104 



BELL SYSTEM TECHNICAL JOURNAL 



The loss is equal at four points, 



OJO, 



CO = coo/Vl — ^^ ^ = ^o/Vl 



= coo/Vl + ^. 



The curves of Fig. 3 show the loss and delay for this mis-matched trans- 

 former for the case where k = 0.5. The double-humped band-pass charac- 

 teristic of the mis-matched transformer can be compensated for in an ampli- 

 fier by de-tuning slightly to equalize the humps and using a single-tuned 

 circuit in another interstage in which, 



Q = ai„.CR ^ Vl/k^ - 3/4 - 3k^/32 



(21) 



The above combination of a mis-matched transformer and a single-tuned 

 transformer, in successive interstages, will give approximately 6 db more 

 gain than if two matched transformers were used. The actual gain obtained 

 will depend upon the ratio of the input and output capacitances. This gain 

 advantage carries with it the penalty of increased sensitivity to tube capac- 



Fig. 4. — Mismatched or unsymmetrically loaded transformer. 



itance variations. However, the mis-matched transformer may be used 

 to advantage in the first interstage of an amplifier to minimize the effect 

 of the second tube on the signal-to-noise ratio. It may also be used in the 

 last interstage to offset any lack of power-handling capacity in the second- 

 last tube. 



(b) Mismatched or Unsymmetrically Loaded Transformer 



A transformer with only one loading resistor, as in Fig. 4, can always be 

 designed to have the same bandpass and phase characteristics as the matched 

 transformer^ shown in Fig. 1. No power transfer will occur, but the ratio 

 of output voltage to the square root of the available input power can be 

 determined, and set equal to this ratio for the matched transformer, except 



* This important principle has been described by S. Darlington in a paper: Synthesis of 

 ReacUnce 4-PoIc8, Journal of Mathematics and Physics, Vol. XVIII, Sept. 1939, pp. 257- 

 353. Independently, this principle was demonstrated to the author by W. J. Albersheim 

 in an unpublished memorandum dealing with the transitionally flat transformer. 



