螺旋式電感之物理模型

Abstract

由於工業技術水準的提升以及人類生活的需求，便於攜帶的無線通訊系統被傾向於整合在高效能的電子元件上。射頻積體電路元件之特性亦被完整的研究與分析。特別是晶片螺旋式電感，其將扮演著射頻積體電路分析上最重要的角色。為了提升射頻積體電路之效率與實用性，此篇論文將提供一套新穎且簡單的物理方法以精準地分析、估計射頻晶片螺旋式電感之感值與共振頻率。有別於以往計算螺旋式電感感值的方法與侷限度，當改變電感的材料參數時，根據Kramers-Kronig relations、電磁場論以及固態物理所推導而成之物理公式，本論文所提供之電感模型將可以協助尋求最佳的電感感值與共振頻率。更進一步地，本論文亦為提供計算螺旋式電感之共振頻率方法的先驅者。共振頻率的決定將可以協助電路分析人員以及微波工程師去選擇最為適當的電感頻寬。因此，本論文將提供了一套便利且精準的方法以輕易地解決設計層面的問題，並可以簡化且履行晶片射頻螺旋式電感在高頻積體電路的設計與應用。

On-Chip spiral inductors have been developed and widely used for RFIC designs. Their relative characteristics including inductance, quality factor, self-resonant frequency, and loss mechanism…etc., have already been investigated in details. Especially, the prediction of inductance and self-resonant frequency of a spiral inductor will easily help circuit designers and microwave engineers to manufacture the RFICs. There are several methods to calculate inductance and self-resonant frequency of a spiral inductor, such as calculating circuit parameter, S-parameter, simulations utilizing computers, closed-form models, and measurement from experiments. The applied methods, however, are based only on the circuit designs parameters. Meanwhile, there are non-physical expressions. The physical meaningless factors in the circuit could not explain how to search out the optimum design based on a physical sense. All of these methods could not determine the self-resonant frequency and evaluate the inductance while altering the material of inductors. The computer simulations could assist the engineers in circuit analysis, but it should spend great deal of hours to obtain the approximate results. Although this approach could precisely determine the self-resonant frequency, it is time-consuming in calculation and non-physically straightforward which could not help circuit designer to easily reach for an optimal design. Therefore, in order to surmount those predicaments this thesis will provide a physical method for predicting the inductance and self-resonant frequency of a spiral inductor.