IDEAL FILTERS 251 



The loss characteristic reveals that no very high degree of suppression 

 is attained. In fact, the loss falls to about 16 db in the trough beyond 

 the first reflection peak. So serious a prejudice in favor of the phase 

 characteristic would render the design unsuitable for certain engineer- 

 ing purposes. There are open, however, several possibilities for in- 

 creasing the attenuation. Small modifications in the theoretical 

 design parameters of the type which have been described, and in 

 particular, slight separations of the theoretically coincident impedance 

 controlling frequencies in the two arms of the lattice, enable the loss 

 to be somewhat improved without much degradation of the phase 

 characteristic. If very much higher attenuation is demanded, it can 

 be provided by two simple structures of this type, separated by a 

 resistance pad to preserve the reflection effects upon which the phase 

 characteristic depends. 



Further possibilities are suggested by combination of two principles 

 already developed. It has been observed that a reduction in the 

 three-quarter spacing of the cut-off would improve the selectivity of 

 the structure but would also unduly increase the slope of the phase 

 characteristic in the transition interval. We have also seen, however, 

 that the result of uniform dissipation in the network elements is to 

 diminish the phase shift in this region. Hence our analysis suggests 

 that we may be able to obtain the desired phase characteristic in 

 conjunction with the shorter cut-off spacing necessary for high 

 selectivity if we deliberately increase the dissipation in the network. 



A concomitant result of such procedure is seen to be an increase in 

 the uniform loss in the transmission band, which may not always be 

 desirable. Neither does the attempt to provide the phase property 

 without sacrifice of high loss through the introduction of uniform 

 dissipation represent the most effective attack on the problem. To 

 achieve this end, resistances must be associated with the reactive 

 elements of the lattice impedances in a precisely determined manner, 

 not to be deduced solely from the foregoing theory of reactive net- 

 works. The elaboration of the theory to include also resistive im- 

 pedance elements serves to determine a filter whose attenuation 

 changes continuously from a low, uniform value in the pass-band to an 

 arbitrary value in the attenuation bands with linearity of phase shift 

 and, in addition, the third ideal property of constant impedance. 

 The general theory, however, can more appropriately form the subject 

 of a subsequent paper. 



The solution of this problem completes the application of the 

 methods for realizing ideal filter properties. We have seen that if all 



