The new hilberg's iteration schemes of elliptic integral function for designing all of microstrip antenna based on CPW structure

This paper propose new iteration schemes to facilitate Hilberg's approximations in formulating logaritmic argument of elliptic integral function. The implementation of Joukowski identity in the new method transforms the rational form of the original Hilberg's logaritmic argument into Joukowski function. The solution of quadratic equation of Joukowski function can formulate the higher order logaritmic argument explicitly in form of logaritmic argument of the lower order. It is different with each original Hilberg's approximation that needs several iterations. Derivation of accurate Pi formulas required for designing all of microstrip antenna based on CPW (Coplanar Waveguides) structure using the propose method are also presented. It is shown that the accurate geometric parameters of the CPW designed by using quartic formula of the third order approximate modulus giving accuracy of double precission.