ALLPCB
Abstract
After Heinrich Hertz invented the antenna, antenna theory developed along two main lines: antenna circuit theory, which focuses on current distribution on antennas, and antenna modal theory, which focuses on electromagnetic field distributions. This article first reviews three representative results in antenna circuit theory from 1897 to 1938, then three representative results in antenna modal theory from 1941 to 1981, and finally briefly introduces recent progress in modal antenna theory. Biographical notes and anecdotes about several antenna theorists are interspersed.
1. Antenna Circuit Theory
Antenna circuit theory studies current distributions on antennas and the relationship between antennas and electrical networks.
The earliest work in antenna circuit theory dates to Henry Cabourn Pocklington's 1897 paper. In it Pocklington explained that currents and charges on an ideal thin conductor propagate approximately at the speed of light and that the current distribution is approximately sinusoidal. His representative result is the well-known Pocklington equation. Pocklington was born in Exeter, UK, in 1870 and had an academic career that included degrees from the University of London and Cambridge; later he chose to teach at a secondary school in Leeds and was elected a Fellow of the Royal Society in 1907. He died in Leeds in 1952.
An important advance was made by Erik Hallén, who in the 1930s published an integral equation for current distribution on thin wires based on Pocklington's equation, later known as Hallén's integral equation. Hallén was born in 1899 in Sweden, obtained degrees from Chalmers Technical University and Uppsala University, and was appointed professor of electromagnetics at the KTH Royal Institute of Technology in 1945. He visited Harvard and Caltech as a visiting professor, promoting antenna research at those institutions. Hallén died in 1975.
Another significant contribution was by P. S. Carter in 1932, who first simplified antenna coupling problems into intuitive equivalent-circuit representations. Carter's work deeply influenced subsequent research on antenna coupling.
2. Antenna Modal Theory
Antenna modal theory studies electromagnetic field distributions of antennas and the relationship between antennas and resonators or transmission lines.
Although modal questions trace back to 1897, a formal antenna modal theory appeared in 1941. Julius Stratton and L. J. Chu published solutions for modes of a conducting sphere in April 1941, and S. A. Schelkunoff published theory for a conducting cone in September 1941.
Schelkunoff praised the spherical-antenna modal theory of Stratton and Chu, noting that while spherical antennas are not used in practice, the theory reveals similarities between antennas and leaky resonators: an applied source excites resonant current modes in the antenna, which radiate electromagnetic energy and thus lose energy by radiation.
The conical-antenna theory is likewise of theoretical importance because it reveals relations between antennas and transmission lines. Schelkunoff devoted a chapter to his modal theory in his 1952 book Advanced Antenna Theory. The Chinese physicist Zhi-Xun Huang wrote highly of Schelkunoff's contributions, noting foundational theorems, principles, concepts, and methods in engineering electromagnetics, antenna theory, and waveguide theory that have entered textbooks. To honor Schelkunoff's contributions, the IEEE Antennas and Propagation Society renamed its annual best-paper award the Schelkunoff Paper Award in 1985. In 2018, Professor Jun Hu of the University of Electronic Science and Technology of China became the first scholar from a Chinese research institution to receive that award.
J. A. Stratton, a collaborator of L. J. Chu, was a prominent electromagnetics researcher. Born in 1901, Stratton earned degrees from MIT and ETH Zurich, was elected to the U.S. National Academy of Sciences in 1950, served as MIT provost from 1959 to 1966, helped found the National Academy of Engineering in 1964, and died in 1994.
The invention of the microstrip antenna in the early 1970s ushered in the era of modern antennas. A major feature of modern antennas is that dielectric substrates are integral to the antenna; any complete theory must account for substrate effects. Professor Y. T. Lo and collaborators developed microstrip antenna modal theory in 1979 and 1981, producing the first modal theory that incorporated dielectric substrates. This theory provided a textbook-level foundation for understanding, analyzing, and designing microstrip antennas. Professor Y. T. Lo was born in 1920 in Wuhan and had an academic career that included degrees from the National Southwest Associated University and the University of Illinois at Urbana-Champaign. He served on the faculty at UIUC and was elected to the U.S. National Academy of Engineering in 1986 for innovations in antenna theory and design. He received the IEEE Antennas and Propagation Society's Distinguished Achievement Award in 1996 and died in 2002.
Unlike spherical and conical antennas, microstrip antennas have found widespread practical applications.
3. Recent Advances in Modal Theory
The micro-convex antenna is a basic antenna system with a new structure and operating mechanism. Its invention marks a paradigm shift from two-dimensional printed and integrated antenna designs toward three-dimensional structures. The micro-convex antenna effectively addresses the very low radiation efficiency of extremely thin-substrate microstrip antennas. A modal theory for a micro-convex antenna consisting of a circular patch loaded with a microsphere has been completed. A modal theory for conical radiation from micro-convex antennas is available on IEEE Xplore. A side-radiating micro-convex modal theory is under review.
Detailed derivations are omitted here. Early-career antenna researchers are encouraged to derive the formulas and implement computational verification; doing so provides practical mastery of modal antenna theory.
Figure 1 shows HFSS simulations of current distributions on a circular microstrip patch and on a hemispherical metal surface. The patch lower-surface current density is distributed radially outward, while the hemispherical surface current density is directed upward. In the equations referenced in the original article, Q denotes the quality factor of the micro-convex antenna, with Qp and Qb denoting the quality factors of the microstrip and the hemispherical radiator, respectively. The micro-convex antenna has a lower quality factor than either the microstrip or the hemisphere alone, indicating a wider impedance bandwidth for the micro-convex design.
An expression for radiated power separates contributions from the microstrip, the hemisphere, and their interaction. The radiation efficiency of the micro-convex antenna is higher than that of the microstrip antenna primarily because the microsphere reduces microstrip conductor losses, and because cooperative radiation from the microstrip and the hemisphere provides an additional radiative contribution. Conductor loss reduction can be understood qualitatively: the hemisphere diverts current, so if the current to the microstrip is halved, conductor loss on the microstrip can decrease by a factor of four.
Figure 1. HFSS simulation of current density distributions
4. Conclusion
Heinrich Hertz was not only the inventor of the antenna but also the initiator of antenna theory, giving antennas clear physical meaning. Subsequent antenna research has focused on mathematical solutions of Maxwell's equations. Antenna circuit theory deals with integral equations derived from Maxwell's equations and antenna boundary conditions. Antenna modal theory uses separation of variables to directly solve Maxwell's equations subject to antenna boundary conditions. Since separable solutions are rare, modal theory has a narrower range of practical applicability than circuit theory. Faced with this limitation, antenna researchers have sought new solution methods. From the 1970s onward, improved computing power enabled extensive use of numerical methods for complex antenna problems. Chinese researchers worldwide have contributed many numerical methods to computational antenna engineering, while development of commercial antenna software has been relatively limited.
The invention of the micro-convex antenna reflects trends in wireless system development: seeking simple structures, low cost, good performance, and ease of integration. The micro-convex antenna modal theory, grounded in classical modal ideas, helps to understand radiation mechanisms, analyze characteristics, and accelerate design.
Micro-convex antennas have potential applications in terahertz wireless integrated systems.
