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Skin Depth in COMSOL Multiphysics

What is skin depth ?

The skin effect is the tendency for an alternating electric current (AC) to be dispersed throughout a conductor so that the current density is highest at the conductor's surface and exponentially declines as the conductor is drilled deeper. Between the conductor's outer surface and a depth known as the skin depth, the "skin" of the conductor is where the majority of the electric current flows. Alternating current frequency affects skin depth because as frequency rises, current flow comes closer to the surface and reduces skin depth. The conductor's effective resistance rises as a result of skin effect, which decreases the conductor's effective cross-section. The alternating current's changing magnetic field induces opposing eddy currents that result in skin effect. The skin depth in copper at 60 Hz is about 8.5 mm. High frequencies cause the skin depth to significantly decrease.

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By using specially woven litz wire, the skin effect's increased AC resistance can be reduced. Tubular conductors, like pipe, can be used to reduce weight and cost because a large conductor's interior carries so little of the current. The analysis and design of radio-frequency and microwave circuits, transmission lines (or waveguides), and antennas must take the skin effect into consideration. It is also crucial at mains frequencies (50–60 Hz) in the transmission and distribution of AC electrical power. It is just one of the benefits of choosing high-voltage direct current for transferring power over long distances.

Cause of skin depth effect ?

Alternating current can be used to transmit electrical energy or signals through conductors, which are typically in the form of wires. Due to the source of electrical energy, an electric field drives the charge carriers that make up that current, which are typically electrons. A magnetic field is created within and outside of a conductor while it is conducting electricity. The magnetic field in a conductor fluctuates along with the current's strength. An electric field is produced in response to a change in the magnetic field that opposes a change in the strength of the current. The term "counter-electromotive force" refers to this opposing electric field (back EMF). According to the figure on the right, the back EMF pushes conducting electrons to the conductor's outside edges where it is greatest.

Regardless of the driving force, it is discovered that the current density is highest at the conductor's surface and decreases significantly deeper in the conductor. The skin depth is a measurement of the depth at which the current density drops to 1/e of its value near the surface. This decrease in current density is also referred to as the skin effect. Within a layer four times the depth of the skin from the surface, more than 98% of the current will flow. Unlike direct current, which typically disperses uniformly over the wire's cross section, this behaviour is different.

According to the law of induction, an alternating magnetic field can also induce an alternating current in a conductor. This explains why electromagnetic waves are reflected off of metals. An electromagnetic wave impinging on a conductor will typically result in the generation of such a current. The skin depth describes the exponential decay of the electric and magnetic fields, as well as the density of induced currents, inside a bulk material when a plane wave impinges on it at normal incidence, although the term "skin effect" is most frequently associated with applications involving the transmission of electric currents.

Skin depth is important

Skin depth is a frequency-dependent indicator of how much electrical conduction occurs in a conductor. No matter how thick the conductor is, it is utilised completely at DC (0 Hz). According to Ohm's law, the DC resistance per unit length reduces by half when a wire's cross-sectional area doubles. The relationship between a conductor's conductance and thickness is nonlinear at RF frequencies (actually, a negative exponential.) There is a limit to the conductance that can be achieved, hence precious metals should be thicker to minimise losses. If you don't know what you're doing with RF, it can be a waste of money. The surface of a conductor on which the RF current is being carried is a typical misperception concerning skin depth. It is (mostly) always the surface closest to the medium through which the EM wave travels. The RF currents are greatest at the bottom surface of the microstrip line, as seen below in a cross-section of the microstrip. Because of this, the initial metal in a microstrip multi-metal stack-up is crucial to conductivity. Please take notice that the converse is true for waveguides; the surface plating is what matters, not the underplating.

Skin depth in COMSOL Multiphysics ?

Check out the official COMSOL blog explaining skin depth

Check the Youtube video explaining how to calculate skin depth

Screenshot showing calculation of skin depth in COMSOL 6.1 (introduced)

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