106 BELL SYSTEM TECHNICAL JOURNAL 



The last three equations were simplified by the use of equation (8), 

 Equations (25) yield the five relations below: 



coi = coo 



C02 = C0o/VT+T2 



k' = 





\ (26) 



Summary of Design Formulas 



A transformer must usually meet certain requirements as to bandwidth 

 and mid-frequency. Loss curves for various values of k^ plotted against 

 relative frequency may be used. To a very close approximation the geo- 

 metric mean frequency fm = oim/2ir, may be used for the mid-band fre- 

 quency, and A/, the bandwidth between cut-off points, may be used for the 

 bandwidth between one db points. Then, 



And, from (15), 



= w-v/r^TP (27) 



' = Vi + W/UY ^''^ 



The other necessary relations for the matched transformer and for the 

 mismatched transformer with the same transmission characteristics, as 

 derived from equations (3), (8) and (26) are given below. 



(a) Matched Transformer. 



1 



1 



M 



coo 



O30 



R\Ci = R2C2 



= k 



(aak 



(29) 



