Incident and Load Power Relations in a Mismatched Lossless Transmission Line

IF 1.8 3区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Circuits, Systems and Signal Processing Pub Date : 2024-06-16 DOI:10.1007/s00034-024-02741-y

Disala Uduwawala, Roshan Weerasekera

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Abstract

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.

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失配无损耗输电线中的入射功率与负载功率关系

本文导出了一组方程，可根据无损传输线中与源阻抗和负载阻抗不匹配的负载反射系数和源反射系数，明确求出入射功率和负载功率。如果源阻抗和负载阻抗与频率有关，则传输线会随着频率的变化而失配。与传输线与信号源或负载匹配的情况不同，当信号源和负载阻抗与传输线不匹配时，入射功率和负载功率取决于传输线的长度。推导出的方程表明，功率随传输线长度变化，周期为半个波长。得出了相应线路长度的最大和最小入射功率和负载功率。此外，还介绍了如何使用史密斯图表找出这些长度以及最大值与最小值之比。最后，还介绍了结果的三个应用，包括 Friis 传输方程的附加版本以及频率相关源阻抗和负载阻抗的功率传输带宽改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Circuits, Systems and Signal Processing 工程技术-工程：电子与电气

CiteScore

4.80

自引率

13.00%

发文量

321

审稿时长

4.6 months

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.