A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 363 



6.0 

 5.5 



5.0 

 4.5 

 4.0 



3.5 



EFFI. 



C 3.0 

 (SAT.) 



2.5 

 2.0 

 1 .5 

 1.0 

 0.5 



0.5 



1.0 



1.5 



b 



2.0 



2.5 



3.0 



Fig. 2 — The saturation eff./C versus fe, for k = 2.5, QC = 0.2, and C = small, 

 0.1 and 0.15. The dotted curves indicate the values of h for m = \, 0.94, 0.67, and 

 0.3 of ;ui(max) respectively. 



output in the presence of the backward wave. For simphcity, we shall 

 use the approximate solution (12b) which can be written in the form 



B{z, t) ^ Real Component of 



ZqIq c 



4C 2(1 + hC) 



dax(y)Y ^ (da,{y)\- j^^-v,.-,y+j^\ (12d) 



with 



tan ^ = 



dij 



(laiiyT 

 dy , 



dy 



dchiyY 

 dy , 



As mentioned earlier that the complete solution of (6) is obtained by 

 adding to (12b) a complementary function such that 



-yu 1+ r Qz 



ZqIq 



+ 



c 



4C 2(1 + bC) 



dy:) ^\dy ) ' 



-hy+ji 



(25) 



