Characteristic mode analysis

Characteristic mode analysis is a method used in electromagnetics to solve for currents and fields generated by a scattering object of any size or material.^[1]

Background

When an electromagnetic wave is scattered by an object, currents are induced on said object which subsequently re-radiate electromagnetic energy. The structure of the currents (and fields) are unique to the physical dimensions of the scatterer and incident frequency of radiation. From this perspective, a scatterer can be viewed as a parasitic antenna that radiates electromagnetic radiation in the same way that the original incident wave was radiated.^[1][2]

Principle

The principle behind characteristic mode analysis is based on optimizing the currents in any given structure by minimizing the stored power and maximizing the total radiated power.^[2] The characteristic modes of any structure can be solved by first calculating the impedance matrix of a structure. This is most commonly done by solving for the impedance matrix of the scatter, referred to as the $Z$ matrix, using the boundary element method. Once the impedance matrix is solved, the characteristic modes for the scatterer can be solved through the weighted eigenvalue equation:

$X(J_n) = \lambda _n R(J_n)$^[2]

In this equation, $R$ and $X$ represent the real and imaginary parts, respectively, of the $Z$ matrix, $\lambda _n$ represents the characteristic eigenvalues, and $J _n$ represents the characteristic currents or eigencurrents of the scatterer. It is important to note that both $R$ and $X$ are real and symmetric matrices. This means that all $\lambda _n$ and $J _n$ must also be real.

The eigenvalue has a unique meaning. The larger the absolute value of the characteristic eigenvalue, the more stored energy the scatter contains. When an eigenvalue is zero the mode is resonant and does not store any power. The following equations must also be satisfied for each characteristic eigencurrent when $m \neq n$:

$\left \langle J_m,RJ_n \right \rangle = 0$^[2]

$\left \langle J_m,XJ_n \right \rangle = 0$^[2]

$\left \langle J_m,ZJ_n \right \rangle = 0$^[2]

This particular identity states that each eigencurrent and radiated eigen far-fields are fully orthogonal to every other eigencurrent and eigen far-field. In 2007, it was first noted that due to this unique identity, characteristic modes facilitate extremely low correlation and hence will maximize MIMO performance.^[3] From this initial idea, a resurgence of interest in characteristic modes for the design of MIMO antennas took place.^[4] Since 2007, characteristic modes have been used to design chipless RFID tags,^[5] WiFi antennas,^[6] low frequency multi-band chassis antennas,^[7] UAV antennas,^[8] HF ship antennas,^[9] microstrip patch antenna designs,^[10] and dielectric resonator antenna designs.^[11]

References

1. Garbacz, R.J.; Turpin, R., "A generalized expansion for radiated and scattered fields," Antennas and Propagation, IEEE Transactions on , vol.19, no.3, pp.348,358, May 1971, doi: 10.1109/TAP.1971.1139935
2. Harrington, Roger F.; Mautz, J.R., "Theory of characteristic modes for conducting bodies," Antennas and Propagation, IEEE Transactions on , vol.19, no.5, pp.622,628, Sep 1971, doi: 10.1109/TAP.1971.1139999
3. Chaudhury, S.K.; Schroeder, W.L.; Chaloupka, H.J., "MIMO antenna system based on orthogonality of the characteristic modes of a mobile device," Antennas, 2007. INICA '07. 2nd International ITG Conference on , vol., no., pp.58,62, 28–30 March 2007, doi: 10.1109/INICA.2007.4353932
4. Hui Li; Yi Tan; Buon Kiong Lau; Zhinong Ying; Sailing He, "Characteristic Mode Based Tradeoff Analysis of Antenna-Chassis Interactions for Multiple Antenna Terminals," Antennas and Propagation, IEEE Transactions on , vol.60, no.2, pp.490,502, Feb. 2012, doi: 10.1109/TAP.2011.2173438
5. Rezaiesarlak, R.; Manteghi, M., "Design of Chipless RFID Tags Based on Characteristic Mode Theory (CMT)," Antennas and Propagation, IEEE Transactions on , vol.63, no.2, pp.711,718, Feb. 2015, doi: 10.1109/TAP.2014.2382640
6. Manteuffel, D.; Martens, R., "Multiple antenna integration in small terminals," Antennas and Propagation (ISAP), 2012 International Symposium on , vol., no., pp.211,214, Oct. 29 2012-Nov. 2 2012
7. Miers, Z.; Hui Li; Buon Kiong Lau, "Design of Bandwidth-Enhanced and Multiband MIMO Antennas Using Characteristic Modes," Antennas and Wireless Propagation Letters, IEEE , vol.12, no., pp.1696,1699, 2013, doi: 10.1109/LAWP.2013.2292562
8. Yikai Chen and Chao-Fu Wang, "Electrically Small UAV Antenna Design Using Characteristic Modes," Antennas and Propagation, IEEE Transactions on , vol.62, no.2, pp.535,545, Feb. 2014, doi: 10.1109/TAP.2013.2289999
9. Yikai Chen and Chao-Fu Wang, "HF Band Shipboard Antenna Design Using Characteristic Modes," Antennas and Propagation, IEEE Transactions on , vol.63, no.3, pp.1004,1013, March 2015,doi:10.1109/TAP.2015.2391288
10. Yikai Chen and Chao-Fu Wang,"Characteristic-mode-based improvement of circularly polarized U-slot and E-shaped patch antennas". IEEE Antennas and Wireless Propagation Letters (IEEE) 11 (1)
11. Yikai Chen and Chao-Fu Wang. "Dual-band directional/omni-directional liquid dielectric resonator antenna designs using characteristic modes". Antennas and Propagation Society International Symposium (APSURSI), 2014 IEEE (IEEE).