TRANSFORMER COUPLING CIRCUITS 613 



satisfy the coupling coefficient of equation (6). To facilitate adjust- 

 ment C2 may include a small adjustable condenser to comjiensate for 

 \ariations in winding capacities as well as in the input capacity of 

 the vacuum tube. 



The following analysis shows that maximum voltage amplification 

 is obtained with practically uniform transmission for all frequencies 

 within the transmitted band when the secondary circuit is terminated 

 only in its tuning condenser. 



Referring to Fig. 2 and assuming that Zi, 2 = Zq and Zu = Z-j, 4, 

 we find that the voltage drop across Zr is 



or 



- _ 1 77 Zz, 4 



- _ EfJL IZs^ 4 



'''-Tyjzr,' 



(12) 



Now from Thevenin's Theorem,^ assuming Zo = Zi, 2, we can 

 obtain the following expression for the output current for any value 

 of the impedance Zr : 



Ir= ^ f V ' (1^^ 



where £2 is the open-circuit voltage at terminal 3, 4 and Ir is the 

 current flowing in the terminating impedance Zr. 



The actual voltage across the terminating impedance Zr is 



77 _ r 7 _ E^Zr 

 TL,R — Ir^r — 



Zr -\- Zz, 4 



Where Zr is equal to Z3, 4 the output voltage has the value 



The effect of matching the terminating impedance to the impedance 

 Z3, 4 is thus to cut the output voltage in half. 

 Then 



£2 /Z3, 4 _ /Ci ,... 



E^''\z7rr ''\Q' ^^^^ 



where n = voltage amplification constant of the first tube. 



Generally the effect of leaving the output end of a filter open- 



3 " Transmission Circuits for Telepiione Communication," by K. S. Johnson, 

 p. 79. 



