## EMC Question of the Week: May 30, 2022

For a rectangular metal enclosure whose length is greater than its width, and whose width is greater than its height, the lowest resonant frequency is a function of its

1. length only
2. length and width only
3. length, width and height
4. height only

The best answer is “b.” The resonance frequencies of a dielectric-filled rectangular metal enclosure are given by the expression,

$f mnp = 1 2 με m L 2 + n W 2 + p H 2$

where L, W and H are the dimensions of the enclosure; μ and ε are the permeability and permittivity of the dielectric that fills the cavity; and m, n and p are non-negative integers (at least two of them non-zero). When L>W>H, the lowest resonant frequency is f110. The two longest dimensions determine the lowest resonant frequency.

For cavity resonances between planes in a rectangular circuit board, the lowest resonant frequency is the TM001 mode. This is because the edges are not shorted and can support a non-zero tangential electric field. The lowest resonant frequency supported by planes in a rectangular circuit board is therefore a function of the longest dimension only. It occurs when the longest plane dimension is approximately one half-wavelength in the cavity dielectric.

The lower resonant frequencies of rectangular enclosures and circuit boards can be calculated using a cavity resonance calculator.

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