LearnEMC - EMC Question of the Week, June 7, 2021

A computer with labeled dimensions (40 cm by 38 cm by 16 cm)

EMC Question of the Week: June 7, 2021

The first (lowest) resonant frequency of a 40-cm x 16-cm x 38-cm rectangular metal enclosure is

below 10 MHz
approximately 380 MHz
approximately 540 MHz
above 1 GHz

Answer

The best answer is “c.” The resonance frequencies of an air-filled rectangular metal enclosure are given by the expression,

f_{m n p} = \frac{c}{2} \sqrt{{(\frac{m}{a})}^{2} + {(\frac{n}{b})}^{2} + {(\frac{p}{d})}^{2}}

where a, b and d are the dimensions of the enclosure; c is the propagation velocity; and m, n and p are non-negative integers (at least two of them non-zero). The assignment of dimensions corresponding to a, b and d is arbitrary, but for a<b<d the lowest resonant frequency is f₀₁₁. For this enclosure,

\begin{matrix} f_{011} = (1.5 \times 10^{8} m/s) \sqrt{{(\frac{0}{0.16})}^{2} + {(\frac{1}{0.38})}^{2} + {(\frac{1}{0.40})}^{2}} \\ = 544 M H z \end{matrix}

Of course, we have assumed that the question is asking about the first electromagnetic (not acoustic) resonance, and that the enclosure is mostly empty (e.g., not filled with a dielectric).

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