TRANSMISSION LOSS DUE TO RESONANCE OF CONVERTED MODES 901 



Matrices 1 and 1' describe the system completely and from them, the 

 transmission coefficient results, 



ao 



— 1 oie 



rlze 



-jlBiA* 



1 + 



o ri2 



(2) 



[1 - (r?2 - TnT,,)e-'''^^'''Y - (rue"^'' + r226-^''^)^ 



where 



A = 1 + 



£02^ 



.roi/ 



-y(92-«i) 



A * is the complex conjugate of A 

 Toi* is the complex conjugate of Toi 

 ro2* is the complex conjugate of ro2 

 Furthermore, let us make the following simplifying assumptions 



I 



|ro2 



/3=2 



|3=0 I^U, 



-,/l. 



Equation (3) indicates that if in Fig. 1, lines 1 and 2 were matched, 

 line would also be matched looking toward the junction. Equation (4) 

 states that almost all the transmission is made from to 1 , or that there 

 is small mode conversion to the spurious mode 2. Equation (5) assumes 

 that the transition is nondissipative. The first two conditions are ful- 

 filled when the transition is made smoothly. The last is probably the 

 most stringent one, especially if the transition is a long tapered wave- 

 guide section, but it is always possible to imagine the transition as 

 lossless and attribute its dissipation to the waveguides. 



0- — 



- — bo ^ — aa 





—2 



Fig. 1 — Schematic of a three-port junction. 



