Section 7.3 · Home exercises · 1 of 4
Home exercise 7.3.1: A honeycomb vent below cutoff
A honeycomb vent below cutoff
#The ventilation panel of a microwave oven (or of a shielded room) is a honeycomb of square metal tubes, in cross-section and long.
- Find the cutoff frequency of the lowest mode of one tube.
- Find the attenuation constant of that mode at , and the attenuation of the field through the tube in dB.
- Repeat (b) at .
- Which frequencies would the panel let through?
A square tube of side has two degenerate lowest modes, TE and TE, with . Below cutoff each decays as with by Eq. (7.3.6), and the field drops by over the length .
, for TE and TE alike. The next modes, TE and TM, start at .
:
: through the tube.
Only fields above propagate through the tubes. Below that the panel attenuates by roughly per tube width of depth, almost independently of the frequency, and more for deeper tubes.
Far below cutoff : , the limit that the value approaches. A wave with has a reactive wave impedance and carries no power through the tube: the panel reflects, it does not absorb.
The attenuation depends on the depth-to-width ratio of the cells, not on the hole size alone: tube widths give about . A wire pushed through a cell turns it into a coaxial line with a TEM mode and no cutoff (Section 7.5), which destroys the shielding.