INDUCTANCES, CAPACITANCES AND RESISTANCES 



transmission and phase characteristics but the terminal impedance of the 

 pi version is 



Z=R 



Summary 



Low-pass 



L/2 L/2 



X 



inmr 



o— j-q 



.7'^' T 



C/2 



' CO 



.2co, 



+ J 



ft)/ 



CO 



\2col_ 



L= 2R/cv^ 



C-.2lw(^R 



wc=2/(LC)^'^ 



High -pass 

 2C 





URl2w^ 

 0.-1/2 0^/? 

 cye--V2ac;'/2 



OTHER L-C FILTERS 



The subject of filters is a vast one, and we can do no more than mention 

 some of the other types. Readers faced with particularly stringent filter 

 problems should refer to a speciahst work on the subject (E. A. Guillemin, 

 Communication Networks, New York; Wiley). 



The transmission characteristic of the classical filter is of the type known 

 as Butterworth or maximally flat. It is possible to obtain a squarer character- 

 istic by using a Tchebycheff type of filter, whose response is typically of the 

 form shown in Figure 5.26; evidently the transition between the horizontal 



3 



:i9 



Tchebycheff 



ButtcrwortK 





U> 



Ol> 



^»c' ^n 



Figure 5.26 Figure 5.27 



and sloping parts of the curve is more abrupt. Tchebycheff filter sections are 

 similar in configuration to the Butterworth type, but the component values 

 are different. 



If the filter has to discriminate between two frequencies rather close together, 

 a useful device is the m-derived section, which has — in the low-pass version — 

 a characteristic like Figure 5.27. This is a Butterworth response with a 

 bottomless trough in the transition region; that is, it is a null-transmission 

 network. If the frequency of null-transmission is to be cji).^, then to get an 



90 



