K.ixsMissioN cn.-tR.icii:Risrics or MAVT.-I-ILI I.KS 5M 



The substitution of (3G) or (.S7) in Ft gives an identical loiili, as 

 shown by relations (JJo), provided .v is the same in both. .1 single 

 terminal loss I.x may then apply to either, wliicli is (IdiiuMl frum ((j) as 



R'/K.i+R K,i+R 



gi\ing by (35) 



\^l I \l+ Uk+tvul / 



A comparison of (34) and (38) shows tliat when w = l and x = .'•>, 

 Lm = Lx as should be the case. 



3. Interaction Losses 



The interaction loss defined in (6) is expressible in its genera! form as 



Lr = \og,\l-rarte--T\. (39) 



It depends not only uf)on the transfer constant 7', includiiit; both 

 diminution and angular constants, but also upon the complex reflec- 

 tion coefficients, r^ and r^, at the two ends. That is, it is a function 

 both of the internal structure and of the terminations of the wave- 

 filter. For this reason its determination offers the most complexity 

 of all the three types of losses and, in fact, requires a knowledge of 

 the transfer loss. On the other hand, it is usually the least important 

 part of the total transmission loss and may usually be omitted except 

 at frequencies within a transmitting band and near a critical frequency. 



The transfer constant T = D + iS is given by the relations aiul 

 formulae developed when considering the transfer loss. 



The multiplication of the reflection coefiicients and the square of 

 the transfer factor is simplified to a problem in addition by expressing 

 each of these coefficients in the exponential form, 



and 



rt, = e-^''-'"K 



Then, putting r^rtf -^ = e~''~'<', 



Lr = l log, {l+e-^P-2e-'' cos Q), f lOt 



where P = Ga + Gt-\-2D. 



and Q = Ha + ni,+2S. 



