Section 7.2 · Home exercises · 3 of 4
Home exercise 7.2.3: An evanescent TE_1 field
An evanescent TE field
#In an air-filled parallel-plate guide with , a sheet of current flowing along (parallel to the plates) at is driven at .
- Explain why this source excites TE modes only.
- Find and show that TE cannot propagate.
- Find the attenuation constant of TE in Np/m and dB/m, and its wave impedance.
- At what distance is the TE field below its value at the source?
A source drives only field components along its current. Below cutoff with , and the wave impedance becomes imaginary.
An -directed current can drive only . In the parallel-plate guide only the TE modes have an component (TE: , TM: , TEM: ).
, so is imaginary: TE (and every higher mode) is evanescent.
The impedance is inductive.
in field: .
With purely reactive, : the evanescent field stores energy near the source but carries no power.
The decay is almost independent of frequency well below cutoff, : about per plate spacing. Higher TE modes die even faster (TE: ). This is the principle of the waveguide-below-cutoff attenuator and of shielded ventilation openings (Exercise 7.1.3 in Section 7.1).