PARALLEL-TUNED TRANSFORMER DESIGN 



90 



The transmission loss, £, defined as the ratio of the maximum available 

 power from the generator to the output power may be obtained from (10), 



(12) 





-{p['- ©"<■-'■']■ 

 ■ +^'[0"<'-«-^«+'''-^?] 



or the loss m decibels equals 10 log >^. 



The transmission delay, 8, may be obtained from (11). 



d(f> 

 doi 



_&)'"-«■-©'<'- 



k'f + 4*' - 1 + 



(:)' 



1^ 



(13) 





seconds. 



The input impedance seen from the generator terminals is. 



Zin — Rl 



Q. vr^. -,-[■.- fey a_.. )] 



The formulas (12), (13) and (14) give the important characteristics of this 

 transformer. Table I gives expressions for these characteristics in the 

 general case, and for k = 0.5, for several picked frequencies. Of these 

 frequencies ojo and coo/\/l — k^ are the frequences of zero transmission loss, 

 coo/^v^l — k^ is the geometric midband, and coo/\/l + k and coo/a/i — k 

 are the cut-ofT frequencies of an infinite filter made of identical transformers 

 of this type. 



The input impedance, transmission loss, and the transmission delay are 

 plotted against co/a-o for a matched transformer with k = 0.5 in Fig. 2. From 

 these curves, and from Table I the following important characteristics of 

 this transformer will be noted: 



(1) The pass-band is approximately symmetrical with frequency, rather 

 than with the logarithm of frequency, as in circuits which have a low-pass 

 analog. 



