## Skin, Symbols, and General Consideration Effect

Added by: Claire

On: 07 Jul, 2017

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Category: Circuit

**skin, symbols, and general consideration effect**can be download for free. This circuit and wiring diagram: skin, symbols, and general consideration effect has been viewed 645 times which last viewed at 2018-08-17 03:33:00 and has been downloaded 0 times which last downloaded at 0000-00-00 00:00:00 added by Claire on 07 Jul, 2017.

**Symbols **

*A *= correction coefficient

*D *= diameter of conductor in inches

*f *= frequency in hertz

Rac = resistance at frequency *f *RdC = direct-current resistance

Rsq = resistance per square

*T*= thickness of tubular conductor in inches

*T1*= depth of penetration of current

= skin depth

A = free-space wavelength in meters

*Pr*= relative permeability of conductor material

*(ILr *= I for copper and other nonmagnetic materials)

p = resistivity of conductor material at any temperature

= resistivity of copper at 20 °C *= *1.724 microhms-centimeter

**Skin Depth **The skin depth is that distance below the surface of a conductor where the current density has diminished to

*lie*of its value at the surface. The thickness of the conductor is assumed to be several (perhaps at least three) times the skin depth. Imagine the conductor replaced by a cylindrical shell of the same surface shape but of thickness equal to the skin depth, with uniform current density equal to that which exists at the surface of the actual conductor. Then the total current in the shell and its resistance are equal to the corresponding values in the actual conductor.

The skin depth and the resistance per square (of any 6 = *(1.50 ***X ***104A”2)k1 *size), in meter-kilogram-second (rationalized) units, = (2.60/f 2)k1 inch

are

*6m*= (2.60/fmc112)ki

**mu**

Rsq =

*(4.52*x I03/A”2)k2

*8 (A/ircric)U2*= (2.61

**X**

*10f112)k2*ohm

= [(l/iLr)P/Pj1’

Rsq =

*1/8o k2*=

*(I4P/P)*

k1, k2= unity for copper

k1, k2

where,

*Example:*What is the resistance/foot of a cylindrical

6 = skin depth in meters, copper conductor of diameter

*D*inches?

*R*= resistance per square in ohms,

*c*= velocity of light

*in vacuo R*= (l2/3TD)Rsq

= 2.998

**X**iO meter/second,

= X iO

**hen/meter, =**

*!Lr**(l2/D)*

**X**2.61

**X**iO_?(fU2)

I/o- = 1.724 X 10—8 p/p ohm-meter.

= 0.996 X 106(f”2)/D ohm/foot

For numerical computations

6 = (3.82 X iO

*A”2)k1*If

*D*= 1.00 inch andf= 100

**X**106 hertz, then

*R*=

= (6.61/f’2)k1 centimeter 0.996 x 10-6 x iO 1 x 10-2 ohm/foot.

**General Considerations **Fig. 7 shows the relationship of Rac/RdC versus

*D(f”2)*for copper, or versus

*D(f02)(pp/p)”2*for any conductor material, for an isolated straight solid Cond uctor of circular cross section. Negligible error in the equations for Rac results when the conductor is spaced at least lOD from adjacent conductors. When the spacing between axes of parallel conductors carrying the same current is

*4D,*the resistance Rac is increased about 3 percent, when the depth of penetration is small. The equations are accurate for concentric lines due to their circular symmetry.

For values of *D(f112)(I.LrPc/p)”2 *greater than 40

Rac/Rdc = 0.0960 *D(fU2)(,.L,p/p)2 *+ 0.26 (Eq. 1)

The high-frequency resistance in ohms/foot of an isolated straight conductor (either solid or tubular for *T *<D/8 or *T1 <D/8) *is given in Eq. (2). If the current is along the inside surface of a tubular conductor, *D *is the inside diameter.

Rac = *A[(f112)/D1[I.Lr(P/Pc)1 *1/2 x 106

(Eq. 2)

The values of the correction coefficient *A *for solid conductors and for tubular conductors are given in Table 4.

The value of *T(f02)(/Irpc/P)02 *that just makes *A *= *I *indicates the penetration of the currents below the surface of the conductor. Thus, approximately

*T1 *= *[3.5/(f2)l(P/prPc)U2 *

(Eq. 3)

where *T1 *is in inches.

When *T1 <D/8, *the value Of Rac as given by Eq. (2) (but not the value of Rac/Rdc in Table 4, “Tubular Conductors”) is correct for any value *T * *T1. *Under the limitation that the radius of curvature of all parts of the cross section is appreciably greater than

*T1,*

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