Skin effect statement check: “Depth of penetration (skin depth) does not depend on frequency.” Is this statement correct for good conductors under standard RF conditions?

Introduction / Context:
Skin depth is the characteristic distance over which an alternating current becomes attenuated to about 37 percent of its surface value in a good conductor. It is a key parameter in RF design because it determines conductor loss and the useful thickness of plating in cables, waveguides, and PCB traces. The question tests whether you remember the functional dependence of skin depth on frequency.

Given Data / Assumptions:

• Good conductor with conductivity sigma and magnetic permeability mu that are roughly constant across the band considered.
• Angular frequency omega equals 2πf.
• Classical skin effect model applies.

Concept / Approach:

The classical relationship for good conductors is delta = sqrt(2 / (omega * mu * sigma)). This shows an explicit inverse square root dependence on frequency: delta is proportional to 1 divided by the square root of f. As frequency increases, currents crowd closer to the surface, which increases effective resistance and insertion loss unless geometry or materials are optimized.

Step-by-Step Solution:

Verification / Alternative check:

A practical rule of thumb for copper is delta in micrometers approximately equals 66 divided by the square root of frequency in megahertz. This empirical relation aligns with lab measurements from HF through microwave bands and confirms the 1 over square root frequency trend.

Why Other Options Are Wrong:

• Any statement that delta is independent of frequency contradicts the classical formula.
• Superconductors and exotic materials are not the subject of the standard good conductor model used here.
• Zero permeability or other limiting cases do not occur in typical RF metals and would not make delta independent of frequency in practical design.

Common Pitfalls:

Using direct current resistance values at RF, overlooking that surface roughness and plating porosity can increase loss beyond the ideal prediction, and assuming thicker metal always helps even when thickness already exceeds several skin depths.

Final Answer:

False