960 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



/3o -fTT^Tfo COT 5^ 



Fig. 6 — Real and imaginary parts of the reverse propagation constant /3_ 

 of a fiat helix versus a for various p and for a = 0.1 (the parameter a is marked 

 along the curves). The forward propagation constant has a ver\- small imaginary 

 part which hardly varies with a. 



are shown in Figs. 9(a), (b) and (c), where /3 is plotted against Xq for 

 various fixed a for two vahies of p. It is to be noted that the introduction 

 of any characteristic length or scale into the problem, such as is provided 

 here by the distance .to immediately produces a great complication in the 

 mode spectrum. The plane helix with the ferrite in contact may be 

 thought of as a highly degenerate problem. 



To carry out loss calculations using the appropriate expressions for 

 IX -\- K sgn (3 would be very tedious in the separated case. However, it 

 was pointed out in Part 1 that to order a the expressions for /x and k 

 are given correctly if we put a + ja in place of a in the lossless formulae 

 and that, in consequence, for small a, the imaginary part of the propa- 

 gation constant is approximately given by 



a — • 

 da 



In Figs. 10(a) and 10(b) the loss calculated in this way for the cases 

 considered in Figs. 9 is shown. 



