Multi-Mode Resonant Antennas

Theory, Design, and Applications

Wen-Jun Lu, Lei Zhu

• Publisher: CRC Press
• Year: 2022
• Topic: Technology & Engineering
• eBook ISBN:
  9781000593952
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

This title provides a unique theoretical framework for multi-mode resonant antennas and different approaches to their implementation, with an emphasis on mode gauge functionality, a new concept for a clear identification and flexible control of all usable resonant modes in multi-mode resonant antenna design.

The book commences by advancing a generalized odd-even mode theory as a general theoretical framework for resonant elementary antennas, offering new insights into the classical problem of coupling effects between antenna and transmission lines and helping reveal the operation mechanism of elementary antennas under multi-mode resonance. Then, the concept of "mode gauge" is developed and employed for wideband elementary antenna design by simultaneously exciting and tuning multiple resonant modes within a single radiator. Apart from theoretical explorations, the authors also provide analysis of up-to-date implementation of multi-mode resonant elementary antennas with different functionalities, including wideband antennas, circularly polarized antennas, multiband antennas, frequency scanning antennas and low-profile antennas.

Academics, students and professional engineers at all levels will greatly benefit from the book and will be provided with historical background, state-of-the-art methodology, useful design tools and multiple applications of multi-mode resonant antennas.

CHAPTER 1 Generalized Theoretical Framework for Multi-Mode Resonant Antennas

DOI: 10.1201/9781003291633-1

1.1 General Design Guidelines of Resonant Antennas: Mathematical and Physical Models

In the classical antenna theory, an arbitrary resonant antenna (e.g., electric dipole, slot, loop, microstrip patch antenna, etc.) under investigation should use its principal resonant mode for radiation only, with an external excitation applied at $\stackrel{\rightharpoonup }{r}={\stackrel{\rightharpoonup }{r}}^{\prime }$ that can be mathematically emulated by the Dirac delta function $\delta \left(\stackrel{\rightharpoonup }{r}-{\stackrel{\rightharpoonup }{r}}^{\prime }\right)$. Physically, the Dirac delta function should be expanded into the Fourier series and matched to the antenna on its surface in terms of its resonant modes, i.e., the eigenfunctions (Zhang 1982, Collin 1991), which implies that the antenna system with external feed network should operate under multi-mode resonance. Therefore, a multi-mode resonant antenna design approach based upon the “one radiator, multiple resonant modes” idea and “multi-mode matching” concept should be rigorously advanced and depicted by a general mathematical model. Once such model is readily available, practical examples of dipole, slot, loop, and microstrip patch antennas (MPAs) will be employed to validate its correctness, effectiveness, and generality.

The problem of simultaneously exciting multiple resonant modes within a single resonator or an antenna can be generally described in the perspective of eigenvalue equation and the interior Green’s function of $G\left(\stackrel{\rightharpoonup }{r},{\stackrel{\rightharpoonup }{r}}^{\prime }\right)$, which is corresponding to the antenna’s surface field/current distribution. In this regard, the “interior Green’s function” should be distinguished from the “Green’s functions” in free space, open space, or half-open space that have been widely discussed in traditional electromagnetic radiation and scattering problems. The “multi-mode resonance problem” discussed herein should be quite similar to the classical guided wave problem (Rayleigh 1897, Barrow 1936) by solving homogenous or inhomogeneous wave equations under closed interval, finite closed cross section or closed cavity with specific boundary conditions. As extensively formulated in many classical textbooks, this is a boundary value problem of Helmholtz’s equation under specific finite-range, closed boundary conditions (Zhang 1982, Collin 1991).

Generally, suppose that the resonator or antenna under investigation should have an arbitrary size with a source of excitation at $\stackrel{\rightharpoonup }{r}={\stackrel{\rightharpoonup }{r}}^{\prime }$, thus the interior problem can be mathematically defined on a closed, finite interval of V with homogeneous boundary conditions on its smooth, twice continuous differentiable bounded surface ∂V, such that

(1.1a) $$\begin{array}{l}-\left({\nabla }^2+k^2\right)G\left(\stackrel{\rightharpoonup }{r},{\stackrel{\rightharpoonup }{r}}^{\prime }\right)=\delta \left(\stackrel{\rightharpoonup }{r}-{\stackrel{\rightharpoonup }{r}}^{\prime }\right),\stackrel{\rightharpoonup }{r},{\stackrel{\rightharpoonup }{r}}^{\prime }\in V\\ {\alpha \frac{\partial G}{\partial n_s}+\beta G=0|}_{\stackrel{\rightharpoonup }{r}\in \partial V}\end{array}$$

where n_s denotes the direction of the outer normal vector of the bounded surface ∂V. Correspondingly, the homogeneous equation and boundary condition of the resonator/antenna’s eigenmodes should satisfy

(1.1b) $$\begin{array}{l}-\left({\nabla }^2+k_n^2\right)\psi \left(\stackrel{\rightharpoonup }{r}\right)=0,\stackrel{\rightharpoonup }{r},{\stackrel{\rightharpoonup }{r}}^{\prime }\in V\\ {\alpha \frac{\partial \psi }{\partial n_s}+\beta \psi =0|}_{\stackrel{\rightharpoonup }{r}\in \partial V}\end{array}$$

where $\left\{{\psi }_n\left(\stackrel{\rightharpoonup }{r}\right)\right\}$ is the full, discrete set of accordingly defined eigenfunctions,...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Acknowledgments
• Authors
• 1 Generalized Theoretical Framework for Multi-Mode Resonant Antennas
• 2 Multi-Mode Resonant Electric Dipole Antennas
• 3 Multi-Mode Resonant Slot and Loop Antennas
• 4 Multi-Mode Resonant Complementary Dipole Antennas
• 5 Multi-Mode Resonant Microstrip Patch Antennas
• 6 Applications of Multi-Mode Resonant Antennas
• 7 Summarization
• Appendix A
• Appendix B
• References
• Index