Skin effect with frequency — qualitative trend As signal frequency is increased in a conductor, how does the skin effect change?

Introduction / Context:Skin effect describes the tendency of alternating current to concentrate near the surface of a conductor. It is a central concept in RF design, affecting resistance, loss, and heating. Understanding its frequency dependence helps in choosing conductor size, plating, litz wire, and surface finishes for RF/microwave hardware and high-speed interconnects.

Given Data / Assumptions:

• Good conductor with conductivity sigma and permeability mu.
• Angular frequency ω = 2 * pi * f.
• Skin depth δ is the characteristic penetration depth.

Concept / Approach:The standard relation is δ = sqrt(2 / (ω * mu * sigma)). As frequency f increases, ω increases, causing δ to decrease. A smaller skin depth means current is confined to a thinner surface region, effectively reducing the cross-sectional area available to carry current. The effective AC resistance R_ac therefore increases with frequency. Consequently, we say the skin effect “increases” with frequency because its impact on current crowding and losses becomes more pronounced.

Step-by-Step Solution:

Verification / Alternative check:Measured insertion loss of copper microstrip increases with frequency chiefly due to skin effect and dielectric loss; plating with silver (lower surface resistance) improves high-frequency performance, consistent with stronger skin effect at higher f.

Why Other Options Are Wrong:

• Decreases: contradicts δ shrinking with frequency.
• Remains the same / either (b) or (c): skin effect is frequency-dependent; it does not stay constant.

Common Pitfalls:Mixing skin effect with proximity effect; assuming DC behavior applies at RF; ignoring magnetic materials which further reduce δ through higher mu.

Final Answer:increases