290 



BELL SYSTEM TECHNICAL JOURNAL 



line to connect two high-frequency pentodes. As shown by Salzberg 

 and Burnside,^ the output impedance of a high-frequency pentode at 

 100 megacycles may be in the order of 30,000 ohms due to the high- 

 frequency shunting loss of the tube. On the other hand, due to active 

 grid loss, the impedance looking into the grid of the next tube may be 

 in the order of 20,000 ohms. Hence in order to obtain the most gain 

 from such tubes, the coupling circuit should be able to work from 

 30,000 ohms when connected with the output to 20,000 ohms for the 

 input of the next tube. If we employ the simple coupling circuit 

 shown in Section III, Fig. 1, this can be made impedance transforming 

 by making the second-series conductor of a different characteristic 

 impedance from the first-series conductor. Such a combination is 

 shown in Fig. 8. The equations of the combination are easily solved 



L 



Fig. 8— A narrow-band transformer for coupling vacuum tubes, 

 with the result that 



«r = ti 



. Co/i (Jill 



J ry , „ sm — COS — 



„w/i Zo, . „co/i , Zo, V V 



cos- -~ sm- h ^ J 



V Z03 V Z02 ^__ o^h 



tan 



V 



jei 



Zoj -\- Zdr, . Oil I Oil I 



— ~—^ — - sm — cos — 



Z01Z03 V V 



cos^ 



-7 ^ '^^2 



Z02 tan — 



Co = ei 



. Oili Oili 



J ry , ^ sm — cos — 



^Oilx Z03 . ^Oilx I Z03 V V 



cos^ —2 sm2 — + ^ -J 



V Zoi V Z02 ^__. w/2 



tan 



V 



Pj 



sm^ — 



(Zoi + Z03) sm — cos ^ j- 



V V Zo, Oilo 



tan — 



(38) 



'"Recent Developments in Miniature Tubes," Proc. T. R. E., Vol. 23, No. 10, 

 p. 142, Oct. 1935. 



