Ig4 BELL SYSTEM TECHNICAL JOURNAL 



From this \vc then get in Case (A) 



and, assuming that Rp> >Uo (L^ + M), 



L2 + M 



Hence, defining the voltage amplification K of the first stage as the 

 voltage impressed upon the grid of tube II divided by the voltage 

 impressed upon the grid (^f tube I, we ha\e 



e, "wo^Lo + My'+RpR' ^^ 



In order to find the stci)-up ratio, which gi\es maximum amplifica- 

 tion w'e have to soKc for L2 + .I/ in the ecjuation 6K &{L2 + M) =0, 

 which gives 



Rp= ^7 =Za-b, (.Oj 



and by inserting this in ('([uation (4) w'e get 



^ VRpVr' 



From etjuation (o) it is seen that the condition for maxinunn xoltage 

 amplification is exactly the same as the well-known condition for 

 maximum power amplification; namely, that the external impedance 

 Za-b inserted in the jilate circuit must be etiual to the internal tube 

 impedance Rp. 



By repeating the calculations gi\en above for Case (B) in Fig. 2, 

 it W'ill be found that this condition again holds good, and also it will 

 be found that the expression for Kmax is the same. 



As already' mentioned the resistance R' in the formulas ,ii)o\e 

 includes the etjuix^alent series resistance introduced in the tuned circuit 

 by the impedance of the input circuit of tube II, but in many cases 

 this extra resistance will be negligible as compared to the resistance of 

 the coil itself, and equation ((>) thus gives us the very interesting 



