ELECTRIC WAVE-FILTERS 289 



manner, but uses the wave-filters of Sequence 2 and begins with the 

 shunt .l/-type. 



Any pair of these transducers ha\ing the same number and values of 

 the parameters have identical transfer constants; moreover, either 

 netw^ork might be obtained from the other, as inverse networks of 

 impedance product R'-. 



Theoretically, with dissipation neglected, the solution of the terminal 

 wave-filter impedance problem, as outlined above, can be carried to any 

 degree of approximation desired toward a constant resistance terminal 

 image impedance in all transmitting bands. Practically, however, it 

 is here found unnecessary to go beyond the MM'-types which follow in 

 sequence directly after the well-known J/-types and are thus com- 

 paratively simple extensions. They meet the desired impedance ideal 

 well and are in this respect a considerable improvement over the 

 J/-types just as the latter are an improvement over the "constant k" 

 wave-filter, as we might expect. By a proper choice of the parameters 

 m and m' it will be shown later that the J/J/'-types can be made to 

 have image impedances which are equal to the same constant resistance 

 within 2 per cent over the greater part of all transmitting bands. In 

 low pass and band pass wa\'e-filters this nearly constant resistance 

 extends over a frequency range which is approximately equal to 96 

 per cent of the theoretical band width. Similar characteristics apply 

 to wave-filters of other classes. Such a range includes all of a trans- 

 mitting band except a small region next to each critical frequency 

 where, how^ever, the wave-filter attenuation makes it practically 

 useless for transmitting purposes. Each terminal transducer would 

 then be a composite wave-filter made up of a mid-half section of the 

 associated M-type of parameter m and a mid-half section of such an 

 MM'-type of parameters m and m'. While, as already stated, the 

 Jl/-types and MM'-types have potentially the same propagation 

 characteristics, the particular values of the parameters m and m' 

 chosen from the impedance standpoint give attenuation peaks which 

 in these J/-types are farther away from the critical frequencies, and in 

 these MM'-types nearer, than in an J/-type of parameter m = .6, 

 which is generally desirable. Two such fixed designs '" are given here 

 for connection to the "constant ^" wave-filter of any class at mid- 

 series or at mid-shunt, respectively. The particular forms these take 



^ The reader should keep in mind that such a terminal wave-filter network is 

 itself a true composite wave-filter of the same class as the standard or "constant k" 

 wave-filter. Its image impedance at one end is the same as a mid-point image 

 impedance of the standard, while that at the other end is the mid-point image 

 impedance of the MM'-type which is desired at the terminal. 



