A Note on Parallel-Tuned Transformer Design

T HE parallel-tuned transformer has been used in radio-frequency amplifiers for many years. 1 In an excellent paper, 2 Christopher based design formulas on the principles of the broad band filter. In other publications, 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 conditions3 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. I I . 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-humped 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.