Beyond Elementary Physics #1_ The Effect Of Frequency On The Conductivity Of A Dielectric

An elementary Physics student would profess without any atom of doubt that copper, Silver, aluminium and some other metals are pure conductors of electricity at all conditions and would tend to see as inferior anyone who antagonizes his knowledge. Growing up as a science student, I conformed to the elementary Physics idea that copper and aluminium are pure conductors of electricity in all conditions. However, with advancement in the knowledge of Electrical engineering, I discovered through studies that no element on earth is a conductor at all conditions. So, the idea of dielectric replaced conductors. In transmission line, all materials are called dielectrics. Though terms like conductivity, dielectric constant and impedance could be use to describe a dielectric. A material that behaves like conductor might behave as a resistor with change in frequency; for this fact, all materials are called dielectric while operating with alternating current or voltage

_{Source: Wikipedia under Creative Commons}

Conduction of electricity occurs at the surface of dielectrics, that is, voltage or current flows majorly at the skin(surface) of dielectrics. This is the reason why some manufacturers would coat or galvanize some metals with copper and push it to the market for sale.

Skin Effect And Skin Depth

Current flows majorly at the surface of a dielectric an attenuates as it gets to the axis or center of the dielectric. Skin effect is the probability of an alternating current to distribute itself in such a way that current density is more at the surface of a dielectric and reduces with depth. This depth into which current can flow is the effective skin depth of a dielectric. So, in operation with alternating currents, current flows from the surface of the dielectric to a certain depth called skin depth.
The skin depth of a dielectric is affected by frequency of the alternating current, the relationship between skin depth and frequency is as below:

Image credit: @ikchris

where
ω= angular frequency= 2πF
ρ = resistivity of the material
µ= µ_o µ_r
µ_o= the permeability of free space
µ_r = relative magnetic permeability of the conductor
ε= ε_oε_r
ε_o= the permittivity of free space
ε_r= relative permittivity of the material

The resistivity and permeability of a material is constant. So, the only variables are the frequency and permittivity. From the mathematical expression above, as the frequency increases, the skin depth decreases; lower skin depth implies higher resistance of a dielectric, as alternating current can only cluster at a small portion of the surface of the dielectric and cannot flow even to the axis of the dielectric.

The resistivity and permeability of copper are 1.72 x 10^-8 Ωm, 1.256629×10^-6H/m. So, at 60Hz , the skin depth of cooper is around 8.5mm. But, what happens when the frequency of current is in GHz just as in radio stations and some electronic devices? The skin depth decreases of course
A lower skin depth makes the thickness of the dielectric a waste of material, this is the reason a hollow dielectric is used most frequently in radio broadcasting stations operating in frequency of GHz
Finally, at a very high frequency, copper ceases to be a good conductor at it uses to be in lower frequency or operation with DC.

Conclusion

The frequency of alternating current affects immensely the conductivity of a dielectric. Some materials which are good conductors at low frequency might be a bad conductor at higher frequencies due to skin depth. Anyway, there is a way to mitigate increased resistance due to skin effect which would be a publish of another day.
Anticipate!!!!!

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References

• The skin Effect
• Skin dept
• Permeability of a material
• Transmission Line