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Radiated Emission Estimate

Estimate far-field radiated emissions from a PCB current loop using the small-loop antenna model. Compare against CISPR 22/FCC Class B limits.

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Formula

E ≈ 263 × f² × A × I / r [V/m, f in MHz, A in m²]

Reference: Henry Ott, Electromagnetic Compatibility Engineering

f— Frequency (MHz)
A— Loop area (m²)
I— Loop current (peak) (A)
r— Distance (m)

How It Works

Radiated emissions from PCBs are primarily caused by current loops — traces carrying high-frequency current form small loop antennas. The electric field at distance r from a small current loop in free space is approximated by E ≈ 263 × f² × A × I / r [V/m], where f is in MHz, A is the loop area in m², and I is the peak current in A. Converting to the common measurement unit: E [dBμV/m] = 20·log₁₀(E × 10⁶). CISPR 22 Class B sets a radiated emission limit of 40 dBμV/m at 3 m for frequencies 30–230 MHz. Margin = 40 − E_measured [dBμV/m]. Reducing loop area (tighter ground return routing) or switching frequency is often more effective than post-design shielding.

Worked Example

Problem
A PCB switching converter draws 10 mA peak at 100 MHz through a 1 cm² loop. What is the estimated E-field at 3 m, and what is the margin versus CISPR 22 Class B?
Solution
1. Convert units: I = 10 mA = 0.01 A; A = 1 cm² = 1×10⁻⁴ m²; f = 100 MHz; r = 3 m 2. E = 263 × 100² × 1×10⁻⁴ × 0.01 / 3 = 263 × 10,000 × 10⁻⁴ × 0.01 / 3 = 263 × 10,000 × 3.33×10⁻⁶ = 8.77 μV/m 3. E [dBμV/m] = 20·log₁₀(8.77) = 18.9 dBμV/m 4. Margin = 40 − 18.9 = 21.1 dB Result: 21 dB margin is comfortable but there are likely multiple loops on the PCB, so the cumulative effect may be higher. Reduce loop area or switching current to improve margin.

Practical Tips

  • ✓Minimise loop areas: route return currents directly under signal traces, use a solid ground plane, and keep decoupling capacitors close to the IC.
  • ✓Use the rule of thumb: halving the loop area reduces E-field by 6 dB — this is usually cheaper than adding a shielded enclosure.
  • ✓For pre-compliance scanning, use a near-field H-field probe to identify the dominant emission loop before making changes.

Common Mistakes

  • ✗Assuming the formula gives an accurate absolute value — it is a simple far-field estimate that ignores ground-plane reflections, antenna factor of the receiving antenna, and multiple source coupling.
  • ✗Forgetting that emissions increase as f² — doubling frequency quadruples the emitted field; this is why high-frequency clocks are the dominant emission source.
  • ✗Measuring only at 3 m and passing — CISPR 22 requires sweeping from 30 MHz to 1 GHz; peak emissions often occur at higher harmonics of the switching frequency.

Frequently Asked Questions

CISPR 22 (now superseded by CISPR 32) sets limits for multimedia equipment, primarily used in Europe. FCC Part 15 Class B uses similar limits (40–43 dBμV/m at 3 m below 230 MHz). Both converge to approximately the same values in practice.
Yes, but only approximately. A microstrip trace over a ground plane forms a partial loop; the effective loop area is determined by the trace height above the plane and its length. The formula gives a useful order-of-magnitude estimate for pre-compliance design decisions.
Only as a rough indicator. The formula assumes a single isolated loop in free space. Real products have many loops, resonances, and reflections. Use it for comparative design analysis (which fix reduces emissions more?) rather than absolute pass/fail prediction.

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