I. Overview
Improving the communication capacity and quality of wireless systems has always been a central goal in the field of wireless communication. As wireless technologies continue to evolve rapidly, there is an increasing demand for advanced antenna designs that can meet higher performance requirements. Ultra-wideband (UWB) and Multiple Input Multiple Output (MIMO) technologies have shown great potential in enhancing data transmission rates and improving signal reliability. MIMO technology enhances the signal-to-noise ratio, increases channel capacity, and mitigates fading effects in mobile communication systems. To achieve this, integrating multiple antenna units into a compact structure is essential, which requires low mutual coupling between the MIMO elements to ensure minimal signal correlation. The feature mode technique based on the method of moments is an effective approach for achieving this.
The eigenmode analysis method is a relatively new analytical technique that combines the method of moments with eigenmode theory to solve electromagnetic problems. It offers valuable insights for antenna designers by revealing how different modes contribute to the overall performance of an antenna. By analyzing the resonance characteristics and radiation patterns of various modes, designers can determine optimal feeding positions to excite the desired mode. This helps guide the design process and allows for fine-tuning of the antenna’s resonant frequency through slotting or other structural modifications. In this paper, the characteristic mode parameters of several common antenna structures are simulated using FEMO V14 software. The mode method defines a set of orthogonal eigenmodes that describe the intrinsic properties of complex electromagnetic structures. These modes provide a clear physical interpretation of the problem, making it easier for designers to understand and optimize their antenna designs.
II. Principle
The concept of eigenmode theory was first introduced by Garbacz in his PhD thesis in 1968. Later, Harrington and Mautz developed a more practical formulation based on the diagonalized impedance matrix of conductors. This version of the theory, known as the characteristic mode theory, is more straightforward to derive and verify for arbitrary geometries. Harrington and colleagues further extended the theory to include materials such as dielectrics, magnetic media, and hybrid configurations. Since its introduction, the characteristic mode theory has gained significant attention in computational electromagnetics and antenna design due to its ability to describe the inherent behavior of electromagnetic structures.
The eigenmode theory defines a set of mutually orthogonal modes for conductors of any shape. These modes represent the natural resonant characteristics of the structure and are independent of the source location. This makes them highly useful for guiding engineering design. The eigenmode equation is derived from the method of moments and is given by:
$$
\mathbf{Z} \mathbf{J}_n = \lambda_n \mathbf{R} \mathbf{J}_n
$$
where $\mathbf{J}_n$ represents the characteristic current, $\lambda_n$ is the eigenvalue, and $\mathbf{R}$ and $\mathbf{Z}$ are real and complex operators, respectively. The current distribution can be expressed as a linear combination of these characteristic currents:
$$
\mathbf{J} = \sum_{n=1}^{N} \alpha_n \mathbf{J}_n
$$
Here, $\alpha_n$ is the mode excitation coefficient, and the importance of each mode is determined by the Modal Weighting Coefficient (MWC). Additionally, the Modal Excitation Coefficient (MEC) indicates how easily a particular mode is excited by an external source.
The eigenvalues $\lambda_n$ and the corresponding characteristic currents $\mathbf{J}_n$ are real and orthogonal, satisfying the following orthogonality conditions:
$$
\langle \mathbf{J}_m, \mathbf{R}\mathbf{J}_n \rangle = \delta_{mn}
$$
$$
\langle \mathbf{J}_m, \mathbf{X}\mathbf{J}_n \rangle = \lambda_n \delta_{mn}
$$
$$
\langle \mathbf{J}_m, \mathbf{Z}\mathbf{J}_n \rangle = (1 + j\lambda_n)\delta_{mn}
$$
These relationships help define the energy storage characteristics of each mode. When $\lambda_n$ is close to zero, the mode is near resonance; positive values indicate magnetic energy storage, while negative values suggest electric energy storage. To quantify the significance of each mode, the Modal Significance (MS) and the Characteristic Angle (CA) are used:
$$
MS = \frac{1}{1 + |\lambda_n|}
$$
$$
CA = 180^\circ - \tan^{-1}(\lambda_n)
$$
The MS value ranges from 0 to 1, with higher values indicating stronger resonance. Similarly, a CA of 180° suggests a resonant mode. These parameters are also used to determine the radiation bandwidth of each mode, defined as the frequency range where the radiated power is at least half of the peak value.
III. Application
Using eigenmode analysis, key parameters such as eigenvalues, characteristic currents, and modal significance can be directly obtained. After applying port excitation, additional information such as mode excitation coefficients, radiation efficiency, and reflection coefficients can be extracted. This provides a comprehensive understanding of the antenna’s performance across different frequencies.
In this section, several common line antennas and MIMO PCB antenna structures are analyzed using FEKO V14 software. For wideband applications, mode tracking is essential because the dominant modes change with frequency. Techniques like mode tracking help maintain consistency in identifying the same mode across a frequency range, although some modes may disappear or new ones emerge. A typical eigenmode analysis process involves selecting the desired mode based on geometry, determining the optimal feeding position, and verifying the antenna’s performance against design specifications.
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