the coupling between discrete hole on the broad walls of two parallel rectangular waveguides is studied. Optimum characteristic limitation of single hole (or hole-pair) in the [u1
u2] band is obtained: the optimum coupling smoothness ismin the maximum limit of minimum directivity in the band is(dB)It was proved that: the circular holes cannot fulfill the two optimum limits simutaneously. The conditions of optimum single hole (or hole-pair) should beIn general
there exsists the following inequalitywith optimum limit of the bandwidth