Conductor resistance skin depth

As frequency increases, the current is forced out of the center of the conductor toward its periphery, a phenomenon known as the skin effect . A measure of the depth of penetration of the current into the conductor is the skin depth, defined as 8 = V(p/ir/p,), where / is the frequency and x is the conductor permeability (1.26 X 10 6 H/m for nonmagnetic conductors). For copper, the skin depth is 2 p,m at 1 GHz. When the skin depth is less than the conductor thickness, the line resistance becomes greater than the dc resistance. 

Therefore, when using round wires, if we choose the diameter as twice the skin depth, no point inside the conductor will be more than one skin depth away from the surface. So no part of the conductor is unutilized. In that case, we can consider this wire as having an ac resistance equal to its dc resistance — there is no need to continue to account for high-frequency effects so long as the wire thickness is chosen in this manner. 

Qualitatively different low-frequency, shielding,and skin effect losses were found depending upon the value of the classical skin depth for the transverse resistivity of the composite, in comparison with the twist length and conductor radius. This general set of solutions agrees with losses calculated for particular field situations... 

The skin depth for microwaves is quite small as shown in Fig. 1 due to their high operating frequencies. For a given material and operating frequency, the thickness of the conductor must be several 5 to minimize resistive losses. 

At high frequencies, the surface of the insulator may have a different resistivity from the bulk of the material owing to impurities absorbed on the surface, external contamination, or water moisture hence, electric current is conducted chiefly near the surface of the conductor (i.e., skin effect). The depth, S, at which the current density falls to 1/e of its value at the surface is called the skin depth. The skin depth and the surface resistance are dependent upon the AC frequency. The surface resistivity, R, expressed in 2, is the DC sheet resistivity of a conductor having a thickness of one skin depth ... 

The other two parameters on which the skin depth depends are the resistivity of the conductor and tire relative permeability of the material ... 

However, conductor loss depends on the resistance (surface resistance) of the conductor. As the frequency increases, there is a tendency for the current to concentrate in the surface parts of the conductor. The part where the current flows is known as skin depth (the depth where current density falls to 1/e = 0.37 of its value at the surface), and it decreases in inverse proportion to the square root of the frequency. Surface resistance Rs is determined by skin depth d and conductor conductivity o as in the formula below. It is inversely proportional to the square root of conductor conductivity, and increases proportional to the square root of the frequency. 

To reduce conductor loss in high frequency ranges, it is necessary to take an proach that reduces conductor resistance to the minimum (refer to Chapter 1). Since the inductance of the conductor inside increases at high frequencies, current flows only near the surface of the conductor layer. The thickness of the area where the current flows is called skin depth. Figure 10-1 shows the relationship between the frequency of each type of conductor and the skin depth. The relationship with skin depth ( ) is in accordance with the formula below, and there is a tendency for the skin depth to become shallower as the frequency increases with materials that are not magnetized. 

In a d.c. system the current distribution through the cross-section of a current-canying conductor is uniform as it consists of only the resistance. In an a.c. system the inductive effect caused by the induced-electric field causes skin and proximity effects. These effects play a complex role in determining the current distribution through the cross-section of a conductor. In an a.c. system, the inductance of a conductor varies with the depth of the conductor due to the skin effect. This inductance is further affected by the presence of another current-carrying conductor in the vicinity (the proximity effect). Thus, the impedance and the current distribution (density) through the cross-section of the conductor vaiy. Both these factors on an a.c. system tend to increase the effective... 

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