Inductance Formula for Square Spiral Inductors with Rectangular Conductor Cross Section

IF 0.8 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC

Advanced Electromagnetics Pub Date : 2019-09-10 DOI:10.7716/aem.v8i4.1074

H. Aebischer

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引用次数: 4

Abstract

Planar spiral coils are used as inductors in radio frequency (RF) microelectronic integrated circuits (IC’s) and as antennas in both radio frequency identification (RFID) and telemetry systems. They must be designed to a specified inductance. From the literature, approximate analytical formulae for the inductance of such coils with rectangular conductor cross section are known. They yield the direct current (DC) inductance, which is considered as a good approximation for inductors in RF IC’s up to the GHz range. In principle, these formulae can simplify coil design considerably. But a recent comparative study of the most cited formulae revealed that their maximum relative error is often much larger than claimed by the author, and too large to be useful in circuit design. This paper presents a more accurate formula for the DC inductance of square planar spiral coils than was known so far. It is applicable to any design of such coils with up to windings. Owing to its scalability, this holds irrespectively of the coil size and the inductance range. It lowers the maximum error over the whole domain of definition from so far down to . This has been tested by the same method used in the comparative study mentioned above, where the precise reference inductances were computed with the help of the free standard software FastHenry2. A comparison to measurements is included. Moreover, the source code of a MATLAB® function to implement the formula is given in the appendix.

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矩形导体截面方形螺旋电感的电感公式

平面螺旋线圈在射频（RF）微电子集成电路（IC）中用作电感器，在射频识别（RFID）和遥测系统中用作天线。它们必须设计成特定的电感。从文献中，已知具有矩形导体截面的这种线圈的电感的近似解析公式。它们产生直流（DC）电感，这被认为是RF IC中高达GHz范围的电感器的良好近似值。原则上，这些公式可以大大简化线圈设计。但最近对引用最多的公式进行的比较研究表明，它们的最大相对误差通常比作者声称的要大得多，而且太大，在电路设计中没有用处。本文提出了一个比目前已知的更精确的方形平面螺旋线圈直流电感公式。它适用于具有多达绕组的此类线圈的任何设计。由于其可扩展性，这与线圈尺寸和电感范围无关。它将整个定义域的最大误差从目前的范围降低到。这已经通过上面提到的比较研究中使用的相同方法进行了测试，其中精确的参考电感是在自由标准软件FastHenry2的帮助下计算的。包括与测量值的比较。此外，附录中给出了实现该公式的MATLAB®函数的源代码。

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

Advanced Electromagnetics ENGINEERING, ELECTRICAL & ELECTRONIC-

CiteScore

2.40

自引率

12.50%

发文量

审稿时长

10 weeks

期刊介绍： Advanced Electromagnetics, is electronic peer-reviewed open access journal that publishes original research articles as well as review articles in all areas of electromagnetic science and engineering. The aim of the journal is to become a premier open access source of high quality research that spans the entire broad field of electromagnetics from classic to quantum electrodynamics.