Synthesis of Tapered Distributed RCG Networks

Abstract

The synthesis of a broad class of tapered distributed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RCG \overline{(RCG)}</tex> networks, which include uniform <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{(URCG)}</tex> , exponential <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{(ERCG)}</tex> , hyperbolic cosine-squared <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{(HCRCG)}</tex> , hyperbolic sine-squared <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{(HSRCG)}</tex> , trigonometric <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{(TRCG)}</tex> , and square <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{(SRCG)}</tex> tapered networks, is investigated. The necessary and sufficient realizability conditions are presented. It is shown that by using some suitable transformations, this class of networks may be obtained from any of the known lumped passive or active <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> synthesis methods. A complete synthesis procedure is given. Relations among sensitivity functions of this class of networks are presented. The stability conditions of this class of networks are discussed. The necessary and sufficient conditions for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{URC}</tex> network are presented and proven. It is demonstrated that those for other members of this class of networks may be obtained in a similar way.