A Note on a Parallel-Tuned Transformer Design 



By V. C. RIDEOUT 



An analysis of the parallel-tuned transformer used in radio-frequency ampli- 

 fiers has been made for a slightly over-coupled case. The resulting design 

 formulas are simple and practical. 



Two cases are discussed: (a) the so-called matched transformer, with resist- 

 ance loading on each side; (b) a transformer with loading on one side only, 

 which has the same pass-band and phase characteristics as the matched trans- 

 former, but gives 3 db more gain when used as an interstage. 



A special arrangement of (a) where the matched transformer design is used 

 with one resistor removed, giving a transformer with a considerably double- 

 humped pass-band characteristic and about 6 db more gain, is also discusseH 



Introduction 



THE parallel-tuned transformer has been used in radio-frequency 

 amplifiers for many years.^ In an excellent paper,^ Christopher based 

 design formulas on the principles of the broad band filter. In other publica- 

 tions, simple circuit analyses have been used and design formulas have been 

 based on the assumption of a small ratio of bandwidth to mid-frequency 

 which often fails to be adequate when the wide bands required for modern 

 television and multiplexing services are encountered. 



A transitionally flat transformer design may be obtained by setting the 

 first three derivatives of the absolute value of the transfer impedance, with 

 respect to frequency, equal to zero. The resulting design formulas are 

 somewhat unwieldy. 



The transformer design to be described here is based upon two simple 

 circuit conditions^ applied to the fundamental case of a parallel- tuned 

 transformer with resistance loading on each side : 



I. Both sides of the transformer are tuned to the same frequency. 



II. The transmission loss is zero at the tune frequency. (This condition 

 is responsible for the term ' 'matched transformer" used to describe this 

 case). 



The resulting transformer has a slightly double-hurnped characteristic 

 with less than 0.005 db dip for a coupling coefficient of 0.5. Because of the 

 slight overcoupling this transformer design gives a little more gain and 

 bandwidth than the critically coupled case. Its main advantage lies in the 

 fact that simpler design formulas can be used. 



» H. T. Friis and A. G. Jensen, High Frequency Amplifiers, B. S. T. /., Vol. Ill, April 

 1924, pp. 181-205. 



* A. J. Christopher, Transformer Coupling Circuits for High-Frequency Amplifiers, 

 B. S. T. /., Vol. XI, Oct. 1932, pp. 608-621. 



' This analysis is based on an old unpublished report by H. T. Friis. 



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