The Tech Blog

Back to Basics: Skin Depth

Posted under Uncategorized on March 26th, 2023 by Amaldev

Skin effect is a phenomenon that occurs in conductors carrying alternating current (AC), in which the current density is highest near the surface of the conductor and decreases towards the centre. It’s measured as the distance from the outer surface of a conductor to the point where the current falls to 37%(1/e) of the max current value. It depends on the frequency of the signal travelling in the cable. Higher the frequency, lower the depth from the surface it travels. For a DC signal(f=0Hz), it travels through the entire cross-section of the signal.

So Why does it occur? When an alternating current flows through a conductor, it generates a changing magnetic field around the conductor. This magnetic field, in turn, induces an opposing electric field within the conductor, which creates eddy currents that flow in a circular path around the conductor. These eddy currents produce a secondary magnetic field that opposes the original magnetic field. This field is strongest in the centre and hence it pushes the current towards the outer surface of the conductor.

This means that to carry a high-frequency signal, it’s relatively wasteful to have a very thick conductor as most of the current is on the outside surface. Hence you would see the usage of multi-stranded wires than solid core wires to carry these types of signals. Induction cooktops you use to cook food in your kitchen also rely on high-frequency switching coils. Due to its high freq, the skin depth kicks in and heating only happens in a thin region of the bottom surface of your pan. Skin depth depends inversely on the conductivity of the material and magnetic permeability. Better a conductor, lower the skin depth. Similarly, more magnetic a material, lower the skin depth. For PCB designs in very high frequencies, Skin depth usually would need to be factored in the field solver as impedance will get affected.

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Back to Basics: Equivalent Series Inductance(ESL)

Posted under Back to Basics, Educational, Product Design, Technology on March 19th, 2023 by Amaldev

For a real-world capacitor, there are 2 elements worth exploring, ESR(Check older posts to know more about this) and ESL. ESL refers to the inductance that is present in the leads and terminals of a capacitor, as well as any inductance that is present in the capacitor itself. As you see in the equivalent of a capacitor, it’s an RLC circuit, and RLC circuits have a self-resonant freq when the effective inductance and capacitance “cancel” each other and show a minimum impedance. You would have seen those in the V-shaped impedance curves for capacitors. The lowest point of the V shape is the resonant frequency.

After the resonant frequency, Capacitor doesn’t work like a capacitor. An ideal capacitor is supposed to have a lower impedance for larger frequencies of operation. Xc is inversely proportional to Freq. What we see after the resonant freq in the graph, is due to ESL. The inductance of a capacitor starts dominating and the impedance rises. Now, what’s the problem if impedance rises? Suppose you are using a capacitor beyond the resonant freq in your circuit, impedance seen by your power supply rails will be higher, meaning it will actually resist the flow of high freq components creating noise problems or spikes at the switching instant. Hence we always want to use capacitors with lower ESL in our circuits.

The amount of inductance in a capacitor is primarily influenced by the length of its constituent elements. As the length, or loop area, increases, so does the inductance. Consequently, electrolytic capacitors tend to exhibit significantly higher ESL than their 1206 or 0402 (which is even lower than 1206) counterparts. It is therefore advisable to use the smallest possible footprint size that is compatible with the required voltage rating, in order to minimize ESL. You see that on the graphs, the resonant point shits right and the vertical impedance axis value reduces as you go down in size. Another way to reduce it is to use a flipped capacitor(Check older posts on how they work) with a lesser length.

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