ELECTRIC WA VE-FILTERS 



295 



2. It has both standard image impedances, each of which passes 



through the same cycle of values in all transmitting bands. 



3. Each il/-type or wave-filter of higher order derived from it can 



have an improved impedance characteristic which is the same 

 in all transmitting bands. 



4. The assumption that its impedances Zik and z^k are general in the 



analysis makes the results independent of any particular class 

 of wave-filter and hence applicable to all classes. 



5. This method of analysis sorts out certain valuable properties which 



are common to all classes by treating known groups of meshes, 



Zifc and S2fc, as units, thereby eliminating the necessity of 



considering each individual mesh which may be present in the 



interior of Zik and z^u of any particular class. 



It will be appreciated by the reader that the difficulties of the problem 



for one of the higher classes of wave-filters are thus greatly reduced 



over what they would be if each mesh had to be taken into account, as 



might be required by other methods. 



-o-Y^\/-o- 



2 ^/A/ 2 '^ikj 



-o-Y/V-o O o-IS/\f\rO- 



:^2/v 



Kk. 2^2^? W.vt^'^zh^ 



Fig. 2 — -"Constant k" wave-filter, the initial prototype; 

 ZikZ-ik = kr = R^ = Si constant, independent of frequency. 



The "constant ^" wave-filter of any class, shown in Fig. 2, will 

 be assumed known and is the starting point for obtaining the other 

 structures which are to follow. It has the formulas 



and 



cosh r, = cosh {Ak + IB,) - 1 + 2{Uk + iV,), 

 W,k = i?VH- Uk + iVk = Rik + iXik, 



W.k = 



R 



i?2 



diere 



Vl+ Uk + iVk 



Wi 



= R2k + iX-2k; 



Tk = transfer constant of a full section, 

 \Tk = transfer constant of a mid-half section, 

 Wik = image impedance at a series mid-point, 

 Wik = image impedance at a shunt mid-point, 



Zik ^ / ZlfeV 



(6) 



Uk+iVk = 



4z.,k 



2RJ 



