SKIN EFFECT and SKIN DEPTH Impedance Is the Relationship Between Voltage As a Consequence of Minimizing Inductance, the and Current in a Conducting Circuit

NOVEMBER 2018 I SS U E #119 TECHNICALTIDBITS MATERION PERFORMANCE ALLOYS

SKIN EFFECT AND SKIN DEPTH Impedance is the relationship between voltage As a consequence of minimizing inductance, the and current in a conducting circuit. It is made up of current in a conductor moves to the outer surface, resistance, inductance, and capacitance. Together, which reduces the internal magnetic fields in the inductance and capacitance create reactance. conductor. The current density is maximum Beauty is only skin on the surface, dropping off exponentially toward Resistance (R) is determined by the electrical deep, and so are high conductivity (inverse of the electrical resistivity) of the the center of the conductor. This phenomenon is frequency electrical conductor. Inductance (L) is determined mostly by the known as the skin effect. The skin depth ( ) signals. – How high geometry of the circuit (the amount of loop area that is where the current density drops off to 1/e of its δ frequency electrical signals the circuit encloses). Capacitance (C) is determined original value, so 74% of the current flows within by both geometry (distance between conductors) and 1 skin depth of the surface. Please note that while stay largely near the outer material properties (dielectric constant and loss tangent the skin depth and the loss tangent have the same surface of conductors. of materials around the conducting element). symbol ( ), the two are unrelated. Inductive reactance (X ) is defined as the driving L Skin depthδ may be calculated as: frequency multiplied by the equivalent circuit inductance 1 0 r 0 r Impedance (Z) (XL= L). Capacitive reactance (XC) is defined as the inverse of the driving frequency multiplied by the ω δFrom = √ this,/σπμ you canμ f =see √ thatρ/ πμ skin μ depth f depends only Inductive equivalent circuit capacitance (XC=1/ C). Resistance, on the conductivity (or resistivity) of the metal, Reactance (X ) inductive reactance, and capacitive reactance all have L units of ohms. ω its relative magnetic permeability, and the Capacitive frequency of the AC signal. Under DC conditions, Recall that the overall impedance of a circuit or circuit Reactance (X ) the frequency goes to 0, and the skin depth goes C element is defined as follows: to infinity, meaning that the current is uniform 2 - 2 2 1/ 2 Current Density Z= +(XL XC) +( ) ], where throughout the cross section of the conductor. Note ωC that his applies to a single conductor. For a coaxial Skin Effect So,√[R while resistance] = √theoretically [R ωL - does not changeω=2 πf with frequency ( ), inductive and capacitive reactance cable, where the return line surrounds the signal line, Skin Depth ( ) do, and impedance depends greatly on whether the the skin effect pushes the current to the outside f circuit is more inductive or more capacitive. diameter of the inner conductor and the inside Magnetic diameter of the outer conductor, which minimizes δ Permeability ( ) DC currents, by definition, have no change in voltage the current loop area. or current over time. Therefore, they do not expe- At very high frequencies, such as at RF frequencies, μ rience reactance, and the path of least impedance is simply the path of least resistance. Under these the skin depth is less than the typical plating thickness, conditions, current will flow uniformly throughout so most of the current flows in the plating.Surface the cross section of a conductor, following the path roughness affects the impedance, as the signal follows of least resistance, minimizing energy loss due to the contours of the plating. The plating surface resistive heating. should be as smooth as possible, which also means that the base metal and any underplating layers AC currents, on the other hand, must strike a should be smooth as well. Pay special attention to balance between energy lost due to resistive heating the surfaces where the current will be flowing, such and energy lost due to reactance. At high frequen- as the inside diameter of the outer conductor in The next issue of Technical cies, the reactive loads (capacitive and inductive) tend coaxial cables. Tidbits will discuss discuss to dominate impedance far more than the resistive dielectric breakdown and loads. In fact, very high frequency AC currents may related characteristics. even follow the path of greatest resistance, if it means that the overall impedance is lower. ©2018 Materion Brush Inc. MATERION PERFORMANCE ALLOYS SKIN EFFECT AND SKIN DEPTH (CONTINUED) Figure 1 shows the idealized skin depth in metal as Skin depth is also important in electromagnetic a function of conductivity and magnetic perme- shielding. As electromagnetic waves attempt to Written by Mike Gedeon of Materion ability. The charts are linear, but for a lot of high pass through metallic shielding, they generate Performance Alloys Marketing permeability materials, the relative permeability is currents in the metal, which take energy out of Department. Mr. Gedeon’s primary also a function of frequency, so real skin depth vs. the wave. The skin effect ensures that most of the focus is on electronic strip for the frequency charts would be much more complex. energy is removed within a few skin depths. For automotive, telecom, and computer markets with emphasis on The geometry of the conductor may also come each skin depth, the signal strength is reduced by application development. into play as well. approximately 8.7 decibels. It takes only 11 skin depths to attenuate a traveling electromagnetic References: One consequence of the skin effect is that the wave by a whopping 100 dB (99.99999999% resistance of a conductor does become dependent Eric Bogatin reduction in strength). A nice consequence of the Signal and Power Integrity on frequency. Resistance is calculated as follows: skin affect in electromagnetic shielding is that as the Simplified 2nd Edition R= L/A, where L is the length of the conductor frequency of the signal increases, the shielding can © 2010 Pearson Education Inc. and A is the cross-sectional area through which the be made thinner, so less metal is required. currentρ flows. If the skin effect pushes the current Thierauf, Stephen C. toward the outer surface, the overall cross-sectional Understanding Signal Intregrity © 2011 Artech House area is effectively reduced, increasing the resistance. Since more current is being carried in the outer Nicholas Braithwaite surface, more heat will be generated as well. and Graham Weaver Electronic Materials 2nd Edition © 1998 The Open University

Armstrong, Keith “Skin Effect and Surface Currents” In Compliance July 2018

Figure 1 – Effects of Electrical Conductivity (Left) and Magnetic Permeability (Right) on Please contact your local Skin Depth. sales representative for In the conductivity graph, the relative permeability is held fixed at 1.0, which is a reasonable approximation for further information or conductor metals like Cu, Au, Al, etc. In the relative permeability chart, a constant electrical conductivity of questions pertaining to 20% IACS was chosen. Every metal or metallized substance will have a unique combination of conductivity Materion or our products. and permeability. Health and Safety Handling copper beryllium in solid form poses no special health risk. Like many industrial materials, beryllium-containing materials may pose a health risk if recommended safe handling practices are not followed. Inhalation of airborne beryllium may cause a serious lung disorder in susceptible individuals. The Occupational Safety and Health Administration (OSHA) has set TECHNICALTIDBITS mandatory limits on occupational Materion Performance Alloys Sales respiratory exposures. Read and 6070 Parkland Blvd. +1.216.383.6800 follow the guidance in the Safety Mayfield Heights, OH 44124 800.321.2076 Data Sheet (SDS) before working [email protected] with this material. For additional information on safe handling Technical Service +1.216.692.3108 practices or technical data 800.375.4205 on copper beryllium, contact [email protected] Materion Performance Alloys or your local representative.