Extension of Bode's Constant Resistance Lattice Synthesis of Transfer Impedance Function

An i m p o r t a n t characteristic of c o n s t a n t resistance lattice n e t w o r k s is the absence of reflection effccts when such t w o - p o r t lattice n e t works are connected in t a n d e m . T h e synthesis of a given t r a n s f e r impedance function is simplified by representing t h e function by a p a r t i a l p r o d u c t expansion. T h u s the t r a n s f e r impedance m a y b e r e p resented by a t a n d e m connection of a n u m b e r of c o n s t a n t resistance structures (one for each p a r t i a l p r o d u c t ) . T h i s process will result in * Some results presented in this paper are based upon the author's thesis, "Explicit Formulas for Constant Resistance Lattice Synthesis of Transfer Impedance," presented to the Moore School of Electrical Engineering, University of Pennsylvania in December 1965 in partial fulfillment of the requirements for the degree of Master of Science in engineering. 637 638 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1969 realizable, simpler, t r a n s f e r i m p e d a n c e f u n c t i o n s provided t h a t t h e c o n s t a n t multiplier of t h e given t r a n s f e r i m p e d a n c e f u n c t i o n is m a d e large enough to p e r m i t each of t h e constituent n e t w o r k s to h a v e nonnegative loss on t h e real axis. 1 In general, t h e n , t h e r e will be a d d i tional fixed loss for t h e overall t w o - p o r t n e t w o r k . F o r physical realizability, it is required t h a t both m e m b e r s of a n y c o n j u g a t e complex pair of zeros or poles be r e t a i n e d within a given p a r t i a l product.