576 BELL SYSTEM TECHNICAL JOURNAL 



total transmission loss is usually appreciable in the transmitting band 

 of a \va\'e-filter near the critical frequencies. 



The three types of losses will now he considered separately and in 

 detail. 



1. Transfer Losses 



The transfer loss, L/, is by (6) equal to D, the diminution constant, 

 which is the real part of the transfer constant, T, of the \va\e-tilter 

 mid-part taken between mid-points. 



We have previously established the following: 



(1) T is the sum of the transfer constants of all the individual 

 sections, i.e., T = '2Tj; and (2) the transfer constant of a mid- 

 series or mid-shunt section is equal to the propagation constant, 

 V=A-\-iB per full section, of the corresponding ladder type; that 

 of a mid-half section is V /2. 



Hence, to get the transfer loss we need to know only the attenuation 

 constant, A, of each full mid-section, the half or whole of which forms 

 a part of the composite wave-filter structure. However, since the 

 interaction factor which is to be discussed later requires a knowledge 

 of the phase constant, B, as well, we shall consider both iiarts of liio 

 propagation constant at this point. 



Propagation Constant of Ladder Type Network. The relation between 

 the propagation constant T =A-\-iB. and the series and shunt im- 

 pedances, Zi and Zi, respectively, of the ladder type in Fig. 1 is known 

 to be 



coshr = i+i-. (8) 



Tlii> ai>plifs as well l(i an\- recurrent structure if c, and c_. c<irr('>i)nn(l 

 to the analytically equivalent ladder type. 



Let us introduce two variables U and F by making the substitution 



^ = U-\-iV. (0) 



The reason for this choice is that this ratio appears freciuentK' in 

 impedance formulae. Then in non-dissipative wave-filters, where 

 V=0, the transmitting bands include all frequencies at which U 

 satisfies the rclatii)n 



-l^U^O. (10) 



