Total active reflection coefficient
The total active reflection coefficient (TARC) within mathematics and physics scattering theory, relates the total incident power to the total outgoing power in an N-port microwave component. The TARC is mainly used for multiple-input multiple-output (MIMO) antenna systems and array antennas, where the outgoing power is unwanted reflected power. The name shows the similarities with the active reflection coefficient, which is used for single elements. The TARC is the square root of the sum of all outgoing powers at the ports, divided by the sum of all incident powers at the ports of an N-port antenna. Similarly to the active reflection coefficient, the TARC is a function of frequency, and it also depends on scan angle and tapering. With this definition we can characterize the multi-port antenna’s frequency bandwidth and radiation performance. When the antennas are made of lossless materials, TARC can be computed directly from the scattering matrix by Γ a t = ∑ i = 1 N | b i | 2 ∑ i = 1 N | a i | 2 , {\displaystyle \Gamma _{a}^{t}={\frac {\sqrt {\sum _{i=1}^{N}|b_{i}|^{2}}}{\sqrt {\sum _{i=1}^{N}|a_{i}|^{2}}}},} where [ b ] = [ S ] [ a ] . {\displaystyle [b]=[S][a].} [ S ] {\displaystyle [S]} is the antenna's scattering matrix, [ a ] {\displaystyle [a]} is the excitation vector, and [ b ] {\displaystyle [b]} represents the scattered vector. The TARC is a real number between zero and one, although it is typically presented in decibel scale. When the value of the TARC is equal to zero, all the delivered power is accepted by the antenna and when it is equal to one, all the delivered is coming back as outgoing power (thus the all power is reflected, but not necessarily in the same port). The normalized total accepted power is given by ( 1 − | Γ a t | 2 ) {\displaystyle (1-|\Gamma _{a}^{t}|^{2})} . Since antennas in general have radiation efficiency 0 ≤ ϵ ≤ 1 {\displaystyle 0\leq \epsilon \leq 1} , the normalized total radiated power is given by ϵ l = ϵ ( 1 − | Γ a t | 2 ) {\displaystyle \epsilon _{l}=\epsilon (1-|\Gamma _{a}^{t}|^{2})} . If the directivity of the antenna array is known, the realized gain can therefore be computed by multiplication by ϵ l {\displaystyle \epsilon _{l}} . As with all reflection coefficients, a small reflection coefficient does not guarantee a high radiation efficiency since the small reflected signal could also be due to losses.
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The total active reflection coefficient (TARC) within mathematics and physics scattering theory, relates the total incident power to the total outgoing power in an N-port microwave component. The TARC is mainly used for multiple-input multiple-output (MIMO) antenna systems and array antennas, where the outgoing power is unwanted reflected power. The name shows the similarities with the active reflection coefficient, which is used for single elements. The TARC is the square root of the sum of all outgoing powers at the ports, divided by the sum of all incident powers at the ports of an N-port antenna. Similarly to the active reflection coefficient, the TARC is a function of frequency, and it also depends on scan angle and tapering. With this definition we can characterize the multi-port antenna’s frequency bandwidth and radiation performance. When the antennas are made of lossless materials, TARC can be computed directly from the scattering matrix by
where is the antenna's scattering matrix, is the excitation vector, and represents the scattered vector. The TARC is a real number between zero and one, although it is typically presented in decibel scale. When the value of the TARC is equal to zero, all the delivered power is accepted by the antenna and when it is equal to one, all the delivered is coming back as outgoing power (thus the all power is reflected, but not necessarily in the same port).
![{\displaystyle [b]=[S][a].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/198035cfb6372e1b8cbbbf989786a22addf71dd2)
![{\displaystyle [S]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/292bbb82029aa583c5d2ac5fa1d7e4fedf537d8b)
![{\displaystyle [a]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea82bc70a8e322f13a3c4e5b9d5d69e8ef097ad8)
![{\displaystyle [b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e016d81a1b29bb79b275e446042b925b7dd6b6d7)
The normalized total accepted power is given by . Since antennas in general have radiation efficiency , the normalized total radiated power is given by . If the directivity of the antenna array is known, the realized gain can therefore be computed by multiplication by . As with all reflection coefficients, a small reflection coefficient does not guarantee a high radiation efficiency since the small reflected signal could also be due to losses.
See also
[edit]References
[edit]- Majid Manteghi; Yahya Rahmat-Samii (22–27 June 2003). "Broadband characterization of the total active reflection coefficient of multiport antennas". IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450). Vol. 3. pp. 20–23. doi:10.1109/APS.2003.1219779. ISBN 0-7803-7846-6. S2CID 23610526.
{{cite book}}: CS1 maint: multiple names: authors list (link) - Majid Manteghi; Yahya Rahmat-Samii (January 2005). "Multiport characteristics of a wide-band cavity backed annular patch antenna for multipolarization operations". IEEE Transactions on Antennas and Propagation. 53 (1): 466–474. Bibcode:2005ITAP...53..466M. doi:10.1109/tap.2004.838794. S2CID 24527268.
{{cite journal}}: CS1 maint: multiple names: authors list (link) - Daniel Valderas; Pedro Crespo & Cong Ling (April 2010). "UWB portable printed monopole array design for MIMO communications". Microwave and Optical Technology Letters. 52 (4): 889–895. doi:10.1002/mop.25047. S2CID 8234509.
- Sung Ho Chae; Se-keun Oh; Seong-Ook Park (2007). "Analysis of Mutual Coupling, Correlations, and TARC in WiBro MIMO Array Antenna". IEEE Antennas and Wireless Propagation Letters. 6 (11): 122–125. Bibcode:2007IAWPL...6..122C. doi:10.1109/lawp.2007.893109. S2CID 22725306.
- Po-Chuan Hsieh; Fu-Chiarng Chen (July 2008). "The relation of TARC-based radiation efficiency and port termination for multiple antenna systems". 2008 IEEE Antennas and Propagation Society International Symposium. pp. 1–4, 5–11. doi:10.1109/APS.2008.4619408. ISBN 978-1-4244-2041-4. S2CID 38985848.
- Z. B. Zainal-Abidin; et al. (2011). "Design of 2 x 2 U-shape MIMO slot antennas with EBG material for mobile handset applications" (PDF). Progress In Electromagnetics Research Symposium Proceedings. Electromagnetics Academy. pp. 1275–1278. hdl:10454/5467. ISBN 978-1-934142-16-5.
- A. R. Mallahzadeh; S. Es'haghi & A. Alipour (2009). "DESIGN OF AN E-SHAPED MIMO ANTENNA USING IWO ALGORITHM FOR WIRELESS APPLICATION AT 5.8 GHz" (PDF). Progress in Electromagnetics Research. 90: 187–203. doi:10.2528/PIER08122704.