Conversion of a beline cycle with an ideal transformer into a cycle without an ideal transformer

O. Brune1 has proved that any rational ¿positive real¿ function possesses a one terminal-pair network configuration containing a finite number of linear passive elements. Brune suggested the ladder synthesis for positive real functions. In general his synthesis procedure contains mutual couplings which are not desirable from a practical standpoint. Thus, there has always been a great desire to eliminate ideal transformers from the picture. As steps towards this goal, H. W. Bode2 suggests resistance padding, and E. A. Guillemin3 often uses some practical methods for eliminating the ideal transformer in special cases. The existence proof, along with a synthesis procedure without an ideal transformer, was first given by R. Bott and R. J. Duffin4.