Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks
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 an...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2015/946289 |
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| _version_ | 1832550218331062272 |
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| author | Nelson Jorge G. Fonseca |
| author_facet | Nelson Jorge G. Fonseca |
| author_sort | Nelson Jorge G. Fonseca |
| collection | DOAJ |
| description | 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 general M×N multiple beam forming network. A more practical example is then given, discussing a specific 4×8 Nolen matrix design and comparing theoretical aspects with simulation results. |
| format | Article |
| id | doaj-art-6dd94df8ff894d9db409d99815d881de |
| institution | Kabale University |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-6dd94df8ff894d9db409d99815d881de2025-02-03T06:07:27ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772015-01-01201510.1155/2015/946289946289Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming NetworksNelson Jorge G. Fonseca0Moltek Consultants Ltd. for the European Space Agency (ESA), Antenna and Sub-Millimetre Wave Section, Keplerlaan 1, P.O. Box 299, 2200AG Noordwijk, NetherlandsThe 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 general M×N multiple beam forming network. A more practical example is then given, discussing a specific 4×8 Nolen matrix design and comparing theoretical aspects with simulation results.http://dx.doi.org/10.1155/2015/946289 |
| spellingShingle | Nelson Jorge G. Fonseca Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks International Journal of Antennas and Propagation |
| title | Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks |
| title_full | Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks |
| title_fullStr | Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks |
| title_full_unstemmed | Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks |
| title_short | Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks |
| title_sort | discussion on reciprocity unitary matrix and lossless multiple beam forming networks |
| url | http://dx.doi.org/10.1155/2015/946289 |
| work_keys_str_mv | AT nelsonjorgegfonseca discussiononreciprocityunitarymatrixandlosslessmultiplebeamformingnetworks |