Electromagnetic Shielding Efficiency for Critical Rooms Calculator – IEC, IEEE

Electromagnetic shielding efficiency is critical for protecting sensitive equipment in specialized rooms. Accurate calculations ensure compliance with IEC and IEEE standards.

This article explores detailed formulas, practical tables, and real-world examples for electromagnetic shielding efficiency. It guides engineers through IEC and IEEE methodologies for critical room design.

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  • Calculate shielding efficiency for a 1 GHz frequency, copper shield, 2 mm thickness.
  • Determine shielding effectiveness for a steel enclosure at 100 MHz, 5 mm thickness.
  • Evaluate shielding for a critical room with aluminum panels, 0.5 mm thickness, at 500 MHz.
  • Compute shielding efficiency for a composite shield with multiple layers at 2.4 GHz.

Common Values for Electromagnetic Shielding Efficiency – IEC and IEEE Standards

MaterialConductivity (S/m)Relative Permeability (μr)Typical Thickness (mm)Shielding Effectiveness (dB) at 1 GHz
Copper5.8 × 10710.5 – 380 – 120
Aluminum3.5 × 10710.5 – 560 – 100
Steel (Carbon)1.0 × 107100 – 2001 – 1070 – 110
Mu-Metal1.0 × 10620,000 – 100,0000.5 – 290 – 130
Copper Mesh (Fine)5.8 × 1071Mesh size dependent50 – 90
Frequency (Hz)Skin Depth (δ) in Copper (μm)Skin Depth (δ) in Steel (μm)Shielding Effectiveness (dB) for 1 mm CopperShielding Effectiveness (dB) for 1 mm Steel
1 × 106 (1 MHz)662104030
1 × 108 (100 MHz)6.6218060
1 × 109 (1 GHz)2.16.612090
2.4 × 109 (2.4 GHz)1.34.1140110

Fundamental Formulas for Electromagnetic Shielding Efficiency

Electromagnetic shielding efficiency (SE) quantifies the attenuation of electromagnetic fields by a shield. It is expressed in decibels (dB) and calculated by combining reflection loss, absorption loss, and multiple reflection effects.

1. Shielding Effectiveness (SE) Total

SE = R + A + B
  • SE: Total shielding effectiveness (dB)
  • R: Reflection loss (dB)
  • A: Absorption loss (dB)
  • B: Correction factor for multiple reflections (dB)

For shields thicker than the skin depth, the multiple reflection term B is often negligible.

2. Reflection Loss (R)

R = 20 × log10 ( (σ / (4πfε))1/2 / 4 )
  • σ: Electrical conductivity of shield material (S/m)
  • f: Frequency of incident wave (Hz)
  • ε: Permittivity of free space (8.854 × 10-12 F/m)

Reflection loss depends on the impedance mismatch between free space and the shield surface.

3. Absorption Loss (A)

A = 131 × t / δ
  • t: Thickness of the shield (mm)
  • δ: Skin depth of the shield material (μm)

Absorption loss increases with shield thickness and decreases with skin depth.

4. Skin Depth (δ)

δ = 503 × (ρ / (f × μr))1/2
  • δ: Skin depth (μm)
  • ρ: Resistivity of the shield material (Ω·m)
  • f: Frequency (Hz)
  • μr: Relative magnetic permeability of the shield material (dimensionless)

Skin depth represents the depth at which the electromagnetic wave amplitude decreases to 1/e (~37%) inside the material.

5. Multiple Reflection Correction (B)

B = -20 × log10 (1 – e-2A/20)

This term accounts for interference effects inside thin shields but is negligible when A > 10 dB.

Detailed Explanation of Variables and Typical Values

  • Electrical Conductivity (σ): Indicates how well a material conducts electricity. Copper has ~5.8 × 107 S/m.
  • Resistivity (ρ): Inverse of conductivity, e.g., copper ~1.68 × 10-8 Ω·m.
  • Frequency (f): Frequency of the electromagnetic wave, ranging from kHz to GHz in critical rooms.
  • Relative Permeability (μr): Magnetic permeability relative to free space. Steel can have μr from 100 to 200.
  • Thickness (t): Physical thickness of the shield, typically 0.5 mm to 10 mm.
  • Skin Depth (δ): Frequency-dependent penetration depth of EM waves into the shield.

Real-World Application Case 1: Shielding Efficiency of a Copper Room at 1 GHz

Consider a critical room shielded with copper panels 2 mm thick. The operating frequency is 1 GHz. Calculate the total shielding effectiveness (SE).

