{"title":"失配无损耗输电线中的入射功率与负载功率关系","authors":"Disala Uduwawala, Roshan Weerasekera","doi":"10.1007/s00034-024-02741-y","DOIUrl":null,"url":null,"abstract":"<p>In this article, a set of equations is derived to find incident and load power explicitly in terms of load and source reflection coefficients in a lossless transmission line mismatched to both source and load impedances. A transmission line can be mismatched as the frequency varies if the source and load impedances are frequency dependent. Unlike in a scenario, where the transmission line is either matched to the source or load, the incident and load power depends on the length of the transmission line when both the source and load impedances are not matched to the line. The equations derived show that the power varies with the line length with a period of half wavelength. The maximum and minimum incident and load power with the corresponding line lengths are derived. The use of the Smith chart to find these lengths and the ratio of maximum to minimum is also described. Finally, three applications of the results including an additional version of the Friis transmission equation and the bandwidth improvement of power transfer for frequency dependent source and load impedances are presented.</p>","PeriodicalId":10227,"journal":{"name":"Circuits, Systems and Signal Processing","volume":"19 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Incident and Load Power Relations in a Mismatched Lossless Transmission Line\",\"authors\":\"Disala Uduwawala, Roshan Weerasekera\",\"doi\":\"10.1007/s00034-024-02741-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, a set of equations is derived to find incident and load power explicitly in terms of load and source reflection coefficients in a lossless transmission line mismatched to both source and load impedances. A transmission line can be mismatched as the frequency varies if the source and load impedances are frequency dependent. Unlike in a scenario, where the transmission line is either matched to the source or load, the incident and load power depends on the length of the transmission line when both the source and load impedances are not matched to the line. The equations derived show that the power varies with the line length with a period of half wavelength. The maximum and minimum incident and load power with the corresponding line lengths are derived. The use of the Smith chart to find these lengths and the ratio of maximum to minimum is also described. Finally, three applications of the results including an additional version of the Friis transmission equation and the bandwidth improvement of power transfer for frequency dependent source and load impedances are presented.</p>\",\"PeriodicalId\":10227,\"journal\":{\"name\":\"Circuits, Systems and Signal Processing\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Circuits, Systems and Signal Processing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s00034-024-02741-y\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Circuits, Systems and Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00034-024-02741-y","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Incident and Load Power Relations in a Mismatched Lossless Transmission Line
In this article, a set of equations is derived to find incident and load power explicitly in terms of load and source reflection coefficients in a lossless transmission line mismatched to both source and load impedances. A transmission line can be mismatched as the frequency varies if the source and load impedances are frequency dependent. Unlike in a scenario, where the transmission line is either matched to the source or load, the incident and load power depends on the length of the transmission line when both the source and load impedances are not matched to the line. The equations derived show that the power varies with the line length with a period of half wavelength. The maximum and minimum incident and load power with the corresponding line lengths are derived. The use of the Smith chart to find these lengths and the ratio of maximum to minimum is also described. Finally, three applications of the results including an additional version of the Friis transmission equation and the bandwidth improvement of power transfer for frequency dependent source and load impedances are presented.
期刊介绍：
Rapid developments in the analog and digital processing of signals for communication, control, and computer systems have made the theory of electrical circuits and signal processing a burgeoning area of research and design. The aim of Circuits, Systems, and Signal Processing (CSSP) is to help meet the needs of outlets for significant research papers and state-of-the-art review articles in the area.
The scope of the journal is broad, ranging from mathematical foundations to practical engineering design. It encompasses, but is not limited to, such topics as linear and nonlinear networks, distributed circuits and systems, multi-dimensional signals and systems, analog filters and signal processing, digital filters and signal processing, statistical signal processing, multimedia, computer aided design, graph theory, neural systems, communication circuits and systems, and VLSI signal processing.
The Editorial Board is international, and papers are welcome from throughout the world. The journal is devoted primarily to research papers, but survey, expository, and tutorial papers are also published.
Circuits, Systems, and Signal Processing (CSSP) is published twelve times annually.
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