Graeme Innes

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The objective is to improve the linear constraints for optimizing the helical structure (radius and pitch of the conductor winding) of nonuniform helical antennas for desired characteristics such as signal gain or bandwidth. Presented below are equations that allow various higher-order structural constraints to be used in such optimizations. Their efficacy is demonstrated by analogy, using data for a fully optimized Yagi-Uda antenna, before being applied to data available for helical designs. The comparisons confirm the general validity of the higher-order equations to model some of the most advanced antennas produced to date. A simple calculus-of-variations test confirms that an improved optimization is possible by adding curvature terms to previously published linear constraints.


Curvature, Higher-order Constraint, Improved Optimization, Nonuniform Helical Antenna, Simple Test, Structural Constraint

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J.D. Kraus, “Helical Beam Antennas,” Electronics, vol. 20, pp. 109–111, April 1947.

J.L. Wong and H.E. King, “Empirical Helix Antenna Design,” Antenna and Propagation Society International Symposium, vol. 20, pp. 366–369, 1982.

G. Burke and A. Poggio, “NEC Part I: Program Description – Theory”, Technical report, Lawrence Livermore Laboratory, January 1981.

WIPL-D historical benchmarks from 1980 to the present.

Mathworks factsheet citing the initial release of MATLAB® in 1984

K. Schmidt, Java applet source, 1998.

K. Schmidt, Yagi Modeller notes.

A.R. Djordjević, A.G. Zajić, M.M. Ilić and G.L. Stüber, “Optimization of Helical Antennas”, IEEE Antennas and Propagation Magazine, vol. 48, no. 6, pp. 107–115, Dec. 2006.

J.L. Dinkić, D.I. Olćan, A.R. Djordjević and A.G. Zajić, “High-Gain Quad Array of Nonuniform Helical Antennas”, Int'l J. Antennas and Propagation, Article ID 8421809, 12 pp., March 2019.

J. Dinkić, D. Olćan, A. Djordjević and A. Zajić, “Design and Optimization of Nonuniform Helical Antennas with Linearly Varying Geometrical Parameters”, IEEE Access, 12 pp., in press.

K. Schmidt, “Simplified mutual impedance of nonplanar skew dipoles”, IEEE Trans. on Antennas and Propagation, vol. 44, no. 9, pp. 1298–99, 1996.

P.G. Collier, Optimized 15-element Yagi-Uda antenna data.

G.E. Innes, “An Experimental and Theoretical Study of Viscous Lifting in Tribology”, Ph.D. Thesis, Appendix C, Department of Mechanical Engineering, University of Leeds, Leeds, U.K., 1993.

R. Kalmeijer, “Circularly polarized Quagi antennas for space communications”.

W.I. Orr and S.D. Cowan, All About Cubical Quad Antennas, 2nd Edn. Radio Publications, Inc., Box 149, Wilton, Conn. 06897, 1970.

Cubical quad antenna data, www.basictables.com/amateur-radio/antenna/cubical-quad-antenna

J.L. Wong and H.E. King, “Broadband Quasi-Taper Helical Antennas”, N.T.I.S. Report A046067, 35 pp., 30 Sept. 1977.

S. Talari, R. Naraiah, and Dr. Ramakrishna, “Tapered Spiral Helix Antenna”, Int'l J. Emerging Tech. Adv. Eng., vol. 3, no. 3, pp. 318–25, March 2013.

T. Peng, S. Koulouridis and J.L. Volakis, “Miniaturization of Conical Helical Antenna via Optimized Coiling”, A.C.E.S. J., vol. 26, no. 6, pp. 452–58, June 2011.

A.F. Peterson, B.S. Greene and R. Mittra, “Propagation and radiation characteristics of the tape helix with a conducting core and dielectric substrate”, IEEE Trans. on Antennas and Propagation, vol. 38, no. 4, pp. 578–84, April 1990.

S.V. Savić, M.M. Ilić and A.R. Djordjević, “Design of Internal Wire-Based Impedance Matching of Helical Antennas Using an Equivalent Thin-Wire Model”, Int'l J. Antennas and Propagation, Article ID 7365793, 5 pp., Dec. 2017.

S. Sharma, R. Rishi and C.C. Tripathi, “Impedance Matching Techniques for Microstrip Patch Antenna”, Indian Journal of Science and Technology, vol. 10, no. 28, 16 pp., July 2017.

K. Jimisha and S. Kumar, “Optimum design of exponentially varying helical antenna with non uniform pitch profile”, International Conference on Communication Computing and Security, Procedia Technology, pp. 792–98, June 2012.

A. Đorđević, D. Olćan, M. Ilić and A. Zajić, “Design of Optimal Ground Conductor for the Helical Antenna”, In Proceedings of the 50th ETRAN Conference, 3 pp., June 2006.

B. Slade, “The Basics of Quadrifilar Helix Antennas”, Technical Publication, Orban Microwave Inc., 1834 N. Alafaya Trl., Suite B, Orlando, FL 32826.

M. Škiljo and Z. Blažević, “Helical Antennas in Satellite Radio Channel”. In: Dr. Masoumeh Karimi, editor. Advances in Satellite Communications.


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