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THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



elements must be for good performance. As in the previous case, a 

 transistor negative resistance is used to compensate the anti-resonant 

 portion of the shunt arm. The magnitude of this resistance can also be 

 adjusted to serve the additional purpose of compensating for resistance 

 in the series resonant circuit in the shunt arm, as well as the series reso- 

 nant circuits in the series arms. 



The transmission of a non-dissipative m-derived band filter between 

 unit resistive terminations is 



.e = 



kp[{\ — m)'p^ + (2 — 2m -f- /c )p + (1 — 7n)\ 



{m'p^ + A;p + w) [p4 + km'p^ + (A;^ + 2) p^ -f- km'p + 1] 

 where m = A/ 1 — ij- ) 



Assuming no dissipation a peak section with an m of 0.86 will give the 

 characteristic shown in Fig. 7 labeled "Ideal Passive". However, when 

 this filter is constructed with typical elements the curve labeled "Prac- 

 tical Passive" results. By introducing a suitable amount of negative 

 resistance the transmission of the practical filter can be made comparable 

 to that of the ideal filter, as illustrated by the curve labeled "Practical 

 Active". 



For maximum utility active filter sections must be capable of being 

 connected in tandem to form composite filters without instability, re- 

 flections, or interactions. Fig. 8 shows that these filters meet this require- 

 ment by giving the measured transmission of a band filter composed of 

 two dissimilar peak sections. On the basis of attainable electrical charac- 



c — 1( — ^WT" — ^^/\ j_ \AA/ — ^w^ — 1( — 



Fig. 6 — Active M-derived band filter. 



