THE ELECTRIC WAVE-FILTER 17 



Otherwise leaves the curve approximately uinhaiigcd. The full line 

 curves for R^ and A'l show that in the ideal case the iterative im- 

 pedance is pure resistance and pure reactance in the pass and stop 

 bands respectively, and that resistance smooths the abrupt transition 

 at the critical frequency. 



The high pass wave-filter shown by Fig. 9 passes the band which 

 is stopped by the low pass wave-filter of Fig. 8, and vice versa. For 

 this reason the two wave-filters are said to be complementary. 



Another set of two complementary wave-filters is shown by Figs. 

 10 and 11, one of which passes only a single band of frequencies, 

 not extending to either zero or infinity, while the other passes the 

 remaining frequencies only. The single pass band of Fig. 10, em- 

 bracing a total phase change 27r on the B curve, is actually a case of 

 confluent pass bands, each of which embraces the normal angle tt. 

 The tendency of the two simple pass bands to separate, and leave a 

 stop band between them, is shown by the hump in the dotted at- 

 tenuation constant curve at 1,000 cycles. If, instead of the two 

 simple bands having been brought together, one of them had been 

 relegated to zero or infinity, the single remaining pass band would 

 have exhibited the normal angular range r in the B curve, and there 

 would have been no hump in the dotted A curve. The stop band of 

 Fig. 11 also illustrates peculiarities which are not necessary features 

 of a wave-filter with a single stop band in this position. This wave- 

 filter is obtained from Fig. 7 by making all bands vanish except 

 Pi, Sz, So and P3, — by extending P2 to zero, P3 to infinity, and making 

 S3 and Si coalesce, so that the attenuation becomes infinite in the 

 stop band without passing from a stop ( — ) to a stop (-f-) band. 

 The coalescing stop bands are responsible for the rapid changes in 

 the B, Ri, and A'l curves of Fig. 11 which would not have appeared 

 if, in Fig. 7, the same pass band had been obtained by retaining Pi, 

 52 and P2 and making all other bands vanish. 



An extreme case of complementary wave-filters is shown by Figs. 

 12 and 13, where no frequencies and all frequencies are passed re- 

 spectively. The first result is obtained by combining inductances 

 alone, which, as has been pointed out above, can give only an at- 

 tenuated disturbance devoid of wave characteristics. The wave- 

 filter shown for passing all frequencies has inductance coils in the 

 line, and capacities diagonally bridged across the line. This wave- 

 filter combines a constant iterative impedance with a progressive 

 change in phase which is sometimes useful."* An outstanding char- 



* A theoretical use of the phase shifting afforded by the lattice artificial line was 

 made at page 253 of "Maximum Output Networks for Telephone Substation and 

 Repeater Circuits," Trans. A. I. E. E., vol. 39, pp. 231-280, 1920. 



