# Skin Effect in Conductors

Alternating current distribution is non-uniform in real conductors with finite dimensions and rectangular or circular cross-sections. This is because the alternating current flow creates eddy currents in real conductors leading to current crowding, following Faraday’s laws.

AC currents, being time-varying, produce non-uniform distributions across the cross-sectional area of a conductor. The conductor offers a high-frequency resistance, and for the approximation, we can assume the current to flow uniformly in the conductor, in a layer one skin deep, just below the surface. This phenomenon is known as the skin effect. However, this is only a simple explanation, with the actual distribution of current being much more nuanced, even within an isolated conductor.

For instance, what is the current distribution within a cylindrical conductor with a diameter 2.5 times greater than the skin depth at the frequency of interest? For the answer, it may be necessary to look closely at the physics of skin effect, and the way skin depth is typically derived.

Skin effect is caused by a basic electromagnetic situation. This is related to the propagation of electromagnetic waves inside a good conductor. Textbooks typically examine the propagation of a plane wave within a conducting half-space.

Euclidean space is typically three-dimensional, consisting of length, breadth, and height. A plane can divide this space into two parts, with each part being a half-space. Therefore, a line, connecting one point in one half-space to another point in the other half-space, will intersect the dividing plane. Plane waves propagate along the dividing plane in the conducting half-space.

Now, plane waves consist of magnetic and electric fields that are perpendicular to the direction of propagation and each other. That is why these waves are also known as transverse electromagnetic or TEM waves. Moreover, within a plane wave, all points on planes perpendicular to the direction of propagation, experience the same electric and magnetic fields.

For instance, considering the electric field (E) is in the z-direction, the magnetic field (H) will be in the x-direction, while the wave propagates in the y-direction. Therefore, assuming a plane wave propagation, the electric and magnetic fields remain constant along the x or y direction, and change only as a function of y.

Moreover, for a good conductor, the electric field and the current density are interrelated to the conductivity of the conductor. Using these parameters allows us to calculate the current density, and the skin depth, by solving Maxwell’s equation.

Maxwell’s equation tells us that the amplitude of the current density at the skin depth decreases at the surface of the conductor. It also gives an initial idea of the change in current density at any instant in time as we go deeper into the conductor.

The equation allows us to relate the skin depth to the wavelength within the conductor. The attenuation constant and phase constant of a good conductor are inversely related to the skin depth. It is easy to see that a single wavelength within the conductor is about 6 times larger than the skin depth. This also means the current density will attenuate significantly at a distance of one wavelength.

# A Universal Antenna for Wireless Charging

Skin effect is a physical phenomenon that limits the amount of high frequency current flowing through a wire. What happens is AC current flowing through the wire sets up local magnetic fields that impede the flow of current. Therefore, current is forced out from the central core of the wire to its periphery, increasing the current density there. Effectively, the current now flows through a smaller cross sectional area of the wire, and thereby faces more resistance. To keep the wire from heating up, it is necessary to reduce the amount of current through the wire.

Companies producing wireless chargers for mobile devices follow specific standards such as Qi, Association for Wireless Power (A4WP) and Power Matters Association (PMA) standards. Since they operate at different frequencies, battery-charging circuits have to handle different skin effects or skin temperatures. This may sometimes cause the batteries to get too hot, missing a full charge by several watts in a cycle of recharge. This happens because the high frequency currents flow only around the outer edges of the charging wire, causing charging times to increase.

To reduce the skin effect, NuCurrent has invented the ML wire. They describe the wire as equivalent to bundling hundreds of straws together for passing liquid through. With several strands of wire in parallel, and each insulated from the others, the current now flows through an optimized conductive area, based on the skin depth of a frequency. Therefore, NuCurrent can pass more current with lower resistance through such a wire.

NuCurrent has over 50 patents in areas such as circumventing the skin effect. They believe this will bring them success in the market for multi-mode wireless charging. NuCurrent produces antennas that support the different standards used by companies making wireless chargers. For this, NuCurrent uses the same coil for resonant PMA (200-300KHz) and inductive Qi (110 & 205KHz) standards. Since A4WP uses 6.78MHz, NuCurrent has to use a second resonant charging on the same board for accommodating A4WP.

NuCurrent produces antennas of higher quality and lower resistance. According to officials at NuCurrent, the higher quality factor is necessary because that achieves the necessary charging efficiency with antennas made of thinner wires. In turn, smaller antennas are useful to keep the phone or device cooler and maintain a good charging speed.

With ML wire, NuCurrent is able to make antennas as thin as 0.08mm and occupy areas as small as 12.7×12.7mm. Endowed with NFC capability, the antennas power mobile devices ranging from 50mW to 2.5W, even going up to 50W. However, these antennas are not meant for charging higher-power devices such as appliances or electric cars. The charging efficiency NuCurrent antennas offer for wearable devices and mobiles can reach up to 80%.

The Efficient Power Corporation or EPC makes transistors with Gallium Nitride instead of silicon. As NuCurrent is involved with EPC, they have used NuCurrent’s ML wire coil and demonstrated wireless power transfer that delivered 35W into a DC load while operating at 6.78MHz. NuCurrent feels the technology from A4WP is more relevant to the market today and is more likely to survive as the dominant standard for wireless charging.