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Radiated Emission Estimate

Estimate radiated emissions from PCB current loops using the small-loop model. Compare E-field against CISPR 22/FCC Class B limits instantly.

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Formula

E=1.316×10−2×f2×A×I/r[V/m,finMHz,Ainm2]E = 1.316×10⁻² × 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

The Radiated Emission Estimate Calculator predicts E-field strength from PCB current loops — essential for early-stage EMC design review before prototype builds and pre-compliance testing. EMC engineers use this to evaluate design changes (loop area reduction, current reduction) and estimate margin to CISPR 32 Class B limits (40 dBuV/m at 30-230 MHz, 3m distance).

Per Henry Ott's 'EMC Engineering,' a small loop antenna (dimensions << wavelength) radiates E-field E = 263 x f^2 x A x I / r (V/m), where f is frequency in MHz, A is loop area in m^2, I is peak current in A, and r is distance in m. Converting to common EMC units: E(dBuV/m) = 20 x log10(E x 1e6). The formula shows emission increases as frequency squared — doubling frequency quadruples emission.

Per Johnson/Graham's 'High-Speed Digital Design,' the dominant emission source in digital systems is the high-frequency current loop formed by signal trace, load, and ground return path. A 1 cm^2 loop carrying 10 mA at 100 MHz produces 8.77 uV/m at 3m, equivalent to 18.9 dBuV/m — well below CISPR 32 Class B limit of 40 dBuV/m. However, multiple loops combine: 10 similar loops produce approximately 29 dBuV/m (10 dB increase).

Loop area is the critical parameter — halving loop area reduces emission by 6 dB (50%). Per Ott, placing traces directly over ground plane (H = 0.1mm versus H = 1mm) reduces loop area by 10x, cutting emissions 20 dB. This is why controlled impedance stackups with adjacent ground planes provide inherent EMC benefit.

Worked Example

Problem: Estimate radiated emission from SMPS with 50 mA ripple current at 500 kHz switching frequency through a 2 cm^2 input loop. Compare to CISPR 32 Class B limit at 5th harmonic (2.5 MHz).

Solution per Ott:

  1. Parameters: f = 2.5 MHz, A = 2 cm^2 = 2e-4 m^2, I = 50 mA = 0.05 A, r = 3 m
  2. E-field: E = 263 x (2.5)^2 x 2e-4 x 0.05 / 3 = 263 x 6.25 x 2e-4 x 0.05 / 3 = 0.55 uV/m
  3. E in dBuV/m: 20 x log10(0.55) = -5.2 dBuV/m
  4. CISPR 32 Class B limit at 2.5 MHz: N/A (radiated starts at 30 MHz)
  5. At 30 MHz (60th harmonic, assuming -20 dB/decade rolloff from 2.5 MHz): E approximately -5.2 - 20 = -25 dBuV/m? No, use direct calculation:
  6. f = 30 MHz, assuming current rolloff to 5 mA: E = 263 x 900 x 2e-4 x 0.005 / 3 = 7.9 uV/m = 18 dBuV/m
  7. Margin to 40 dBuV/m limit: 22 dB — comfortable if this is only emission source
Note: Real SMPS has multiple loops; aggregate emissions typically 10-20 dB higher than single-loop estimate.

Practical Tips

  • ✓Target loop area reduction first — per Ott, halving loop area reduces emissions 6 dB; halving current also reduces 6 dB, but current reduction often requires different topology. Route returns directly under signal traces for minimum loop area.
  • ✓Use near-field H-probe to identify dominant loop — per Ott, map emission sources with loop probe before making changes. Often one loop (clock, SMPS input) dominates; fixing that loop provides 10-20 dB improvement while other changes have minimal impact.
  • ✓Calculate at 3rd and 5th harmonics of clock — per CISPR 32, digital clock harmonics often set worst-case emission frequency. 100 MHz clock has 300/500 MHz harmonics in the 30-1000 MHz radiated band where limits apply.

Common Mistakes

  • ✗Using formula for absolute pass/fail prediction — per Ott, the small-loop formula is a far-field estimate assuming single isolated loop. Real products have multiple loops, ground-plane reflections, and cable antenna effects. Use for comparative analysis ('which fix helps more?') not absolute compliance prediction.
  • ✗Forgetting emissions scale as f^2 — per Johnson/Graham, a 100 MHz emission is 4x (12 dB) stronger than 50 MHz for the same loop current. High-frequency harmonics dominate emissions even if fundamental current is larger. Always analyze at highest significant harmonic.
  • ✗Ignoring that multiple loops add — per Ott, N similar loops produce sqrt(N) times the field of one loop when incoherent, or N times when coherent (phase-aligned). Budget 10-15 dB margin for aggregate emissions from multiple on-board sources.

Frequently Asked Questions

Per CISPR 32 Class B: 40 dBuV/m at 3m from 30-230 MHz; 47 dBuV/m from 230-1000 MHz. FCC Part 15 Class B: 40 dBuV/m at 3m from 30-88 MHz; 43.5 dBuV/m from 88-216 MHz; 46 dBuV/m from 216-960 MHz; 54 dBuV/m from 960 MHz-40 GHz. Limits are similar below 1 GHz; above 1 GHz, FCC is slightly more permissive. Most designs that pass CISPR 32 also pass FCC.
Approximately yes per Ott — a microstrip trace over ground plane forms a partial loop with effective area = trace length x height above ground. A 50mm trace at 0.2mm height has loop area = 50 x 0.2 = 10 mm^2. The formula gives order-of-magnitude estimate; use near-field probe measurements for accuracy above 100 MHz.
Only as rough indicator per Ott — use for comparative design analysis ('reducing loop from 2cm^2 to 0.5cm^2 should improve by 12 dB') rather than absolute pass/fail prediction. Real emissions aggregate from many sources, reflections, and antenna effects not captured in simple formula. Budget 15-20 dB margin in estimates for production confidence.
Per antenna theory (Pozar), small loop radiation efficiency increases as (circumference/wavelength)^2. Since wavelength = c/f, efficiency scales as f^2. This has major EMC implications: a clock's 5th harmonic radiates 25x (28 dB) stronger than fundamental for same current. High-frequency harmonics dominate radiated emissions even with lower current levels.
Per Johnson/Graham: controlled impedance trace (0.2mm above ground, 50mm long) = 10 mm^2; power trace (1mm above ground, 100mm long) = 100 mm^2; SMPS input loop = 200-2000 mm^2 depending on layout. 10 mm^2 loops are generally safe; 100+ mm^2 loops require analysis and possible mitigation (ground plane, ferrite, shielding).

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