PARALLEL-TUNED TRANSFORMER DESIGN 



107 



(b) Mismatched Transformer; 

 1 



1 



coo 



COo 





RiC[ 



= k' = 



VI +^2 



(30) 



E'2 



(b) i. 



R', 



R', 



c; 



C2 E2 



I 



^ L 



^^^2 Q)i\ 



Fig. 5. — Mismatched transformer (a) fed by constant current generator, (b) with input 



and output reversed. 



The ratio of the output voltages in the two cases is given by: 



E2 



N' 



V4^;\ 



y^Rj 



^RiC2 



R1C2 



El 



(31) 



The relative gains of the two transformers, as given by equation (31), 

 will be examined for three important cases: 



(1) Input Transformer — In this case Ri = R/, and C2 = Ci\ so that 

 from (31), the mismatched transformer gives four times, or 6 db more 

 gain. 



(2) Output Transformer — The voltage source in Fig. 4 may be replaced 

 by the constant current source // = Ei/Ri\ by Norton's Theorem, as 

 shown in Fig. 5(a). By the Reciprocity Theorem we may exchange the 

 positions of the current source and the output voltage as shown in Fig. 5(b), 

 without changing the value of the latter. This may also be done for the 



