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

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, , 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, , by assuming the function is also analytic at the boundary point 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.