On boundary analysis for derivative of driving point impedance functions and its circuit applications

Abstract

In this study, a boundary analysis is carried out for the derivative of driving point impedance (DPI) functions, which is mainly used for the synthesis of networks containing resistor-inductor, resistor-capacitor and resistor-inductor-capacitor circuits. It is known that DPI function, $Z\lpar s\rpar $Z(s), is an analytic function defined on the right half of the s-plane. In this study, the authors present four theorems using the modulus of the derivative of DPI function, $\vert Z<^>{\prime}\lpar 0\rpar \vert $|Z '(0)|, by assuming the $Z\lpar s\rpar $Z(s) function is also analytic at the boundary point $s = 0$s=0 on the imaginary axis and finally, the sharpness of the inequalities obtained in the presented theorems are proved. It is also shown that simple inductor-capacitor tank circuits and higher-order filters are synthesised using the unique DPI functions obtained in each theorem.