332 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



Under these conditions the network can be represented by the eciuiva- 

 lent circuit shown in Fig. 1(c). This circuit consists of a parallel com- 

 bination of resistance and capacitance in which the capacitance is that 

 of the original two capacitances in series and the resistance is negative 

 and equal to four times the feedback resistor, Rj . Hence the magnitude 

 of the generated shunt negative resistance can be controlled b}^ adjust- 

 ment of Rf . One measure of the accuracy of this approximation is how 

 much the "constants" of the equivalent circuit change with freciuency. 

 Calculations of a typical case show that deviations in frequenc\^ of 

 ±5 per cent cause deviations in both capacitance and negative resis- 

 tance of ±0.05 per cent. Hence this approximation is very accurate for 

 narrow band applications. 



This circuit can now be used to advantage in a band filter. 



Confluent Band Filter 



A conventional confluent band filter is shown in Fig. 2(a). In this 

 structure the presence of dissipation in the series branches impairs 

 performance by introducing flat loss, whereas any dissipation in the 

 shunt branch not only produces flat loss, but, Avorse still, causes round- 

 ing of the transmission characteristic at the edges of the band. For 

 narrow filters having a small percentage band width, any appreciable 

 dissiptation in the shunt arm can degrade the transmission characteristic 

 beyond a reasonable tolerance. One good answer to this problem is to 

 use elements having an extremely low resistive component such as 

 quartz crystals. However, quartz is expensive and has other limitations. 

 Another solution is to build a negative resistance into the filter so as to 

 reduce the inherent element dissipation to zero or at least to a tolerable 

 value. In the present case a shunt negative resistance will be used to 

 compensate the shunt branch. This is done by splitting the shunt ca- 

 pacitance of Fig. 2(a) and inserting the circuit of Fig. 1(a). This can be 

 illustrated by an example. When the filter of Fig. 2(a) is designed to 

 give a 5 per cent band at a midfreciuency of 10 kc and impedance level 

 of 600 ohms the shunt branch offers an undesirably low impedance to 

 the compensating transistor circuit and in addition requires cumbersome 

 element values. Both difficulties can be corrected by using capacitative 

 impedance transformations on each side of the shunt branch, thereby 



