At RF It’s Only Skin Deep
     

Show Me Some Skin
(Exam level: CBRE)

In the Feb. 22 issue of RWEE, we asked:
What is skin effect in alternating current and what is its relationship to current flow?

a. Skin effect is the tendency of all current flow on printed circuit boards to concentrate on the area against the non-conductive surface and create a capacitor.
b. Skin effect is the tendency for electrolytic capacitors to change value when touched due to the requirement that the positive plate always be on the outside.
c. Skin effect is the tendency of current to flow through mainly the epitaxis layer of the skin when experiencing an electric shock.
d. Skin effect is the tendency of an alternating electric current to distribute itself within a conductor, with the current density being largest near the surface of the conductor, decreasing at greater depths.
e. Skin effect is the penchant of RF to want to flow through the conductive character of a coaxial line.

To help you get in the SBE certification exam-taking frame of mind, Radio World Engineering Extra poses a typical question in every issue. Although similar in style and content to the exam questions, these are not from past exams nor will they be on future exams in this exact form. For more certification information visit www.sbe.org/sections/cert_index.php.


Let’s start our discussion by eliminating the most obvious wrong answer, (c). The epitaxis layer of the skin does not exist in the body except in your humble author’s imagination.

The great writers of the golden era of sci-fi always described humans as “ugly bags of water.” Probably more correct is “ugly bags of salt water.”  

If you remember your high school chemistry and physics classes, you might recall how current flow went up when salt was added to the water. Once past dry skin’s natural surface resistance, any current impressed on the body takes off following its inevitable course to ground and back to the power source generator through all your vital components.

Also wrong is (e) as RF (which is electricity) flows through the electron path of the copper conductors.

Answer (b) is not correct as there is no convention covering the manufacture of electrolytic capacitors although most do, in fact, have the negative plate on the outside.

Answer (a) does have one element of the skin effect phenomenon; current tends to flow on the surface of any conducting material. But currents don’t create capacitors.

This leaves us with (d), which is the correct answer.

INDUCTANCE AND CONDUCTORS

No matter the major theory of electrical current flow to which you subscribe (the electrons move or just the charges move), the physics is about the same. Horace Lamb in 1883 annotated the skin effect phenomenon for the case of spherical conductors, and in 1885, Oliver Heaviside, the same gentleman who gave us the radioactive Heaviside layer in the ionosphere, related the effect to conductors of any shape.

Genius must have run in Heaviside’s family, as his uncle was Sir Charles Wheatstone, co-inventor of the telegraph and progenitor of the Wheatstone bridge. An engineer and mathematician, amazingly Heaviside was self-taught! There’s hope for all of us.

Faraday postulated that any current flowing through a wire sets up a magnetic field. Alternating current sets up a larger field due to the alternation of flow. The strata of atoms and their shells of electrons and related charges form magnetic layers, and where there is magnetism, there is induction. In this case, we have inductive layers caused by the layers of atoms … sort of circulative coils. As we come near to the edges of the conductor, the looser boundary regions exhibit less inductance, which presents to the current flow less inductive reactance.

From the basic formula, inductive reactance is equal to 2 times π times the frequency times the inductance in henries (2πfL); we can see that the higher the frequency, the higher the inductive reactance. Reactance acts on alternating currents similar to the way resistance acts on DC currents: the higher the reactance (resistance), the lower the current. So the AC flow seeks out the lowest reactance towards the edges and in the case of the highest frequencies, like RF, the flow travels mainly along the skin.

A DEEPER LOOK

The way the physics works out is that 63 percent of all the AC current flows near the wire surface to a depth which we’ll call δ (lower case Greek letter delta). See the accompanying graphic.

The AC current density J in a conductor decreases exponentially from its value at the surface JS according to the depth d from the surface, as follows:

img

where δ is called the skin depth. The skin depth is thus defined as the depth below the surface of the conductor at which the current density has fallen to 1/e (about 0.37) of JS. In ordinary cases, the formula for determining δ is

 img

where
ρ = resistivity of the conductor
ω = angular frequency of current = 2π × frequency
μ = absolute magnetic permeability of the conductor

98 percent of all the AC current flows in an area no deeper than 4 times δ.

For virgin copper …
Frequency    Skin depth (δ  in μm, micro meters)
60 Hz    8470
10 kHz    660
100 kHz    210
1 MHz    66
10 MHz    21
100 MHz    6.6

IN PRACTICE
In radio, the skin effect has many practical implications. Skin effect is why we use strap for RF grounding. Since the RF flows along the skin of the conductive material, the interior copper in a large wire is effectively wasted. Strap provides a much higher ratio of conductor skin to interior copper and thus is able to carry high-frequency currents with minimal loss.

So we have a world of 4- and 6- and sometimes 8-inch wide, 1/8-inch thick copper strap running hither and yon in our radio plants. The thickness is really just a function of the minimum sturdiness that will survive soldering, flexing and corrosion over the years.

Coils used in AM tuning units are much larger in diameter than would be required to pass similar magnitude DC currents. These much larger components are required in order to get enough current conduction on their outer skin. Most big RF coils use tubing, since this provides both inner and outer skin surfaces, doubling the conductive area and enhancing cooling.

In circuits much higher than AM and FM, say 11 and 13 gigahertz aural STLs, we have frequencies high enough that the signal flow is mainly along the top few angstroms (a unit of length equal to 10-10 meter) of the conductive material. In these microwave cases, and especially in high-demand locations such as filters, we can plate the device with a deposition of gold to minimize losses and enhance stability.

Gold is an amazing material for a great many reasons, but the one most valuable to us for cost reasons is its very high malleability. Gold can be thinned out in density/thickness until you can actually see through it and still maintain uniform integrity. So we are able to place just such a patina of gold on device surfaces for RF purposes.

Charles “Buc” Fitch, P.E., CPBE, AMD, is a frequent contributor to Radio World. Missed some SBE Certification Corners or want to review them for your next exam? See the “Certification” tab under Columns at radioworld.com.
  
Meter, Meter on the Wall
Question for next time
(Exam level: CPBE)

The analog DC ammeter with an actual full-scale value of 10 milliamperes in your transmitter that measures 1 ampere of plate current has failed and the only linear meter that fits in the same space available is a 1 mA unit. Could you use this available meter as a replacement?

a. Yes, with a series resistor of 10 k
b. Yes, with a series and parallel resistor both 10 k
c. No
d. No because the scale is set by the coil wind count
e. Yes, with a select parallel resistor across the meter contacts

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