crowd current into the conductor surface. The AC winding loss is the AC ripple current squared times this elevated AC resistance. In high-frequency converters this loss can rival or exceed the DC (I²·DCR) loss and is easy to overlook.
Variables
- Pac — AC winding loss (W)
- Iac — RMS ripple current at the switching frequency (A)
- Rac — AC resistance at that frequency (Ω)
Practical Notes
Rac/Rdc grows with frequency and conductor thickness; litz wire or thinner strands reduce it. Add Pac to the DC copper loss (Idc²·DCR) and core loss for the total.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Pac | AC Loss | mW | µW, mW, W, kW |
| Iac | AC RMS Current | mA | pA, nA, µA, mA, A, kA |
| Rac | AC Resistance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: AC RMS Current 20 mA, AC Resistance 0.47 kΩ
- 2. The relation: Pac = Iac(rms)² × Rac
- 3. Substitute: Iac = 20 mA, Rac = 0.47 kΩ
- 4. Result: AC Loss = 0.188 W
Related quantities from the same inputs
- P = I² × R = 0.188 W
Worked examples
Minimum range
Given: AC RMS Current 100 µA, AC Resistance 1 Ω
Result: AC Loss = 0.01 µW
Low range
Given: AC RMS Current 1 mA, AC Resistance 10 Ω
Result: AC Loss = 10 µW
Typical
Given: AC RMS Current 20 mA, AC Resistance 0.47 kΩ
Result: AC Loss = 0.188 W
High range
Given: AC RMS Current 0.5 A, AC Resistance 4.7 kΩ
Result: AC Loss = 1.175 kW
Maximum range
Given: AC RMS Current 5 A, AC Resistance 47 kΩ
Result: AC Loss = 1175 kW
Solving for each variable
Solve for AC Loss
AC RMS Current 100 µA, AC Resistance 1 Ω → 0.01 µW
Solve for AC RMS Current
AC Loss 100 µW, AC Resistance 1 Ω → 10 mA
Solve for AC Resistance
AC Loss 100 µW, AC RMS Current 100 µA → 10 kΩ
How AC Loss changes with AC RMS Current
| AC RMS Current (input) | AC Loss (result) |
|---|---|
| 2 mA | 1.88 mW |
| 5 mA | 11.75 mW |
| 10 mA | 47 mW |
| 15 mA | 105.8 mW |
| 20 mA | 0.188 W |
| 30 mA | 0.423 W |
| 40 mA | 0.752 W |
| 80 mA | 3.008 W |
| 140 mA | 9.212 W |
| 0.2 A | 18.8 W |
The same result in other units
| Unit | Value |
|---|---|
| µW | 188000 |
| mW | 188 |
| W | 0.188 |
| kW | 0.000188 |
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<p><a href="https://vbatpower.com/formulas/inductor-ac-winding-loss/">Inductor AC Winding Loss</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Inductor AC Winding Loss?
Use Pac = Iac(rms)² × Rac. With AC RMS Current 20 mA, AC Resistance 0.47 kΩ, AC Loss works out to 0.188 W.
What is the formula for Inductor AC Winding Loss?
The formula is Pac = Iac(rms)² × Rac. At the switching frequency a winding’s effective resistance rises far above its DC value because of skin and proximity effects that crowd current into the conductor surface.
How do you find AC RMS Current when you know the other values?
Rearrange for AC RMS Current: with AC Loss 100 µW, AC Resistance 1 Ω, AC RMS Current is 10 mA.
How do you find AC Resistance when you know the other values?
Rearrange for AC Resistance: with AC Loss 100 µW, AC RMS Current 100 µA, AC Resistance is 10 kΩ.
What units does Inductor AC Winding Loss use?
AC Loss is shown in µW, mW, W, kW. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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