THE ELECTRIC WAI'E-EILTER 



25 



The lattice network of l*'ig. IS lias in each branch a one-p(jinl im- 

 pedance obtained by means of a duplicate of the given network A^ 

 and an ideal transformer. The two lattice branch impedances are 

 Zq-\-Zr^2Zqr whcrc the three impedances Z,, Zr, Z^r are the 

 efTective self and mutual impedances of the network N regarded as a 

 transformer. This lattice network has identicalK' the same propaga- 



O 



a 



N 



-o 



N 



o 

 o 



Zo 



Fig. 17 — Lattice Unit Equivalent to Two Sections of Fig. 1 Assumed to be 



Symmetrical 



tion constant as the single network N shown on the left. Since the 

 lattice cannot have difTerent iterative impedances in the two direc- 

 tions, it actually compromises by assuming the sum of the two itera- 

 tive impedances presented by N. A physical theory of the equival- 



§®S 



Fig. 18 — Lattice Network Having the Same Propagation Constant as N and an 

 Iterative Impedance Equal to the Sum of the Two Iterative Impedances of A'^ 



ences shown in Figs. 17 and 18 has not been worked up; the analytical 

 proofs were made by applying the formulas given in the appendix 

 under lattice networks. 



Without going to more complex networks it is, of course, not pos- 

 sible to get a symmetrical iterative impedance, but that is not necessary 

 for our present purposes where we are concerned primarily with the 



