The skin effect is a general term for the apparent tendency of AC currents to flow along the outer edge, or skin, of a conductor rather than in an evenly distributed manner. What is really happening in there, and when do you need to care?
Alternating and direct currents both require the use of electrical energy to nudge electrons around en masse. In a direct current situation, the energy applied is constant and the electrons all feel a consistent pull in a certain direction. The resultant magnetic field is constant and current is able to flow evenly through a conductor of any shape, from wires to bus bars.
Alternating current is created using dynamic electrical energy, and the resultant magnetic field is not constant. Electromagnetism classes tend to cover how a changing current in one wire can create a current in a parallel wire, but this effect actually occurs inside individual conductors as well. Though all the electrons should all feel the same force at any given time due to the applied energy, the changing fields create opposing forces, and we start to see eddy currents that cancel out parts of the main current flow.
Eddy currents can be visualized as a neutral circle that starts in the very center of the cross-section of a round conductor. They cancel out the “positive” current flowing in the expected direction, creating a zero-sum area. The size of this circle is proportional to the frequency of applied energy and grows as the AC frequency increases. At low frequencies, it is nearly non-existent and does not affect the overall resistivity of the conductor.
As frequency increases, this dead zone grows and “pushes” positive current out to the edges of the conductor, increasing the effective resistance of the conductor by diminishing the usable area where current may flow. This usable area is called the skin.
The Skin Depth Equation
The depth of the usable area, measured linearly from the outermost edge of the conductor, is called the skin depth. The skin depth of a particular conductor depends not only on the frequency, but also on the resistivity and permittivity of the conductor material.
The skin depth is not an absolute limit, but rather an approximation for where 63% of the current density will occur. There is no hard line inside of a conductor that prevents positive current from flowing, and a small amount of current still flows within this neutral zone.
Skin Depth of Copper vs Aluminum
Math is fun, but when do you need to care about this mysterious dead zone in your conductors? While it would be convenient to be able to say that it does not matter until you are dealing with gigahertz, the skin affects nearly every AC design. At 60Hz in copper wire, the skin depth is 8.5mm. That means that to even see the start of a neutral zone, your conductor would need to be at least 17mm in diameter. This seems huge when you’re looking at hookup wire, or even the standard 12 to 14 gauge wires in your house, but it is a little limiting when you’re trying to use giant wires to move kilowatts or even megawatts of power from a power plant out to homes and businesses.
Aluminum is commonly used in transmission lines because it’s so much lighter than copper and not a terribly worse conductor. The skin effect is more pronounced in better conductors and the skin depth is proportional to the square root of a conductor’s resistivity, so the skin depth is actually greater than it would be in copper carrying the same power. The square root in the equation keeps aluminum from ever actually becoming a “better” conductor than copper, but this extended skin depth strengthens the case for using aluminum in transmission lines because the metal is so much lighter and cheaper.
High Frequency Skin Effect
As frequency increases, the skin depth decreases faster than you may expect and causes problems even in board level designs. At 100kHz (a common power converter switching frequency), the skin depth in copper is only 0.2mm. If you are using a product like ON Semiconductor’s NCP1060 offline switcher to convert 220VAC, you are likely using 2oz or even 4oz copper on your PCB to manage all that power.
The high frequency portion of the board may fail to take advantage of that extra copper due to the skin effect, and your system may behave in unexpected ways because of that increase in resistance. This effect (among other reasons) is why board designers aim to keep the high frequency paths as short and direct as possible in switched designs.
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Luckily, there are a few ways to combat this effect at every scale. The skin depth applies to each individual conductor. If you use several thin conductors instead of one larger conductor, the skin effect does not affect any of the thin conductors and your equivalent resistance can be much lower.
This is why stranded wire is so common in AC applications, even for relatively low frequency applications like power lines. Strands of wire can also be placed around a sturdy, lighter core like steel or even carbon fiber for increased stability across long distances in high power applications. Wider traces on a PCB allow more surface area and keep the trace resistances low.
These simple design considerations can negate the skin effect in most power designs, but RF designs that operate at hundreds of megahertz or even gigahertz require careful planning and the expertise of experienced engineers to function properly. Fiber optic cables that use a non-metal medium to transmit data are typically necessary, because the skin depth of standard conductors would be oppressively shallow.