704 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



ference discrimination even in cases where there is difference between 

 the desired and undesired modes' phase constants, to achieve very large 

 discriminations. In the TMn discriminations listed above, the values for 

 TE31 are not great but are consistent with computed values for the 

 coupling length and the coupling function employed; longer coupling 

 lengths would produce better TMn versus TE31 discriminations. 



A TIGHTLY COUPLED TEio° TO TEoi° WAVE TRANSDUCER* 



A highly efficient means of transferring power from dominant-mode 

 rectangular waveguide to one of the higher modes of a multi-mode wave- 

 guide would be essential in a waveguide transmission system. When 

 several modes can propagate in one or both of the guides, the problem 

 of achieving complete power transfer is more difficult and requires some 

 new techniques. This section describes these techniques and gives ex- 

 perimental data for a circular-electric-wave (TEio° — TEoi°) transducer. 



The desired transducer was reciuired to make the wave transformation 

 between a single-mode rectangular waveguide and the circular electric 

 mode (TEoi°) of an 0.875" round waveguide at a nominal frec^uency of 

 24,000 mc. The 0.875" round waveguide at this frequency will support 

 10 modes of which the circular electric mode and its degenerate partner 

 TMii° are the fourth and fifth in order of appearance. 



The minimum length of the coupling interval reciuired to achieve mode 

 discrimination may be estimated using loose coupling theory (equation 

 4). The mode nearest to TEoi° in phase constant is the TEsi^ and for 

 this mode a coupling length of about 0.18 meters is recjuired in order to 

 produce a A'alue of ^/tt equal to unity. As shown by equation (5) for 

 uniform coupling, it is necessary to have ^/tt ec^ual to unity or greater in 

 order to develop discrimination against the undesired mode. 



The maximum coupling coefficient permissible for a given amount of 

 mode impurity at the complete power transfer point may be estimated 

 using the tight coupling theory of the preceding sections. For example, 

 equations (31) and (32) show that for the ratio (/3i — /32)/c equal to 10, 

 the transfer loss to the undesired wave will always be greater than 14 db 

 (regardless of the length of the coupling interval), corresponding to an 

 energy loss for the desired wave of less than 0.2 db. For the TEoi° and 

 TEsi^ modes the calculated values of /3i and ^2 lead to the conclusion 

 that the coupling coefficient c between TEsi^ and TEio° must be less 



* When discussing the modes of hoHow metallic waveguides of different cross- 

 sectional shapes, it has been found convenient to use a superscript to designate 

 the shape of the cross section. (See G. C. Southworth, Principles and Avplicatinns 

 of Waveguide Transmission, D. Van Nostrand Co., 1950). Thus, TEio^^ refers to 

 the TFio mode in rectangular waveguide. 



