by 7 cm and a wire diameter of 1.3 mm, consistent with the authors’ work. The Hilbert curve fractal antenna has a total wire length of approximately 1.2 m. Using NEC, the resonant frequency of the Hilbert curve fractal antenna was determined to be approx- imately 267.2 MHz, which is consistent with the results presented by the authors. The meander line #1 dipole has the same overall area and similar total wire length (1.12 m), yet it has a resonant frequency of 168.7 MHz, significantly lower than that of the Hilbert curve fractal dipole. This is contrary to the conclusions stated by the authors. Given that the antenna’s resonant frequency is as much, if not more, a function of the antenna’s total wire length as its geometry, it is reasonable to conclude that the wire length in the meander line #1 dipole can be reduced in order to increase its resonant fre- quency to match that of the Hilbert curve fractal-dipole antenna. In this case, the total wire length of the meander line #1 dipole can be reduced from 1.12 m to 0.564 m, resulting in the meander line #2 dipole, which is also depicted in Figure 1. Using NEC, the mean- der line #2 dipole is determined to have a resonant frequency of 267.1 MHz, which essentially matches that of the Hilbert curve fractal-dipole antenna. A relative comparison of the impedance properties of these two antennas is presented in Figure 2. These antennas exhibit remarkably similar performance, even though they have remarkably different geometries and the meander line #2 dipole has approximately 53% less total wire. Contrary to the conclusion stated by the authors, the Hilbert curve fractal-dipole antenna does not exhibit a resonant frequency lower than any other resonant antenna of similar size. The self- similar geometry and plane-filling nature of the Hilbert fractal curve does not result in it being a more effective antenna in terms of exhibiting lower resonant frequencies than other antennas of similar size. REFERENCES 1. K.J. Vinoy, K.A. Jose, V.K. Varadan, and V.V. Varaden, Hilbert curve fractal antenna: A small resonant antenna for VHF/UHF applications, Microwave and Optical Technology Letters, Vol. 29, No. 4, May 20, 2001, pp 215–219. 2. S.R. Best, The Koch fractal monopole antenna: The significance of fractal geometry in determining antenna performance, 25 th Ann An- tenna Appl Symp, University of Illinois, 2001. 3. H. Nakano, H. Tagami, A. Yoshizawa, and J. Yamauchi, Shortening ratios of modified dipole antennas, IEEE Trans Antennas Propagat AP-32 (1984), 385–386. 4. T.J. Warnagirls and T.J. Minardo, Performance of a meandered line as an electrically small transmitting antenna, IEEE Trans Antennas Propa- gat AP-46 (1998), 1797–1801. © 2002 Wiley Periodicals, Inc. AUTHORS’ REPLY TO “COMMENTS ON HILBERT CURVE FRACTAL ANTENNA: A SMALL RESONANT ANTENNA FOR VHF/UHF APPLICATIONS” K. J. Vinoy and V. K. Varadan Center for the Engineering of Electronic and Acoustic Materials and Devices 212 EES Building, University Park Pennsylvania State University, PA 16802 Received 15 July 2002 © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 421, 2002; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/mop.10626 The primary objectives of the original paper [1] were to: ● Introduce a fractal geometry (Hilbert curve) for antenna applications ● Study its fractal characteristics (self-similarity and plane filling nature) and their reflection in antenna properties ● Reinforce its size reduction feature in the context of other fractal geometries (Koch curve), which are previously re- ported to result in small antennas. We regret that this last aspect was not presented explicitly, which is the basis for the comment on the paper in [2]. A primary advantage of fractal geometries that we sought to explore was their ordered nature. The fractal recursive nature of these geometries has been exploited to obtain approximate analytical design expressions for dipole antennas using them in [3]. When put together, [1] and [3] offer a systematic approach to designing small antennas. It is quite possible that geometries suggested in the comment, as well as several others, could lead to still lower resonant fre- quencies. In this context, an apparent comparison in [1] across various geometries was unnecessary, since antenna features need not be unique for any geometry. REFERENCES 1. K.J. Vinoy, K.A. Jose, V.K. Varadan, and V.V. Varadan, Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications, Microwave Opt Technol Lett 29 (2001), 215–219. 2. S.R. Best, Comments on Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications, Microwave Opt Technol Lett 35 (2002), 420 – 421. 3. K.J. Vinoy, K.A. Jose, V.K. Varadan, and V.V. Varadan, Resonant frequency of Hilbert curve fractal antennas, IEEE AP-S Int Symp Digest (2001), 648 – 651. © 2002 Wiley Periodicals, Inc. MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 35, No. 5, December 5 2002 421