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Chassis Resonant Frequency

Calculate the lowest resonant frequency of a metallic enclosure (cavity resonator) to identify potential EMC problems.

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Formula

f_mnp = (c/2)√((m/a)² + (n/b)² + (p/c)²)

a,b,c— Chassis dimensions (m)
m,n,p— Mode indices

How It Works

A metallic enclosure forms a rectangular cavity resonator. At certain frequencies, electromagnetic waves bounce between the walls and create standing waves with very high internal field strengths. The resonant frequencies are given by f_mnp = (c/2)√((m/a)² + (n/b)² + (p/c)²), where a, b, c are the dimensions in metres and m, n, p are integer mode indices (at least two must be non-zero). The lowest resonant frequency is typically the TE₁₀₁ or TE₁₁₀ mode. At resonance, the enclosure can amplify internal noise and radiate it, or allow external fields to penetrate more easily. This is especially problematic for shielded enclosures: the shielding effectiveness is reduced near resonant frequencies. Apertures (ventilation holes, displays) further degrade SE near resonance.

Worked Example

Problem
A steel electronics enclosure is 300 mm long, 200 mm wide, 100 mm tall. What is the lowest resonant frequency?
Solution
1. Dimensions in cm: a=30, b=20, c=10 2. TE₁₀₁ mode: f₁₀₁ = (3×10¹⁰/2) × √((1/30)² + (1/10)²) = 1.5×10¹⁰ × √(0.00111 + 0.01) = 1.5×10¹⁰ × 0.1005 = 1508 MHz 3. TE₁₁₀ mode: f₁₁₀ = 1.5×10¹⁰ × √((1/30)² + (1/20)²) = 1.5×10¹⁰ × √(0.00111 + 0.0025) = 1.5×10¹⁰ × 0.0601 = 902 MHz 4. Lowest resonant frequency = min(1508, 902) = 902 MHz (TE₁₁₀) Result: The first cavity resonance is at 902 MHz. Frequencies above 900 MHz may experience enhanced shielding failure for this enclosure.

Practical Tips

  • ✓If cavity resonances fall within the product's operating frequency range, add lossy RF absorber material (carbon-loaded foam) inside the enclosure to damp resonances.
  • ✓Place the PCB off-centre inside the enclosure — this avoids coupling to the cavity resonance node at the geometric centre.
  • ✓Keep all aperture dimensions below λ/20 (1.5 cm at 1 GHz) to minimise slot antenna efficiency; use multiple small holes rather than one large opening for ventilation.

Common Mistakes

  • ✗Assuming a metal box provides infinite shielding — near resonant frequencies the SE can drop to near zero; this is critical for GHz-range circuits.
  • ✗Ignoring higher-order modes — multiple resonances exist at harmonics; map all modes below your highest clock frequency.
  • ✗Thinking apertures only reduce shielding — apertures near resonant frequencies can detune the cavity, but large apertures also create slot antennas that radiate independently.

Frequently Asked Questions

No — cavity resonant frequencies depend only on the physical dimensions (at first order). Material conductivity affects the Q-factor and resonance sharpness; a higher-conductivity material produces a sharper, higher-Q resonance, while a lossy material (coated steel, aluminium) broadens and damps the resonance.
Yes. Changing the enclosure dimensions changes the resonant frequencies. Adding dividers or baffles inside the enclosure breaks it into smaller cavities, pushing the resonances to higher (and potentially less problematic) frequencies. Adding RF absorber material is the most practical retrofit fix.
Both. At resonance, the cavity can concentrate internal fields and re-radiate them through apertures more efficiently than at non-resonant frequencies. Conversely, external fields at the resonant frequency can penetrate more easily (immunity problem). Good EMC design addresses both emission and immunity scenarios.

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