Global Optimization Method of the Design for Multi-Layer Planar Inductors

李清华; 邵志标; 耿莉

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Global Optimization Method of the Design for Multi-Layer Planar Inductors

更新时间：2025-12-08

- Global Optimization Method of the Design for Multi-Layer Planar Inductors
- Vol. 41, Issue 6, Pages: 665-668(2007)
- 作者机构：
  
  西安交通大学电子与信息工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN4
- Online First：10 June 2007，
  
  Published：2007
- 稿件说明：
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李清华, 邵志标, 耿莉. Global Optimization Method of the Design for Multi-Layer Planar Inductors[J]. 2007, 41(6): 665-668.
DOI：

李清华, 邵志标, 耿莉. Global Optimization Method of the Design for Multi-Layer Planar Inductors[J]. 2007, 41(6): 665-668. DOI：

摘要

为多层平面电感设计提出了一种全局优化方法.该方法在给出等效物理模型的基础上

以获得最大品质因数为设计目标

以工作频率、单位面积电感值、电感线圈的电流承受能力为约束条件

将优化问题表示为平面电感器结构参数的正项式函数

即将优化问题便捷地转换为几何规划

使之在不同条件下均可快速获得优化结果.采用全局优化方法设计的电感器芯片的测试数据表明

在给定的约束条件下

单位面积电感值大于80 mH/m

金属条宽度大于10 μm

频段范围50 ～ 400 MHz

优化得到的品质因数与测试结果的最大误差在10%以内.

Abstract

A global optimization method is presented to optimize the multi-layer planar inductors. The essential idea of the algorithm is as follows. Based on the proposed physical model

acquiring the maximum quality factor is considered as design objective

and frequency

inductance in unit area and current handling capability are regarded as constraints

hence the designed problem is formulized as the posynomial functions of the physical dimensions of inductors

i.e. the optimum problem can be equivalent to geometric programming so as to quickly obtain optimization result under different conditions. From the measurement results of the inductors designed by the method

the maximum error between the measured quality factor and the optimized results is less than 10% under the restrictions where the inductance in unit area is greater than 80 mH per square meter

metal width is no less than 10 millimeter and frequency band is 50-400 MHz.

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references

Li Qinghua,Geng Li,Shao Zhibiao.Optimum double-layer spiral inductor on silicon substrate designed for monolithic buck converters [C]∥Proc of 17th Asia-Pacific Microwave Conference.Piscataway,USA:IEEE,2005:2156-2159.

李清华,邵志标,耿莉.硅基完全集成DC/DC 转换器中多层平面电感设计与建模[J].西安交通大学学报,2007,41(4):463-466.

Li Qinghua, Shao Zhibiao, Geng Li. Design and modeling of multi-layer planar inductor for fully integrated DC/DC converters on silicon substrate [J].Journal of Xi'an Jiaotong University,2007,41(4):463-466.

Boyd S P, Kim S J, Vandenberghe L,et al.Convex optimization [M].Cambridge:Cambridge University Press,2004:397-447.

Mohan S S, del Hershenson M M, Boyd S P, et al.Simple accurate expressions for planar spiral inductances [J].IEEE Journal of Solid-State Circuits,1999,34(10):1419-1424.

Yue C P, Ryu C, Lau J, et al.A physical model for planar spiral inductors on silicon [C]∥International Electron Devices Meeting.Piscataway, USA:IEEE,1996:155-158.

Zolfaghari A,Chan A,Razavi B.Stacked inductors and transformers in CMOS technology [J].IEEE Journal of Solid-State Circuits,2001,36(4):620-628.

del Hershenson M M,Mohan S S,Boyd S P,et al.Optimization of inductor circuits via geometric programming[C]∥Proc of 36th Design Automation Conference.Piscataway, USA:IEEE,1999:994-998.

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