I. Overview
Improving the communication capacity and quality of wireless systems has always been a key focus in the field of wireless technology. As wireless communication advances, the demand for more efficient antenna designs continues to grow. Ultra-Wideband (UWB) and Multiple-Input Multiple-Output (MIMO) technologies are particularly promising in enhancing data transmission rates. MIMO systems can improve signal-to-noise ratios, increase channel capacity, and reduce the effects of fading in mobile environments. To achieve this, it's essential to integrate multiple antenna units while ensuring low mutual coupling between them, which helps maintain low signal correlation. The characteristic mode method, based on the moment method, is an effective approach for achieving these goals.
The eigenmode analysis technique is a relatively new analytical method that combines the moment method with eigenmode theory to solve electromagnetic problems. It provides valuable insights into how antennas function, helping designers better understand their performance. By analyzing different modes, engineers can identify resonance characteristics and radiation behavior, and then choose optimal feeding positions to excite specific modes. This process not only improves antenna design but also enables the creation of new antenna structures. In this paper, we simulate the characteristic mode parameters of several common antenna types using FEKO V14 [2]. The mode method defines a set of eigenmodes that describe the intrinsic properties of electromagnetic problems. These modes are orthogonal, and the magnitude of their eigenvalues determines their contribution to the overall electromagnetic behavior. This makes the moment method more intuitive and useful for antenna design.
II. Principle
The eigenmode theory was first introduced by Garbacz in his PhD thesis in 1968 [4]. Later, Harrington and Mautz developed a similar approach using the generalized impedance matrix of diagonalized conductors [5]-[6], leading to what is now known as the characteristic mode theory. This version is easier to derive and more practical for verifying arbitrary-shaped structures. Harrington and others extended the theory to include dielectrics, magnetic media, and hybrid materials [7]. Since its introduction, the characteristic mode theory has gained widespread attention in computational electromagnetics and antenna design.
The theory defines a set of mutually orthogonal eigenmodes for conductors of any shape. These modes are inherent to the structure and possess convergence and completeness, allowing them to accurately represent electromagnetic solutions. The physical model is clear, making it easier to understand how electromagnetic structures operate. Moreover, the eigenmodes depend only on the geometry, size, and frequency of the structure, not on the source, making them highly applicable in engineering design.
The eigenmode theory is based on the Method of Moments (MoM). Its eigen-equation is:
$$ \mathbf{Z} \cdot \mathbf{J}_n = \lambda_n \mathbf{R} \cdot \mathbf{J}_n $$
The current on the conductor is expressed as a linear combination of characteristic currents:
$$ \mathbf{J} = \sum_{n=1}^{N} \alpha_n \mathbf{J}_n $$
From this, we derive:
$$ \alpha_n = \frac{\langle \mathbf{E}_i, \mathbf{J}_n \rangle}{\langle \mathbf{J}_n, \mathbf{R} \cdot \mathbf{J}_n \rangle} $$
Here, $ \alpha_n $ represents the Modal Weighting Coefficient (MWC), and $ \lambda_n $ is the eigenvalue. The mode excitation coefficient (MEC), $ V_n $, determines which mode is most easily excited when a signal is applied.
Since $ \mathbf{R} $ and $ \mathbf{X} $ are Hermitian and real symmetric operators, the eigenvalues $ \lambda_n $ and characteristic currents $ \mathbf{J}_n $ are real. The characteristic currents satisfy orthogonality conditions:
$$ \langle \mathbf{J}_m, \mathbf{R} \cdot \mathbf{J}_n \rangle = \delta_{mn} $$
$$ \langle \mathbf{J}_m, \mathbf{X} \cdot \mathbf{J}_n \rangle = \lambda_n \delta_{mn} $$
$$ \langle \mathbf{J}_m, \mathbf{Z} \cdot \mathbf{J}_n \rangle = (1 + j\lambda_n) \delta_{mn} $$
These equations help determine the energy storage type of each mode. A positive $ \lambda_n $ indicates magnetic energy storage, while a negative value suggests electric energy storage. When $ \lambda_n $ approaches zero, the mode is near resonance.
To further analyze the resonance characteristics, the Modal Significance (MS) and Characteristic Angle (CA) are used:
$$ MS_n = \frac{1}{1 + |\lambda_n|} $$
$$ CA_n = 180^\circ - \tan^{-1}(\lambda_n) $$
A higher MS means the mode is closer to resonance. When CA is 180°, the mode is at resonance. The bandwidth of each mode can be defined based on the MS value, typically when MS is 0.707, corresponding to a 3 dB bandwidth.
III. Application
Using characteristic mode analysis, engineers can directly obtain parameters such as eigenvalues $ \lambda_n $, characteristic currents $ \mathbf{J}_n $, characteristic angles $ CA_n $, and mode significance $ MS_n $. After applying port excitation, the mode excitation coefficient (MEC), mode weighting factor (MWC), and other parameters like reflection coefficients and antenna efficiency can be calculated.
In this section, we analyze several commonly used line antennas and MIMO PCB antennas using FEKO V14. For wide-band eigenmode analysis, Mode Tracking [8][9] is essential, as resonant modes change with frequency. Some modes may disappear while new ones emerge. Careful tracking is required to ensure all relevant modes are considered. The typical eigenmode analysis process includes selecting desired modes based on geometry, determining feed positions, and validating design parameters against requirements.
30L Agriculture Drone,Fertilizer Drone,Gfrp Agricultural Sprayer,Fold Sprayer Drone
Xuzhou Jitian Intelligent Equipment Co. Ltd , https://www.jitianintelligent.com