An equilateral triangular reflector is inserted into an E-plane symmetrical T-junction in order to improve the wave transmission characteristics from the truncated-guide to the through-guide. The reflector is installed in contact with the wall of the through-guide facing the junction plane. In the case that the truncated-guide width b is equal to the through-guide width c, we find that the larger the top angle of the triangle is made, the better the wave transmission becomes. In particular, we can attain a remarkable improvement in obtuse triangles of the top angle θ100 and the height h0.6b. For instance, in the triangle of θ120 and h0.6b, at least 99.5 percent of the energy fed from the truncated-guide transmits evenly into the other two arms, and 0.5 percent at most reflects over the frequency range of 0.31b/λg0.37. The λg is the guided wavelength.

Upon the close examination of some typical papers treating E-Plane Symmetrical T-junctions, we derive peculiar equivalent circuits of the T-junctions in terms of the direct sum representation of the three-port. We show that the circuit elements can be determined by use of the Weissfloch nodal-shift method and that the circuits give an unified description and some new physical meanings of Lewin's equivalent circuit. Allanson-Cooper-Cowling's one, and others. Then we also give an analytical derivation of the direct sum in terms of a system of integral equations rearranged in a hybrid matrix whose determinant is nearly equal to zero for a tee. This property of the hybrid matrix allows the number of independent parameters to be reduced by one in a good approximation. Further the stationary values of the variational equations equivalent to the integral equations straightforwardly give the circuits elements.

The transmission and reflection characteristics of a H-plane symmetrical T-junction having a reflector near the junction plane are theoretically studied. The reflector is an equilateral triangle post, and it is installed in contact with the wall of the through-guide facing the junction plane to improve the wave propagation from the truncated-guide to the through-guide. In case of equal cross section, we find an optimum reflector, the top angle of which triangle reflector is 0 degree and its height is about half of the guide width. Roughly speaking, the fin, that is, the reflector of 0 degree has the characteristic value of (transmission coefficient |S12| between the truncated-guide and the through-guide) 0.705 over a wide frequency range. This value is nearly equal to the upper limit value of |S12| 1/20.7071. Thus 99.4 percent (0.70522) of the energy fed from the truncated-guide transmits evenly into the other two arms, and 0.6 percent reflects. The problem is treated by a method of combining the boundary-element method and a hybrid-representation circuit equation.

All the elements of the direct-sum representation circuit matrix for E-plane symmetrical T-junctions are shown to be given by the stationary values in a variational principle. It is proved that the matrix is approximately singular.

An analytical basis in given for the direct-sum representation circuit equations that played a central role in a previous paper, where the wave transmission between the truncated-guide and the through-guide of a H-plane symmetrical T-junction was shown to be remarkably improved by instaling a fin about one-half height of the guide width on the wall facing the junction plane. The analytical theory yields simple formulas for some circuit-matrix elements. Furthermore, in the application to the fin it is found that only the top of the fin makes a decisive role for the improvement.