614 BELL SYSTEM TECHNICAL JOURNAL 



circuited would be to introduce irregularities of transmission within 

 the band. However, if the band is relatively narrow the resistances 

 of the filter elements are sufficient to smooth out these irregularities 

 and in certain cases the transmission may be made more uniform by 

 the omission of the impedance Zr. This has been found to be the case 

 with transformers of the type described here. 



Equation (14) shows that the voltage ratio E^IE which is the 

 ratio of the open-circuit voltage of the tuned circuit at terminals 3, 4 

 to the applied grid voltage of the first tube is directly proportional to 



■V 



over the transmitted band. By proper choice of the constants of 



the coupling circuit so that Zi, 2 will equal Zq at a frequency lower 

 and higher than the geometrical mean frequency this voltage ratio 

 will remain practically constant for all frequencies within the band. 



The voltage ratio E1IE for any frequency w outside the transmission 

 band may be obtained from the following equation: 



EzjE = u 



where 



-7^ X -7^ X Z^jZ^ 



Z2 Z.4 



Z, = J-r; Z,^MS-M)+Zu Z,= ^^-^'"^^ 



z ^ 



Z-4 -; — -TT 



Z, = Za + jo^{P - M) ■ Z5 = ^^^~- ; Ze = Z5 + Zc 



Z4 + 



P, S and AI are in henrys and d and C2 in farads. 

 As the effective voltage amplification of the network within the 

 transmission band is directly proportional to 



it is evident that since d is fixed by equation (8), the value of Co 

 must be kept to a minimum to realize maximum voltage step-up. 

 Consequently, greater amplification will be obtained if the second 

 tube in Fig. 1 has minimum input capacitance. The effective dis- 

 tributed capacitance of the winding is kept at a low value by placing 

 the winding in narrow grooves on a spool. 



In actual use the maximum amplification realized at the higher 

 frequencies is somewhat less than that shown in equation (14) since 

 the conductance component of the input impedance of the second 

 tube reduces the effective voltage at this point. It is therefore of 



