570 BELL SYSTEM TECHNICAL JOURNAL 



1, mid-shunt of a mid-series "constant k" equi\alent .l/-type, 

 (Kiiini) ); 



2, mid-series of a mid-sliunt "eonstant k" eciuixalent .l/-lyi)e, 

 {Kn(m) ) ; 



3, .r-shunt of the "constant k" wave-filter, (Kxi); and 



4, a;-series of the "constant k" wave-filter, (Kxi)- 



The terminations in K-n(»'} and Kvi{m) are employed, as stated 

 in a pre\ious jiaper,'' when it is desirable to obtain certain selective 

 characteristics and to minimize reflection losses at the important 

 frequencies to be transmitted, a minimum for the latter occurring 

 where w = .6 approximately. The .r-shunt "constant k" termination, 

 designated by the characteristic impedance Kx2, is a "constant k" 

 type termination in a shunt element, whose admittance is .v times 



(.V from to 1) that of a full shunt "constant k" admittance, — ; 



22* 



thiit is, a shunt elenicnt whose impedance is — . Similarly, the 



X 



.r-series "constant k" type termination corresponding to the charac- 

 teristic impedance Kxi ends in a series element of impedance xzik- 

 In the usual case where two or more wave-filter networks having 

 different transmitting bands are associated together, either termina- 

 tion 1 or 2 is suitable for the unconnected terminals, while terminations 

 3 and 4 are adapted to the terminals connected in series or in parallel, 

 respectively. For two complementary wave-filters, thus connected, 

 minimum reflection losses occur at their junction with a transmission 

 line if .r = .8 approximately. A relation between this case and termi- 

 nation K\2{m) and Knim) has previously been pointed out, namely, 

 that the series or parallel connected wave-filters have a combined 

 impedance in the transmitting band of either wave-filter approxi- 

 mately like that of K\->{in) or Knim), respectively. 



Where the termination is .v-shunt or .v-series we shall consider that 

 the mid-part of the wave-filter begins at the mid-shunt or the mid- 

 series point, respectively, irrespective of whether .v is greater or 

 less than .5. .Also the mid-part need not here necessarily begin in the 

 "constant k" tyjie, but in any wave-filter having an equivalent char- 

 acteristic imiX'dance. 



Transmission Loss 



In the design of a wave-filter network the magnitude of k for die 



corresponding "constant k" wave-filter has been taken equal to the 



* B. S. T. J., Jan., 1923, page 18, gives a diagram for the non-dissipative case of 

 R/Kn{m) and K,i(m)/R in the transmitting band. 



