COUI'LKI) WAVK THKOKY AM) WA V Kdll I)l': A Tl'LlCATIOXS G03 



the vacuum seal. R. Kompfner conceived this form of connection to 

 travelling-wax'e tubes while working Avith the Admiralty in England, 

 and demonstrated the usefulness of the idea here at the Laboratories. 

 Similar work was done by the group at the Ele(;tronics Research Lab- 

 oratory at Stanford University, and was described by S. T. Kaisel at 

 the August, 1953, West Coast LR.E. Convention. Both groups re- 

 (|uested pre-publication copies of this paper for use in their research. 



LOOSE COUPLING THEORY 



On the assumption that negligible power is abstracted from the driven 

 line of two coupled transmission lines, the magnitude and mode content 

 of the forward and backward waves in the side line may be written. With 

 reference to Fig. 2, there is assumed coupling between two uniform Hues 

 in the interval — L/2 to +L/2 along the axis of propagation, and no 

 coupling elsewhere. On the basis of loose coupling a normalized voltage 

 wave on line 2 may be written 



£-2 = i,o,-'^'^i'^^^^+^'^-\ (1) 



in which the phase reference is taken as x = —L/2. The forward current 

 // in the side line at the point x = L/2 is 



L 



If = KFM J I 4>(x)e''''^"^'-"^'^' dx, (2) 



2~ 



where 



— iirtd/Xl+l/Xz) 



" = '— z ■ 



(f){x) = a couplmg function. More precisely, 1/0 (.x) is the ratio of the 

 voltage on line 2, Ei{x), to the equivalent voltage generator in series with 

 line 1 at x. 



K = fraction of the transferred current which travels in the forward 

 direction. 



M = the transfer constant for the various modes which can propagate, 

 relative to the mode for which <p{x) is defined. The backward current lb 

 at the point x = —L/2 is 



h= {I - K)FM fl <t,lix)e-''''^"'''"^'^'' dx. (3) 



