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The coaxial directional coupler of the Bethe-Hole type consists of two coaxial transmission lines crossed at an angle of 60° and coupled by a single circular hole. It has been previously shown that this device should have perfect directivity at any wavelength, provided that (a) the diameter of the coupling hole is small compared with λ/8, (b) the thickness of the hole is infinitesimal, and (c) only the dominant TEM mode is allowed to exist in the transmission lines. These requirements can easily be satisfied in practice. However, with coupling holes small compared with λ/8, the coupling is too weak for many of the conventional applications (a typical coupling is 50 db). If the above requirements on hole size are disregarded and the hole is made large enough to provide stronger coupling, such as 25 db, the device no longer behaves in a simple manner. The directivity is no longer perfect, the angle for optimum directivity is no longer 60°, being dependent upon frequency. A reflection is also caused in the main transmission line due to the presence of this large hole. It was found that the behavior of the large hole coupler could be explained by assuming the presence of higher order modes in the vicinity of the coupling hole. These higher order modes can be represented by an equivalent circuit which consists of a series inductance in the line.