Proximity Effect Estimator
Estimate the combined skin and proximity effect AC resistance factor for layered windings using Dowell's equation.
🔌 What is the Proximity Effect Estimator?
The Proximity Effect Estimator calculates the combined skin-effect and proximity-effect AC resistance factor, Rac/Rdc, for a layered winding conductor using Dowell's equation. Proximity effect is the increase in a conductor's effective AC resistance caused by the changing magnetic fields of neighboring current-carrying turns and layers, on top of any skin effect from the conductor's own field.
Transformer and inductor designers use this calculation to size foil thickness or wire gauge for switch-mode power supply magnetics, compare single-layer versus multilayer winding arrangements, and estimate copper losses at the actual switching frequency rather than at DC.
A common misconception is that only skin effect matters at high frequency. In multilayer windings, proximity effect from adjacent layers is often the dominant loss mechanism, growing with the square of the number of layers, well beyond what skin effect alone would predict for an isolated conductor.
This calculator computes skin depth from your frequency, resistivity, and relative permeability, derives the normalized thickness ratio Delta, then applies Dowell's formula to estimate the combined AC resistance factor for your chosen layer thickness and layer count.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — 4-Layer Copper Foil Winding at 1 MHz
f = 1,000,000 Hz, ρ = 16.8 nΩ·m (copper), μr = 1, h = 0.1 mm, m = 4
Example 2 — Single Layer at 100 kHz (Skin Effect Only)
f = 100,000 Hz, ρ = 16.8 nΩ·m (copper), μr = 1, h = 0.5 mm, m = 1
Example 3 — 8-Layer Winding at 500 kHz (High Proximity Loss)
f = 500,000 Hz, ρ = 16.8 nΩ·m (copper), μr = 1, h = 0.3 mm, m = 8
❓ Frequently Asked Questions
🔗 Related Calculators
What is proximity effect in windings?
Proximity effect is the increase in a conductor's effective AC resistance caused by the magnetic field of nearby current-carrying conductors (adjacent turns or layers), which forces current to redistribute unevenly within the conductor's cross-section, on top of any skin effect from its own field.
What is Dowell's equation?
Dowell's equation is a widely used 1-D analytical formula (Dowell, 1966) for the combined skin and proximity effect AC resistance factor Rac/Rdc of a layered winding, as a function of the normalized layer thickness Delta = h/delta and the number of layers m.
What is Delta in Dowell's equation?
Delta is the ratio of the conductor or foil layer's thickness h to the skin depth delta at the operating frequency. Larger Delta means the layer is thick relative to how far current penetrates, which increases both skin and proximity losses.
Why does the number of layers matter so much?
Dowell's proximity term scales with (m squared minus 1), so adding layers increases the resistance factor much faster than linearly. A winding with 8 layers can have a dramatically higher Rac/Rdc than the same conductor with 2 layers at the same Delta.
How do I reduce proximity effect losses?
Reduce Delta (use thinner foil or finer strands relative to skin depth), reduce the number of layers where possible, or use interleaved winding techniques and Litz wire, which spreads current across many thin, individually insulated strands to keep each strand's own Delta small.
What happens when Delta is very small?
As Delta approaches 0, Fr approaches 1, meaning AC resistance approaches DC resistance since the conductor is thin enough that skin and proximity effects barely reduce its effective cross-section.
Does this formula apply to round wire?
Dowell's original derivation is for rectangular foil layers. For round wire, engineers commonly use an equivalent rectangular thickness (based on wire diameter and packing) as an approximation, exact round-wire behavior differs somewhat and full field simulation is more accurate for critical designs.
What is the difference between skin effect and proximity effect?
Skin effect is caused by a conductor's own changing magnetic field pushing its own current toward its surface. Proximity effect is caused by the magnetic fields of nearby conductors distorting the current distribution in a given conductor. Dowell's equation captures both simultaneously.
Where is this calculation used in practice?
Transformer and inductor designers use Dowell's equation to choose foil thickness, wire gauge, and layer arrangement for switch-mode power supply magnetics, minimizing winding losses at the switching frequency.
What units does this calculator use?
Frequency is entered in Hertz, resistivity in nano-ohm-meters, relative permeability is dimensionless, and layer thickness in millimeters. The resistance factor Fr = Rac/Rdc is dimensionless.