PIERCE. 



THEORY OF COUPLED CIRCUITS. 



309 



may be employed in both cases, provided the value of t^a or </>4 is less 

 than unity. For values equal to unity the wave length for the top 

 branch of the curve is infinite, and for greater values the wave lengths 

 of the top branch become imaginary. In this case the optimum wave- 

 length adjustment becomes single- values and must be read from the 

 lower branch of the curve. 



As an example of the manner 

 of using the auxiliary curve 

 (Figure 6) in the actual calcula- 

 tion of the optimum values of 

 A3 and A4, let us take a special 

 case. Suppose t = .30, rj^ = .1, 

 let us give various values to 774, 

 and compute the corresponding 

 optimum wave-length adjust- 

 ments of the Circuits III and IV. 

 A tabulation of the computation 

 follows as Table III. 



In compiling this table the val- 

 ues of <^3 and ^4 corresponding to 

 the different values of 174 were 

 calculated by equations (36) and 

 (.^7). The corresponding wave- 

 length ratios were then taken 

 from the curve of Figure 6. 



The results contained in Table 

 III are plotted in Figure 7. In a 

 similar way the resonance rela- 

 tions for various values of t 

 and of r]3 may also be obtained, 

 but the single example here com- 

 puted and plotted serves to show 

 the manner in which the coeffi- 

 cient of coupling and the damping factors contribute to determine the 

 optimum resonance adjustment of the two circuits. The important 

 facts to be noted are the following: 



1 . With given values of the coefficient of coupling and the damping 

 factors of the two circuits the adjustment for best resonance is in 

 general double valued. One may in general get best resonance either 

 by setting both circuits to a wave length appropriately longer than that 

 of the incident waves, or by setting both circuits to a wave length 

 appropriately shorter than the incident waves. 



^3 



Figure 6. Auxiliary curve to assist 

 in calculation of the optimum resonance 



adjustment. ^3 = % i/ 1. This 



^ VsVi 

 curve also gives optimum value of X4 if 



^3 is replaced by 1^4 



Vi 



V-- 



