ELECTRIC ir.l VE-FILTERS 



301 



where 



4 *> 



(7 = 1— ni-, 

 a = I — nrni 



111 



a" = \ - nrm'-m"\ etc., 



in an increasing sequence approaching unity. Wxk and Wu- are the 

 "constant ^" image impedances of formulas (6). The continuation of 

 this series of image impedances is quite obvious, a new factor appearing 

 alternately in the numerator and in the denominator. 



Each factor in the numerator gives the image impedance a resonant 

 point in an attenuating band where the image impedance is a reactance 

 and Uk < -1; that is, at Uk = —l/a, or -1/a", etc., neglecting 

 dissipation with Vk = 0. A factor in the denominator gives an anti- 

 resonant point; at Ui: = —1/a', etc. Since a' lies between a and a", 

 etc., these resonant and anti-resonant points alternate as in a general 

 reactance network. Only the resonant or anti-resonant point due to 

 the new factor added coincides with the point of infinite attenuation 

 in the corresponding new structure, as may be seen upon comparing 

 formulas (8) and (10), neglecting dissipation. These properties out- 

 side a transmitting band may or may not be desirable in certain kinds 

 of circuits. They are of importance when considering terminal losses 

 in an attenuating band, as in Section 2.6. 



1.5 Sequence 2 



Here the derived structures are obtained by performing in succession 

 the operations D^im), then Di{m'), Di{m"), etc., where the initial 



"Ccrriblaml hT Shujtil M-Jyyfxe S^aa^ MMzty^ Shwrib MMM-iype 



]]^(7n) 



Dj(7ri) 



R(-^^) 



Fig. 5 — Sequence 2. 



prototype is the "constant k" wave-filter. Using the same notation 

 and terminology as before, the wave-filters of Sequence 2 when ex- 

 pressed symbolically are 



"Constant ^" = |^^^, 

 Shunt if- type = D2{m)[k'], 

 Series J/J/'-type = D,{m')[_D.{fu)[kJ], 

 Shunt .l/,l/M/"-type = D;{m")lD,{m')[_D-,{m)[_k'J]'], etc. 



(11) 