Step 1: Determine Material Properties

  • Conductivity, σ = 5.8 × 107 S/m
  • Resistivity, ρ = 1.68 × 10-8 Ω·m
  • Relative permeability, μr = 1 (non-magnetic)
  • Frequency, f = 1 × 109 Hz
  • Thickness, t = 2 mm

Step 2: Calculate Skin Depth (δ)

δ = 503 × √(ρ / (f × μr))
= 503 × √(1.68 × 10-8 / (1 × 109 × 1))
= 503 × √(1.68 × 10-17)
= 503 × 1.296 × 10-8.5
≈ 2.1 μm

Step 3: Calculate Absorption Loss (A)

A = 131 × t / δ
= 131 × 2,000 μm / 2.1 μm
= 131 × 952.38
≈ 124,761 dB

Note: This extremely high value indicates near-total absorption, but in practice, absorption saturates and is limited by other factors.

Step 4: Calculate Reflection Loss (R)

R = 20 × log10 ( (σ / (4πfε))1/2 / 4 )
First, calculate inside the log:
σ / (4πfε) = 5.8 × 107 / (4 × 3.1416 × 1 × 109 × 8.854 × 10-12)
= 5.8 × 107 / (1.112 × 10-1)
≈ 5.22 × 108
Square root = √(5.22 × 108) ≈ 22848
Divide by 4 = 22848 / 4 = 5712
R = 20 × log10(5712) ≈ 20 × 3.757 = 75.14 dB

Step 5: Calculate Multiple Reflection Correction (B)

Since A is very large (>10 dB), B is negligible:

B ≈ 0 dB

Step 6: Calculate Total Shielding Effectiveness (SE)

SE = R + A + B ≈ 75.14 + 124,761 + 0 ≈ 124,836 dB

In practice, the absorption loss saturates, and the effective SE is limited by construction imperfections and apertures. Realistic SE values for 2 mm copper at 1 GHz are around 100–120 dB.

Real-World Application Case 2: Steel Shielding for a Critical Room at 100 MHz

A critical room uses 5 mm thick carbon steel panels. Calculate the shielding effectiveness at 100 MHz.

Step 1: Material Properties

  • Conductivity, σ = 1.0 × 107 S/m
  • Resistivity, ρ = 1.0 × 10-7 Ω·m
  • Relative permeability, μr = 150
  • Frequency, f = 1 × 108 Hz
  • Thickness, t = 5 mm

Step 2: Calculate Skin Depth (δ)

δ = 503 × √(ρ / (f × μr))
= 503 × √(1.0 × 10-7 / (1 × 108 × 150))
= 503 × √(6.67 × 10-18)
= 503 × 8.16 × 10-9
≈ 4.1 μm

Step 3: Calculate Absorption Loss (A)

A = 131 × t / δ
= 131 × 5,000 μm / 4.1 μm
= 131 × 1219.5
≈ 159,760 dB

Again, absorption loss is very high theoretically, but practical limits apply.

Step 4: Calculate Reflection Loss (R)

R = 20 × log10 ( (σ / (4πfε))1/2 / 4 )
σ / (4πfε) = 1.0 × 107 / (4 × 3.1416 × 1 × 108 × 8.854 × 10-12)
= 1.0 × 107 / (1.112 × 10-2)
≈ 8.99 × 108
Square root = √(8.99 × 108) ≈ 29983
Divide by 4 = 29983 / 4 = 7495.7
R = 20 × log10(7495.7) ≈ 20 × 3.875 = 77.5 dB

Step 5: Multiple Reflection Correction (B)

Negligible due to high absorption loss.

Step 6: Total Shielding Effectiveness (SE)

SE ≈ 77.5 + 159,760 + 0 ≈ 159,837 dB

Practically, steel shields of 5 mm thickness at 100 MHz provide SE in the range of 70–90 dB, limited by construction and apertures.

Additional Technical Considerations for Critical Room Shielding

  • Seams and Apertures: Shielding effectiveness is significantly reduced by gaps, seams, and ventilation openings. Proper gasket and seam design per IEC 61000-5-7 is essential.
  • Frequency Dependence: Shielding efficiency varies with frequency; low-frequency magnetic fields require high permeability materials like Mu-metal.
  • Multiple Layers: Composite shields combining conductive and magnetic layers can optimize SE across broad frequency ranges.
  • Measurement Standards: IEC 61000-5-7 and IEEE Std 299 provide standardized test methods for verifying shielding effectiveness.
  • Environmental Factors: Temperature, humidity, and mechanical stress can affect shield performance over time.

References and Further Reading

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