Some results of the driving point impedance functions

In this paper, a boundary version of the Schwarz lemma has been considered for driving point impedance functions at s = 0 point of the imaginary axis. Accordingly, under Z(0) 0 = condition, the modulus of the derivative of the Z s ( ) function has been considered from below. Here, Z a ( ) and ( ) ( ) ! pZ a p coefficients of the Taylor expansion of the Z s b c s a ( ) ... = + - + p( )p function have been used in the obtained inequalities. The sharpness of these inequalities has also been proved. It is also shown that simple LC tank circuits and higher order filters are synthesized using the unique DPI functions obtained in each theorem.