COUPLED WAVE THEORY AND WAVIXIUIDE APPLICATIONS 



()91 



O -0-6 

 ^ -0.4 



-0.04 

 -0.02 



0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 



CX IN RADIANS 



Fig. 30 — ■ Driven and undriven line wave amplitudes versus cz with (ai — a-ii/c 

 = -2 and (/3, - ,32)/c = 2. ~~ 



errors iii construction of devices intended to produce 71 = 72 . To facili- 

 tate discussion of this case we define 



and 



EJ _ 77- *** -|ai + i(c + ((3i-|-^2)/2)]x 



(37) 

 (38) 



where Ei and E2 are defined by (21) through (24). The relation between 

 £"1*** and El (or £"2*** and Eo) is the same as described in connection 

 with (35) and (36). 



Small deviations from 71 = 72 are represented in Fig. 29, which shows 

 El*** and E.*** versus ex for (ai - a2)/c = -0.03 and (^1 - ^2)/c = 0.5. 

 At ox = x/2 radians, the first complete power transfer point in the 71 = 72 

 case, the above values correspond to a phase difference ((3i — 182) x = 7r/4 

 or 45°, and an attenuation difference (ai — 0:2)0; = 0.03 7r/2 or 0.047 

 nepers (0.41 db) for the path length of the coupling distance. In the ab- 

 sence of the dissipation difference, but for the same difference in phase 

 constants, Fig. 20 shows that E2* reaches a maximum at —0.26 db near 

 ex = t/2, whereas the value including the dissipation difference (Fig. 32) 

 is —0.46 db. The latter two values differ by 0.2 db or one-half of 

 («! — 0:2).'^; when («! — 0:2) /c is small compared to unity, this is a general 

 result. 



More sizeable deviations from 71 = 72 are represented in Fig. 30, which 

 shows El*** and E2*** versus ex for (ai — a2)/c = — 2 and (/3i — /32)/c = 



