## 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

- length only
- length and width only
- length, width and height
- height only

## Answer

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

$${f}_{mnp}=\frac{1}{2\sqrt{\mu \epsilon}}\sqrt{{\left(\frac{m}{L}\right)}^{2}+{\left(\frac{n}{W}\right)}^{2}+{\left(\frac{p}{H}\right)}^{2}}$$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 f_{110}. 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 TM_{001} 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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