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Ground Plane Impedance vs Frequency

Calculate PCB ground plane AC impedance, skin depth, and inductive reactance at high frequencies for EMC analysis.

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Formula

δ = 1/√(πfμσ), R_AC = R_DC × t/(2δ)

δ— Skin depth (m)
σ— Conductivity (S/m)

How It Works

A PCB ground plane is not a perfect zero-impedance conductor — it has DC resistance (R_DC = ρL/Wt), inductance (L ≈ μ₀L/W), and skin-effect-limited AC resistance that rises with frequency. The skin depth is δ = 1/√(πfμσ), where σ is conductivity (58 MS/m for copper). Below the frequency where the copper thickness equals two skin depths, R_AC = R_DC × t/(2δ). Above this, skin effect restricts current to a thin surface layer and R_AC ∝ √f. Inductive reactance X_L = 2πfL also rises linearly with frequency. Total impedance |Z| = √(R_AC² + X_L²). High ground plane impedance causes ground bounce, common-mode noise, and elevated radiated emissions. At 100 MHz, even a small 10 mm path can have milliohm-level impedance that perturbs sensitive signals.

Worked Example

Problem
A copper ground plane (σ = 58 MS/m) is 100 mm long, 50 mm wide, 35 μm thick. Calculate DC resistance, skin depth at 10 MHz, AC resistance, and total impedance.
Solution
1. DC resistance: ρ = 1/(58×10⁶) = 1.724×10⁻⁸ Ω·m; R_DC = (1.724×10⁻⁸ × 0.1)/(0.05 × 35×10⁻⁶) = 985 μΩ ≈ 0.99 mΩ 2. Skin depth at 10 MHz: δ = 1/√(π × 10⁷ × 4π×10⁻⁷ × 58×10⁶) = 20.9 μm 3. AC resistance (t=35 μm > 2δ=41.8 μm, so skin effect partially applies): R_AC = 0.99 mΩ × (35 μm)/(2 × 20.9 μm) = 0.83 mΩ 4. Inductance: L ≈ (4π×10⁻⁷ × 0.1)/0.05 = 0.25 nH; X_L = 2π × 10⁷ × 0.25×10⁻⁹ = 15.7 mΩ 5. |Z| = √(0.83² + 15.7²) ≈ 15.7 mΩ Result: At 10 MHz the inductance dominates, making the ground path 15.7 mΩ. For a 100 mA current this is 1.6 mV of ground bounce.

Practical Tips

  • ✓Keep ground return paths short and wide — the inductance of a ground plane segment scales as L/W, so doubling the width halves the inductance.
  • ✓Avoid ground plane splits under high-frequency traces — the current is forced around the split, increasing loop area and radiating emissions.
  • ✓For frequencies above 100 MHz, the inductive reactance of the plane itself may require via stitching to provide multiple parallel low-inductance return paths.

Common Mistakes

  • ✗Assuming DC resistance is the dominant impedance above a few MHz — inductive reactance overtakes resistance at surprisingly low frequencies for even small ground paths.
  • ✗Using a narrow neck or trace as the only ground return — a 1 mm wide, 10 mm long copper neck has roughly 100× the impedance of the full ground plane.
  • ✗Treating copper thickness as constant — plated-through-hole pads, HASL, or ENIG can reduce the effective current-carrying thickness of thin copper layers.

Frequently Asked Questions

Ground plane impedance determines the magnitude of ground-bounce voltages that appear as common-mode noise. High impedance allows differential-mode circuit noise to couple to the ground reference, creating common-mode current on cables and increasing radiated emissions.
Aluminium (σ = 37 MS/m) has about 60% the conductivity of copper, so DC resistance and skin-effect losses are higher. However, for chassis ground planes (sheet metal enclosures), aluminium is widely used and its skin depth at EMC frequencies is still much smaller than typical sheet thickness.
Use multiple via stitching along ground returns to provide parallel paths. Increase copper weight (2 oz instead of 1 oz). Place the ground plane immediately below the signal layer to minimise the current loop area. Use copper pours on all unused layers connected to ground.

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