Conductor skin depth

The capacity of a cable to carry nonlinear loads may be determined as follows. The skin effect factor is calculated first. The skin effect factor depends on the skin depth, which is an indicator of the penetration of the current in a conductor. Skin depth (5) is inversely proportional to the square root of the frequency ... 

At sufficiently high frequency, the electromagnetic skin depth is several times smaller than a typical defect and induced currents flow in a thin skin at the conductor surface and the crack faces. It is profitable to develop a theoretical model dedicated to this regime. Making certain assumptions, a boundary value problem can be defined and solved relatively simply leading to rapid numerical calculation of eddy-current probe impedance changes due to a variety of surface cracks. 

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. 

This formula does not explicitly contain the temperature as a variable, but it can explain the limiting of the temperature increase at the Curie point. When the ferromagnetic conductor reaches the Curie point, the relative permeability pr of the ferromagnetic conductor suddenly drops. This generates a sudden increase in the skin depth s and therefore a decrease in 1/s and F(d,s) such that the power consumption of the conductor decreases. A further increase in temperature is therefore inhibited. Detailed graphs describing the variation of N as a function of temperature when different parameters are modified in rel. (1) are available in literature [8]. 

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. 

In particular, widespread interest has surrounded claims of exceptionally high microwave conductivities in TTF-TCNQ based upon a surface impedance analysis valid for isotropic conductors. We have devoted considerable effort to theoretical and experimental studies of the microwave response of small, strongly anisotropic conductors under skin-depth limited conditions. Our conclusion is that the isotropic analysis does not apply, and that the reported measurements bear no simple relationship to the true microwave conductivity of TTF-TCNQ. 

When the skin depth is much less than the simple thickness, the loss for a small isotropic conductor is proportional to the surface impedance Z =(l/a)ReK, where K = (1 + i)/6, is the wavevector parallel to the surface inside the body. We find that in the anisotropic case the components of Z retain this form, but K is severely modified. For a rectangular parallelopiped of biaxial TTF-TCNQ with dimensions b a c anti e b, we find that the leading Fourier component of the loss... 

Absorption losses occur as a result of ohmic current induced in the shield and dissipated as heat. That effect creates an exponential decrease of field intensity inside the conductor. The magnitude of these losses is determined by the skin depth which is expressed as ... 

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... 

Eddy currents will set up their own magnetic fields, opposing the external field. The magnetic field will therefore be attenuated as function of depth (skin effect). The skin depth (depth of penetration) 6 in the case of a uniform, plane electromagnetic wave propagating in a volume conductor with a magnetic permeability p. is ... 

In the case of a conductor, the attenuation of waves is very fast compared to insulators, as a result of having a very high conductivity. The distance that a wave must travel to be attenuated by 1/e is defined as the skin depth. ... 

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. 

One of the most important parameters in the heater design is the thickness of the conductive lines employed in the coplanar waveguide [4]. Using a thin conductor increases the conductive losses within the transmission line. Shah et al. use cmiductors with a thickness of 0.5 pm, which is smaller than or close to the skin depth of gold in the frequency band of 300 MHz—40 GHz. As shown in Fig. 6,45-75 % of the total power is dissipated by conductive 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 skin depth is the distance over which electrical conduction will take place in a conductor it could be a thin-film, thick-film, or bulk material. Precisely stated, the skin depth is the distance into the conductor at which the electric field drops off to 1/e. In practice, very little conduction occurs in the portion of the conductor that is greater than a few skin depths. This distance is always from the surface of the conductor carrying the radiofrequency (RF) current, which is always the surface nearest to the media in... 

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

The relative permeability is a measure of how a magnetic field interacts with a material and can often be considered a constant for a given material. The net result of this skin effect is that conduction is limited to a thinner region of a metallization at higher frequencies. Consequently, the net conductor loss may appear lower if the skin effect is taken into account. In practice, conductor thickness of more than a few skin depths is of little value. However, the reader should note that at low frequencies, the skin depth becomes very large. 

Roughness of the conductor and dielectric is an important property for high-frequency performance. The increase in attenuation due to roughness is a complex function of roughness and skin depth [5]. 

This correction factor is plotted in Figure 2.1. In a perfectly smooth surface (no roughness), there is no increase in conductor attenuation as a result of roughness. If the roughness is 50% of the skin depth, there is a conductor attenuation increase of 1.21, or 21% increase in conductor loss over a perfectly smooth conductor, due to roughness. If the roughness equals the skin depth, the increase in conductor attenuation is 1.61, or 61%. 

With increased frequency, the current flow is more concenfrated on the surface of fhe conductor trace (skin effect). The thickness 5 where the current density has dropped down to 1 /e (approximately, 36%), in comparison to the DC current density, is called the skin depth. The skin depth is only related to material constants and to the frequency by Equation 9.34. 

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. 

Figure 10-1 The relationship between frequency and skin depth of various conductors.

Also, it is well known that currents concentrate near the outer surface area of the conductor when the frequency of an applied (source) voltage (or current) to the conductor is high. This phenomenon is called the skin effect. The depth of the cross-sectional area where most of the currents flow is given approximately as the (complex) penetration depth or the so-called skin depth in the following form ... 

In conductive metals, it is difficult to penetrate to much depth with microwave radiation. The magnetic field and the microwave beam are oriented along the surface of the conductor. The circulating electrons will only feel the field when they are within the skin depth of the radiation, so when the applied frequency is some integer times the resonance frequency, absorption will occur. This technique is known as the Azbel-Kramer cyclotron resonance (AKCR) method. 

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... 

Tubular conductors provide the most efficient system for current carrying, particularly large currents. As discussed above, the current density is the maximum at the skin (surface) of the conductor and falls rapidly towards the core. Experiments have been conducted to establish the normal pattern of current distribution in such conductors at different depths from the surface (Figure 31.11). 

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