Synthesis of Rational Transfer Function Approximations Using a Tapped Distributed RC Line with Feedback

T h e progress being m a d e in m i n i a t u r i z i n g electronic circuits h a s s t i m u l a t e d a continuing interest in the synthesis of n e t w o r k s using distributed R C components. N u m e r o u s techniques a r e a v a i l a b l e for synthesizing t r a n s f e r functions using distributed RC components in conjunction with v a r i o u s active n e t w o r k elements. 1 Generally, these synthesis procedures are applicable only if t h e t r a n s f e r f u n c t i o n h a s 2051 2066 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , NOVEMBER 11)08 a very special form. This form is not a rational function of the complex frequency variable s but involves hyperbolic functions of s. If the problem posed to the network designer were merely to realize given transfer functions of this special form using distributed RC networks, there would be no difficulty. However, the problem is generally not this but rather to realize a network which achieves certain system specifications such as bandlimiting or pulse shaping. Thus, a realizable transfer function must be developed which approximates the specifications ( t h a t is, the approximation problem m u s t be solved) before a network can be synthesized. Because the transfer functions realizable by distributed RC networks have a somewhat complicated form, the approximation p a r t of the network designer's work is more difficult when using distributed RC networks. This f a c t has led to a continuing effort to develop distributed RC networks which realize rational transfer functions.