Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks. (9th April 2015)

• Record Type: Journal Article
• Authors: Fonseca, Nelson Jorge G.
• Other Names: Yao Yuan Academic Editor.
• Is Part Of: International journal of antennas and propagation. Volume 2015(2015)
• Publication Date: 2015-04-09
• Subjects: Electronic apparatus and appliances -- Periodicals; Antennas (Electronics) -- Periodicals; Radio wave propagation -- Periodicals; Antennes (Électronique); Ondes radioélectriques -- Propagation; Antennas (Electronics); Electronic apparatus and appliances; Radio wave propagation; Electronic journals; Periodicals; 621.382405
• DOI: 10.1155/2015/946289
• Languages: English
• ISSNs: 1687-5869

Abstract

Abstract : The Lorentz reciprocity theorem enables us to establish that the transmitting and receiving patterns of any antenna are identical, provided some hypotheses on this antenna and the surrounding medium are satisfied. But reciprocity does not mean that the antenna behaves the same in the transmitting and the receiving modes. In this paper, array antennas fed by multiple beam forming networks are discussed, highlighting the possibility to have different values of internal losses in the beam forming network depending on the operation mode. In particular, a mathematical condition is derived for the specific case of a multiple beam forming network with lossless transmitting mode and lossy receiving mode, such a behavior being fully consistent with the reciprocity theorem. A theoretical discussion is provided, starting from a simple 2-element array to a generalM × N multiple beam forming network. A more practical example is then given, discussing a specific4 × 8 Nolen matrix design and comparing theoretical aspects with simulation results.