28 BELL SYSTEM TECHNICAL JOURNAL 



An inference drawn from the study of band niters in the preceding 

 section may be stated as follows: 



The selective figure of merit of a wave-filter designed to select a finite 

 band of frequencies is approximately proportional to the minimum time 

 required for sinusoidal currents within the transmission band to build up 

 their approximate steady values, divided by the number of filter sections. 



Another circuit of practical interest, which has been proposed as 

 a solution of the "static" problem in radio-communication consists 

 of a series of sharply tuned oscillation circuits, unilaterally coupled 

 through amplifiers. 23 This circuit is designed to receive only a single 

 frequency to which all the individual oscillation circuits are tuned. 

 The figure of merit of this circuit is approximately 



L 2 2 *- 2 [(w-l)!] 2 

 R (2n-2)l 



where n denotes the number of sections, or stages, and L and R are 

 the inductance and resistance of the individual oscillation circuits. 

 The outstanding fact in this formula is the slow rate of increase of 

 5 with the number of stages. For example, if the number of stages is 

 increased from 1 to 5, the figure of merit increases only by the factor 

 3.66, while for a further increase in n the gain is very slow. This gain, 

 furthermore, is accompanied by a serious increase in the "sluggish- 

 ness" of the circuit; that is, in the particular example cited, by an in- 

 crease of 5 to 1 in the time required for signals to build up to their 

 steady-state. 24 



The outstanding deduction of practical importance to be drawn 

 from the preceding is that, as regards disturbances which are pre- 

 dominantly random, irregular, or discontinuous, it is useless to employ 

 selective circuits of extremely high selectivity. The gain in signal- 

 to-interference ratio is very small when the selectivity is increased 

 beyond a moderate amount, and is only gotten by making the circuit 

 relatively sluggish and slowly responsive. 



The preceding discussion is, for the reasons discussed above, not 

 applicable to selective circuits like the high pass filter, which transmit 

 an infinite band of frequencies. Considerable information, however, 

 regarding the behavior of the high pass filter to random disturb- 

 ances can be gotten by returning to formula (10) and comparing the 

 energy absorbed by the high pass filter, with that absorbed by a 

 pure-resistance network. Reference to formula (10) shows that the 



23 See U. S. Patent No. 1173079 to Alexanderson. 



24 When the number of stages n is fairly large, the selective figure of merit becomes 

 proportional to V» and the building-up time to n. 



