Skin Effect Calculator June 18, 2007
Electrical current always flows in the path that results in the lowest expenditure of energy. At lower frequencies, current flows in a path that reduces I^2*R losses. This is the path of shortest distance and is fairly intuitive to think about.
At higher frequencies, things get a little strange. Current takes the path of lowest inductance which is also the path of smallest loop area. This results in lower energy being stored in the magnetic field. So current will be concentrated along surfaces so it can be closer to the currents in the return path. In a related phenomenon called the proximity effect, at high frequencies, a PCB trace’s return current in the ground plane will hug along the trace no matter how crooked that trace may be. Although this is not the shortest distance, it results in the smallest loop area.
So, at high frequencies, current does not flow evenly throughout the entire cross-section of the conductor but is more concentrated at the surface. The higher the frequency, the more the current is concentrated on the surface. This results in higher I^2*R losses at higher frequencies.
The current density varies exponentially as a function of depth from the surface of the wire. However, it is helpful to think in terms of a skin depth. The skin depth is defined as the depth at which a hollow conductor carrying DC would have the same loss as a given solid conductor carrying AC. In other words, the conductor is behaving as if it has been hollowed out. Making a conductor thicker than the skin depth does not have much effect on lowering losses. One may design a very thick conductor only to find that most of the copper is not being used.
Although the skin effect is generally associated with RF and microwave circuitry, it often plays a significant role in switching power electronics, transformers, motors, and high power AC transmission lines. Whenever designing conductors for anything other than DC, it is advisable to be aware of the skin depth (a.k.a. depth of penetration).
For copper at 100 deg. C, the skin depth is given by:
Skin_Depth = 7.6/SQRT(Frequency) [cm]
where, Frequency is in [Hz]
References:
[1] http://www-s.ti.com/sc/techlit/slup125.pdf
[2] http://en.wikipedia.org/wiki/Skin_effect
[3] http://en.wikipedia.org/wiki/Skin_depth
User Inputs:
| Frequency |
Results:
| Skin Depth |
- Posted in : Electrical Engineering, PCB
- Author : Brad
Comments
After a third of a bottle of wine, it was extremely nice to find this calculator to verify my math. We agree within three decimal places. I look forward to having fun in the garage on the morrow! Thank you!
Lee,
That’s great to hear. Good luck with your project!
Brad