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64 DESIGN007 MAGAZINE I DECEMBER 2018 Equation 1 π = a fixed number f = frequency μ = permeability σ = conductivity I know some of these formulas can be a little confusing when first looking at them, but this is actually pretty easy. The "μ" value is related to the magnetic properties of the metal and copper has a relative value of about one, so the magnetic property of copper really doesn't have any effect on the equation. The symbol "σ" is related to how conductive the metal is, and copper has one of the best conductivities (high conductivity) for metals. The reason I gave the formula is that relation- ships can be easily seen. For example, if you increase "f" (higher frequency), then "δ" (skin depth) will decrease. If a metal is used that Skin depth is the depth within a conductor where the majority of the radio-frequency (RF) current resides. Imagine looking at a cross-sec- tional view of a circular wire and being able to see how much current is within that cross- section. If the current is supplied by a battery and is direct current (DC), the amount of cur- rent is distributed evenly across the cross-sec- tional area of the wire. The current density is the same everywhere in the area of that wire. If you change the current source to a sinu- soidal alternating current, then you will find that there is more current on the outer edges of the wire than in the middle of the wire. If you increase the frequency a lot, you will notice at some point there is no current in the middle of the cross-sectional area of the wire, and the majority of the current is on the very outside edge (skin) of the conductor. That is the basic concept for skin depth. This formula will help explain some of the relationships with skin depth. A simple defini- tion for skin depth (δ) is: Lightning Speed Laminates by John Coonrod, ROGERS CORPORATION Skin Depth and Its Interaction with Final Plated Finishes

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