612 BELL SYSTEM TECHNICAL JOURNAL 



various elements must be proportioned with respect to the terminal 

 impedances as well as to the limiting frequencies. This is done by 

 making the image impedances about equal to the respective terminal 

 impedances at the mean frequency /,„ of the band. Preferably the 

 impedances should be matched at both ends, but if the transformer 

 normally operates with one end substantially open-circuited, as in an 

 amplifier, it is sufficient to effect the matching at the other end. 

 The following formulas giving the constants of the various elements 

 in terms of the limiting frequencies were derived from the foregoing 

 equations. 



g - h' 



^ ~ f2 I f 2 ' (6) 



__V2/,A_. („ 



^f^'+f: 



or 



^^-27r(/2-/0Z,.,' '(^^ 



^ " 47r2/o'Ci ' ^^^ 



S = -IZWh^' (10) 



477-/0 C 2 



S^ P X~- (11) 



C 2 



As previously mentioned the above equations are based on the 

 ideal condition which assumes the elements to be pure reactances. 

 Actually, a small amount of resistance is present in each element of 

 the transformer which tends to reduce the width of the transmission 

 band. Consequently /i and /2 should be assumed slightly lower and 

 higher respectively than the lower and upper frequencies of the 

 desired transmitted band in order to insure uniform voltage amplifi- 

 cation. It is advantageous to make the impedance Zi, 2 approximately 

 0.8 of the terminal impedance Zo, in which case Zi, 2 and Zq will be 

 equal at two frequencies near the band limits and will not be greatly 

 mismatched at the geometrical mean frequency. This tends to 

 improve the uniformity of transmission within the band. 



In applying the above equations, G is determined first from equation 

 (8). F is then determined from equation (9). From a knowledge 

 of the effective distributed capacity of 5" and the input capacity of the 

 second tube in Fig. 1, 5 is determined from equation (10). The 

 windings P and 5 are then arranged with respect to each other to 



