ELECTRIC WAVE-FILTERS 325 



from computed loaded line impedances (or perhaps from measured 

 impedances), instead of directly from certain primary line and coil 

 data. This makes it comparatively easy to take account of variations 

 with frequency of the constants, such as line leakance and loading 

 coil resistance. 



The mid-load iterative impedance is given by the formula 



'^.^ -1- Sy\/ , , ^L „„,. ^^7 



the mid-section iterative impedance by 



'l+||coth^^ 



K, = k I ^ --' (39) 



l+||tanh^ 



In these formulas y and k are the propagation constant and iterative 

 impedance, respectively, of the non-loaded line which may be computed 

 on the basis that the shunt capacity of each loading coil and its leads is 

 assumed to be concentrated, half at each end, and that each half is 

 added in the formulas to the line capacity of the adjacent section. 

 5' is the load spacing and Zl the load impedance. 



4.2 Mid-Load Basic Netivork 



This basic network has the structure and general design shown in the 

 upper part of Fig. 17. The magnitudes of its elements are fixed 

 when R and/o are known, since 



Llk = R/T^fo, 



and (40) 



Cok = l/irfoR; 



where R is the impedance ^LiklC-ik and /o is the critical frequency. 

 Its impedance in the frequency range considered is quite accurately 

 given by 



which relation will be used for design purposes. The values of R and 

 /o are here determined for any particular loaded line by assuming that 

 at two frequencies, /a and/t, the corresponding values of r, respectively 

 r„ and r;,, are equal to the resistance components of Kx as computed at 

 those frequencies from (38). The frequencies /« and /& are chosen in 



