CURVED WAVE GUIDES 



2i 



modes of propagation in a curved wave guide consists of both TEoi and 

 TMu waves, it follows that both modes must be superimposed in such a 

 manner that at the transition point the TM comi)onents cancel each other by 

 interference. 



Let the relative ampUtudes of the two TE components equal a and b; 

 then the corresponding amplitudes of the TM modes are aAa and bAt, 



20 



Fig. 4 



respectively, where Aa and A^ are the normalized voltage ratios per 1.2-5. 

 .\i the beginning of the curved section 



a -\- b = \ (TE amplitude) 



aAa + bAb = aAa - b/Aa = (TM amplitude) 

 Hence 



b = 



1 + Ai 



Al = W 



The two waves have different phase velocities and therefore interfere 

 with each other. According to 1.2-9, the difference between the phase 

 constants is 



I -4- M^ 



/35 - ^„ - (/32 - /3i) — ^^. 

 1 — W 



By means of equations 4-9, this can be transformed into 



/36 - /3a = 032 - iSiXp + q) 6-1 



