FILTERS FOR CARRIER SYSTEMS 



211 



Analysis of an insertion loss ladder tilter shows Ihat it may be considered 

 a composite of image sections which are not matched in image impedance. 

 As a composite filter this means that the effective pass band has been split 

 into a number of pass bands each separated by a small attenuation region. 

 Darlington has formulated the process by which these bands can be so 

 arranged that advantage can be taken of the fact that the image attenua- 

 tions in these bands for small mismatch are comparable to the terminal 

 effects and that reflection gains up to 6 db are possible in the same regions. 

 The combination of these effects, which can be controlled up to and in- 

 cluding the cut-off, gives the insertion loss -filter its improved performance 

 since the efective and theoretical cut-offs can be made identical, with no 



FREQUENCY, f — ^ 



Fig. 11 — Non-dissipative filter characteristic obtained by use of Tchebychefif param- 

 eters in pass bands and attenuation band. 



frequency space needed for the rounding due to the terminal effects in 

 image filters. 



In general the mathematical steps required to design a filter by this 

 method are as follows: An insertion loss frequency function is chosen which 

 will satisfy the filter requirements and will lead to a structure economical 

 of elements. From this are found the open and short circuit impedances 

 of the proposed network which is normally of the standard lattice or ladder 

 forms. Finally from these expressions the element values are determined. 



The particular form of insertion loss design employed for the filter de- 

 scribed here is a special case of the general theory. The filter requirements 

 lent themselves to the use of Tchebycheff parameters simultaneously 

 in the pass bands and attenuation band. The application of these param- 

 eters was first described by Cauer.^ The typical non-dissipative charac- 

 teristic resulting from their use is shown on Fig. 11. It is seen that the 



