OTHER L-C FILTERS 



m-derived filter we take a classical filter of cut-oif frequency Mq and define 

 m so that 



and 



m 



1 



CO. 



\(0, 



a/2 



(low-pass filters) 

 (high-pass filters) 



Thus, m varies in the range to 1 and is small when a>„ and mc are close 

 together. 



Then a low-pass T section transforms to m-denved by rebuilding it either 

 as in Figure 5.28b or as in Figure 5.28c. In the first of these null-transmission 



L 



2 



2 



<>-'T<nnrv"innJT»--o 



\C 







]-ml 



]-mK 



I'll! r> I i-iii fs, 



'm( 



(a) 



(b) 



Figure 5.28 



(C) 



is obtained by series resonance in the shunt arm, and in the second, by a 

 parallel resonance in each series arm. 



Similarly a high-pass T section, in the m-derived form, is either as in 

 Figure 5.29b, or as in Figure 5.29c. Once again, null-transmission occurs as a 

 result of resonance in the appropriate arm. 



2C 



m 



2C 

 m 



2mL 



41-^rHf 



o — ^ 



ImL 



\-rrP- 



1£. 

 m 



. S m 



hi 

 m 5 



(a) 



(b) 



Figure 5.29 



(C) 



In deciding which of the two alternative m-derived versions of each filter 

 type to use in a particular case, bear in mind that in general, capacitors are 

 more readily available than inductors, and cheaper; work out the values 

 required for each alternative, and see which is the more convenient. 



If m can be arranged to be in the neighbourhood of 0-6, it can be shown 

 that the impedance looking in at either end of the filter remains near to R 

 throughout the pass-band and to a frequency very close to Mq {Figure 5.30). 



The m-derived pi sections may be found by considering a long chain of 



91 



