Analytical Solution of the Problem of Synthesis of Three-Link Stepped Chebyshev’s Microwave Filter
The problem of synthesis of the three-link stepped Chebyshev’s microwave filter is reduced to two independent fourth-degree equations, including a single link wave impedance as unknown. The solution of Descartes—Euler is applied to these equations. It is proved that, in case wave impedances of extre...
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| Veröffentlicht in: | Technical physics letters 2024-02, Vol.50 (2), p.174-177 |
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| creator | Aref’ev, A. S. |
| description | The problem of synthesis of the three-link stepped Chebyshev’s microwave filter is reduced to two independent fourth-degree equations, including a single link wave impedance as unknown. The solution of Descartes—Euler is applied to these equations. It is proved that, in case wave impedances of extreme links are equal, the problem of the filter synthesis has two solutions. Identical phase-frequency responses correspond to these solutions. It is proved that for each link a product of the wave impedances relating to these solutions is equal to a square of the wave impedance of the transmission line including the filter. |
| doi_str_mv | 10.1134/S1063785023180025 |
| format | Article |
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It is proved that for each link a product of the wave impedances relating to these solutions is equal to a square of the wave impedance of the transmission line including the filter.</description><identifier>ISSN: 1063-7850</identifier><identifier>EISSN: 1090-6533</identifier><identifier>DOI: 10.1134/S1063785023180025</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Chebyshev approximation ; Classical and Continuum Physics ; Exact solutions ; Impedance ; Microwave filters ; Physics ; Physics and Astronomy ; Synthesis ; Transmission lines</subject><ispartof>Technical physics letters, 2024-02, Vol.50 (2), p.174-177</ispartof><rights>Pleiades Publishing, Ltd. 2024. ISSN 1063-7850, Technical Physics Letters, 2024, Vol. 50, No. 2, pp. 174–177. © Pleiades Publishing, Ltd., 2024. Russian Text © The Author(s), 2022, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2022, Vol. 48, No. 5, pp. 47–50. 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Lett</addtitle><description>The problem of synthesis of the three-link stepped Chebyshev’s microwave filter is reduced to two independent fourth-degree equations, including a single link wave impedance as unknown. The solution of Descartes—Euler is applied to these equations. It is proved that, in case wave impedances of extreme links are equal, the problem of the filter synthesis has two solutions. Identical phase-frequency responses correspond to these solutions. It is proved that for each link a product of the wave impedances relating to these solutions is equal to a square of the wave impedance of the transmission line including the filter.</description><subject>Chebyshev approximation</subject><subject>Classical and Continuum Physics</subject><subject>Exact solutions</subject><subject>Impedance</subject><subject>Microwave filters</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Synthesis</subject><subject>Transmission lines</subject><issn>1063-7850</issn><issn>1090-6533</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1UEFOwzAQtBBIlMIDuFniHFjHTmwfq4oCUhFI6T1ynA1JSZNip0W58Q2-x0tIVCQOiNPu7M6MdoeQSwbXjHFxkzCIuVQRhJwpgDA6IhMGGoI44vx47GMejPtTcub9GgBUGOkJyWeNqfuusqamSVvvuqptaFvQrkT67Nqsxs0Ik74ZJr7yI1iVDjFYVs0rTTrcbjGn8xKz3pe4__r49PSxsq59N3uki6ru0J2Tk8LUHi9-6pSsFrer-X2wfLp7mM-WgWVadYGOMLO5ErkMJRimJGhrVQa8MCY2hWE6i1lUiEwKsEzYUIDQoYq40kWmgE_J1cF269q3HfouXbc7N_znUw5aScmVFAOLHVjDjd47LNKtqzbG9SmDdMwy_ZPloAkPGj9wmxd0v87_i74BVuN2cw</recordid><startdate>20240201</startdate><enddate>20240201</enddate><creator>Aref’ev, A. S.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240201</creationdate><title>Analytical Solution of the Problem of Synthesis of Three-Link Stepped Chebyshev’s Microwave Filter</title><author>Aref’ev, A. S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-95ebcd84d7270a18709cc8b03faa6afa19b615f4b740c14c24049285389fb803</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Chebyshev approximation</topic><topic>Classical and Continuum Physics</topic><topic>Exact solutions</topic><topic>Impedance</topic><topic>Microwave filters</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Synthesis</topic><topic>Transmission lines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aref’ev, A. 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It is proved that, in case wave impedances of extreme links are equal, the problem of the filter synthesis has two solutions. Identical phase-frequency responses correspond to these solutions. It is proved that for each link a product of the wave impedances relating to these solutions is equal to a square of the wave impedance of the transmission line including the filter.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1063785023180025</doi><tpages>4</tpages></addata></record> |
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| ispartof | Technical physics letters, 2024-02, Vol.50 (2), p.174-177 |
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| subjects | Chebyshev approximation Classical and Continuum Physics Exact solutions Impedance Microwave filters Physics Physics and Astronomy Synthesis Transmission lines |
| title | Analytical Solution of the Problem of Synthesis of Three-Link Stepped Chebyshev’s Microwave Filter |
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