102 BELL SYSTEM TECUMCAL JOVKSAI. 



quency of infinite attenuation occurs and the atleniialion is finite 

 at zero frcfiuency and infinite frec|ucncy. 



As a general rule the phase shift characteristics shown in Fig. 44 

 are similar lo the corresponding characteristics shown in Fig. 7. The 

 phase characteristics of the former, within the pass bands are, in 

 general, however, of a distinctly different character than those of the 

 latter even though the phase constant at the cut-off frequency and the 

 mid-frefjuencN- ma\- he the sjime. Phase characteristics 21 and 24 

 (Fig. 44) are of special interest, however, in that while thc\- Ijelong 

 to the peak type sections, the phase is of the same sign throughout 

 the entire frcciuency range. .Also phase characteristics 22, 29, 30 and 

 32 have a unic|ue property, for band pass structures, in that the phase 

 undergoes a change in sign within one attenuation band. 



In regard to the impedance characteristics, it is noted from Table III 

 that no novel impedance characteristics are obtained in structures 

 having negative inductances as compared to the structures not having 

 negative inductances. This is a \aluable property of the prototype 

 structures listed in Tai)le III as it permits composite filters to be 

 readily formed utilizing both the sections of Tables II and III.'* 



Characteristics of a Typical Filter. In order to illustrate the deriva- 

 tion of design formulae for a specific prolot>'pe having negative 

 inductances, consider as an example the band pass structure 3 — 3' of 

 Table III. W'e shall neglect the effect of dissipation on the character- 

 istics of the structure, as the treatment of dissipation has been pre\i- 

 ously outlined. The proiotyi)e cited is illustrated in I-"ig. 4oA. Two 



~|k5W^-j-^wjr^[-= ' — II 



ABC 



Fig. 45— I'roloiyiK.- Siliiin (.'ont.ilning Negative Inductance, an<l Two uf Its 



I'hysically Realiz^ible Forms 



meth(Kls of physically obtaining >uili a priii(ii\pi' .ire illusiraied in 

 Figs. I.")n and C. In this structure ilie series im|R(lance Zi is 



'"=K-'''-Jc)- 



(92) 



" For a Kfiicral method of provinR the equality of tlio image impedances of sections 

 containing negative inductance and of appropriate sections cont.iining no negative 

 inductance, refer to the Apfx-ndix. 



