Electronics World articles Popular Electronics articles QST articles Radio & TV News articles Radio-Craft articles Radio-Electronics articles Short Wave Craft articles Wireless World articles Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Engineer Jobs LinkedIn Crosswords Engineering Humor Kirt's Cogitations RF Engineering Quizzes Notable Quotes Calculators Education Engineering Magazine Articles Engineering software RF Cafe Archives RF Cascade Workbook 2018 RF Symbols for Visio - Word Advertising Magazine Sponsor RF Cafe RF Electronics Symbols for Visio RF Electronics Symbols for Office Word RF Electronics Stencils for Visio Sponsor Links Saturday Evening Post NEETS EW Radar Handbook Microwave Museum About RF Cafe Aegis Power Systems Anritsu Alliance Test Equipment Amplifier Solutions Anatech Electronics Axiom Test Equipment Berkeley Nucleonics Centric RF Conduct RF Copper Mountain Technologies Empower RF everything RF Exodus Advanced Communications Innovative Power Products ISOTEC KR Filters Lotus Systems PCB Directory Rigol San Francisco Circuits Reactel RFCT TotalTemp Technologies Triad RF Systems Windfreak Technologies Withwave LadyBug Technologies Wireless Telecom Group Sponsorship Rates RF Cafe Software Resources Vintage Magazines Thank you for visiting RF Cafe!
Amplifier Solutions Corporation (ASC) - RF Cafe

Skin Depth (aka Skin Effect)

as a Function of Frequency, Permeability, & Conductivity

Skin Depth of microstrip - RF CafeSkin Depth Equation Formula (aka Skin Effect)

As frequencies increase, conduction begins to move from an equal distribution through the conductor cross section toward existence almost exclusively near the surface. Depending on the conductor bulk resistivity (δs), at sufficiently high frequency all the RF current is flowing within a very small thickness at the surface. Furthermore, the current concentrates nearest to the surface that abuts the highest relative dielectric constant. Lower bulk resistivities result in shallower skin depths.

Skin Depth of round wire - RF CafeIn the case of a microstrip layout (to the right), the current concentrates nearest to the substrate dielectric material, although current does also concentrate at the other surfaces as well (redder regions). For a solid wire (to the left), the current concentrates on the outer surface. For this reason, when skin depth is shallow, the solid conductor can be replaced with a hollow tube with no perceivable loss of performance. Choice of a plating material can degrade performance (increase attenuation) if its bulk resistivity is greater than that of the copper.

Most common conductors have a relative permeability of very near 1, so for copper, aluminum, etc., a µ value of 4π* 10-7 H/m can safely be assumed. Magnetic materials like iron, cobalt, nickel, mumetals, and permalloy can have relative permeabilities of hundreds or thousands.

The equation for calculating the skin depth is given here:

          (click here table of calculated values)

          (click here for a skin depth calculator)

Skin depth equation formula

µ = permeability (4π* 10-7 H/m),  note: H = henries = Ω*s


π = pi

δs = skin depth (m)

ρ = resistivity (Ω*m)

ω = radian frequency = 2π*f (Hz)

σ = conductivity (mho/m),  note: mho [Electrical 'mho' symbol - RF Cafe] = Siemen [S]

Example: Copper @ 10 GHz (ρCu=1.69*10-8 Ωm)

Formula copper skin depth - RF Cafe

Anatech Electronics RF Microwave Filters - RF Cafe

PCB Directory (Manufacturers)
Copper Mountain Technologies (VNA) - RF Cafe
Innovative Power Products Passive RF Products - RF Cafe

Please Support RF Cafe by purchasing my  ridiculously low−priced products, all of which I created.

These Are Available for Free

 

About RF Cafe

Kirt Blattenberger - RF Cafe Webmaster

Copyright: 1996 - 2024

Webmaster:

    Kirt Blattenberger,

    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:

AirplanesAndRockets.com