1246 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009 Improved Formulation for Admittance of Thin and Short Monopole Driving From Coaxial Line Into Dissipative Media Kok Yeow You, Member, IEEE, Zulkifly Abbas, Member, IEEE, Kaida Khalid, and Ngoon Fah Kong Abstract—An improved formulation of the admittance equation for small and thin monopole is presented where the coefficient of the capacitive correction term can be calculated directly from the values of the inner and outer radius of the coaxial line. The re- sults were found to agree well with measurements and the finite el- ement method (FEM). Some rules, features, and limitations of the improved formula are also discussed. Index Terms—End correction, input admittance, monopole, open-ended coaxial line. I. INTRODUCTION A SHORT monopole [1] mounted on the center conductor of a coaxial line has been widely implemented as a sensor for nondestructive material testing and for material testing that requires a high degree of sensitivity [2]–[6]. In general, the ma- terial characterization is based on the calculation of the permit- tivity based on the measured input impedance or admittance of the material under test. However, the input admittance of short monopole is difficult to formulate analytically because of the gap effect at the driving point. Various solutions have been pro- posed to mitigate the resultant problems by using capacitance approaches, but the applications were restricted only to certain exposure length of the monopole in free space [2]. In this letter, we propose a semi-empirical capacitance correction for the ana- lytical admittance formula [4]–[6] over a wide range of length , radius, , aspect ratio and frequency , as well as permit- tivity of the materials. The integral admittance formula as (1) is solved by using Boole’s numerical integration. Manuscript received September 01, 2009; revised October 20, 2009. First published October 30, 2009; current version published November 27, 2009. This work was supported in part by the Ministry of Science, Technology, and Envi- ronment of Malaysia under project IRPA 09-02-04-0460-EA001. K. Y. You is with the Radio Communication Engineering Department, Uni- versiti Teknologi Malaysia, 81310 UTM Skudai, Malaysia (e-mail: kyyou@fke. utm.my). Z. Abbas and K. Khalid are with the Department of Physics, Universiti Putra Malaysia, 43400 UPM Serdang, Malaysia (e-mail: za@fsas.upm.edu.my; kaida@science.upm.edu.my). N. F. Kong is with INSPEM, Universiti Putra Malaysia, 43400 UPM Serdang, Malaysia (e-mail: kongnf@gmail.com). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2009.2035645 II. THIN MONOPOLE EQUATIONS The normalized input admittance, , for short and thin monopole, shown in Fig. 1(a) [4]–[6], can be represented in terms of its normalized impedance, (1) where (2) with , , , and is the monopole length, is the coaxial line propagation constant, is the propagation constant in the ex- ternal medium, and is the radius of monopole. For short monopole driven from a coaxial line, the input ad- mittance is strongly affected by the fringing field at the end of the coaxial line. Thus, the ideal input admittance needs an end correction term, , to correlate the theoretical so- lution to the experimental result [2]. Hence, the normalized ap- parent admittance, is written as (3) where is the relative permittivity of an external medium. is the characteristic admittance in coaxial line, which can be calculated as (4) where and are the inner and outer radius, respectively, for the coaxial line. is a relative permittivity of a material filled in the coaxial line ( for Teflon). Symbol is the weight parameter of the end correction, and is the aperture capacitance between the inner cylindrical conductor and ground plane at the open end of the coaxial line. The capacitance , as shown in Fig. 1(b), can be calculated from [3] (5) 1536-1225/$26.00 © 2009 IEEE