394 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



waves. Unfortunately, coupling to slots in this orientation is small, re- 

 ([uiring several hinidred for complete power transfer. Such a large num- 

 ber would make the coupler too long. 



Coupling through holes in the center of the narrow wall of the rec- 

 tangular waveguide as shown in Fig. 2 allows only the longitudinal mag- 

 netic field Hz to couple when the electric field of the TEii° wave is 

 parallel to the hole containing wall. No coupling exists between the 

 TEio° waves and the TEu^ wave having an electric field perpendicular 

 to the plane of the hole. The use of longitudinal slots where practicable 

 minimizes perturbation of this wave. Since the desired TEio° — TEu 

 coupling decreases by 15 db from the 4 kmc to the 11 kmc bands (for 

 1.872 X 0.872" and 2.2" diam. guide), the layout of Fig. 1 suggests itself 

 since some coupling discrimination is present for the higher frecjuency 

 waves that pass through the lower frequency couplers. 



DESIGN OF ll-KMC COUPLER 



The objective of this design is to transfer all of the power from a 

 dominant mode rectangular guide into one polarization of the TEii° 

 forward traveling wave in an adjacent circular guide. Fundamental 

 coupled-wave theory"* shows that phase velocities must be matched in the 

 two guides to achieve complete power transfer. 



A standard rectangular guide size is selected and the round guide 

 size that has the same phase constant is calculated for the center of the 

 1,000-mc wide band. An approximate total length is selected for the 

 series of coupling holes that permits the holes to be spaced approxi- 

 mately X3/4 apart. The hole spacing is not critical although the non- 

 directional properties of \g/2 spacing must be avoided. The required 

 magnitude of multiple discrete couplings is shown in equation (40) of 

 Reference 4 to be: 



a 



(2) 



where n is the number of coupling holes and a is the amplitude of the 

 wave transferred at a single coupling hole for unit incident amplitude. 



Equation (3) expresses the power coupled from TEii° waves to TEio° 

 waves through a circular hole in a common wall of zero thickness where 

 P2 is the power propagating away from the coupling point in either 

 direction in the undriven guide, and Pi is in the driven guide. This deriva- 

 tion is based on the work of H. A. Bethe^ and some unpublished notes of 

 S. P. Morgan. 



