Page 212 - Maxwell House

192 Chapter 4

Evidently, the factor = characterizes the velocity of the wavefront and energy
1

propagation that is equal to = √ �30 � ⁄ . Typically, in highly conductive
metals 30 ≫ 1, the EM wave moves extremely slow and thus loses a lot of its energy even
⁄
on the short distance. It is ordinarily practice to characterize the energy lost by the value called
−1 or
− 2
skin-depth and define it as the path through the exponential factor =
1 1
= 1 ≅ � ≅ � ≅ 503� [m] (4.89)
�
2
2
120 35
Here in [m], frequency in [Hz] and in [S/m]. Figure 4.4.2 illustrate the skin-depth vs.
8
frequency for several metals and alloys
50 Hz up to 1MHz.
At microwave frequencies (typically
above 300 MHz) the skin-depth shrinks
to a fraction of mm, typically measured
in µm (see table on your left) and
becomes comparable to surface
roughness meaning that the metal
surface slightly deviates from the
perfectly flat as it can be seen in Figure
9
4.4.3a . The roughness is a random
quantity defying generally by the
manufacturing process and it can be
specified in terms of the RMS (root
Figure 4.4.2 Skin-depth vs. frequency mean square) peak-to-valley height of
the surface unevenness. The exemplary
roughness profile tracing small changes in surface height is sketched in Figure 4.4.3b. The RMS
Height (RMSH) is defined as

a) b)
Figure 4.4.3 a) 3D microprofile surface of metal strip, b) Roughness profile measurement for
RMSH definition

2 2 2 2
ℎ +ℎ +ℎ +⋯+ℎ
= � 1 2 3 (4.90)

8 Public Domain Image, source: https://en.wikipedia.org/wiki/Skin_effect
9 Public Domain Image, source: http://www.novacam.com/products/profilometers/