自由空間法分析介質(zhì)蜂窩等效復(fù)介電常數(shù)*

張?jiān)葡?趙志欽,史維光,王 茜

(1.電子科技大學(xué)電子工程學(xué)院,成都611731;2.濟(jì)南特種結(jié)構(gòu)研究所,濟(jì)南250023)

自由空間法分析介質(zhì)蜂窩等效復(fù)介電常數(shù)*

張?jiān)葡?,**,趙志欽1,史維光1,王 茜2

(1.電子科技大學(xué)電子工程學(xué)院,成都611731;2.濟(jì)南特種結(jié)構(gòu)研究所,濟(jì)南250023)

根據(jù)自由空間法介質(zhì)材料介電常數(shù)測試原理,采用商用電磁場仿真軟件給出了介質(zhì)蜂窩材料等效復(fù)介電常數(shù)的分析方法,計(jì)算出了特定材料、格孔周期蜂窩材料的等效復(fù)介電常數(shù)。為驗(yàn)證方法的正確性,對等效介電常數(shù)的平板和相應(yīng)的蜂窩的透射反射系數(shù)的幅度相位進(jìn)行了比較,兩者吻合良好。通過對寬帶范圍內(nèi)蜂窩等效介電常數(shù)的計(jì)算表明,介質(zhì)蜂窩具有微小的色散效應(yīng),隨著頻率增高,蜂窩的相對介電常數(shù)、損耗正切略微減小;蜂窩的磁介電常數(shù)接近為1,磁損耗正切接近為0。

介質(zhì)蜂窩;復(fù)介電常數(shù);自由空間法;周期性邊界條件

1 引 言

芳綸紙蜂窩材料具有低損耗、介電常數(shù)低、容重輕、比剛度、比強(qiáng)度高、良好的隔熱性、阻燃性,良好的機(jī)加工特性,是一種理想的機(jī)載、彈載雷達(dá)罩芯層透波材料。除了在純承力、隔熱結(jié)構(gòu)件外,介質(zhì)蜂窩材料在天線罩設(shè)計(jì)領(lǐng)域、吸波材料、頻率選擇表面等領(lǐng)域具有非常廣泛的應(yīng)用。在對雷達(dá)罩電性能的設(shè)計(jì)過程中,材料的介電常數(shù)是天線罩必須的基本條件之一[1-3]。由于蜂窩是一種周期性人工介質(zhì)材料,格孔壁非常薄,在微米數(shù)量級,格孔周期在毫米數(shù)量級,在電磁性能設(shè)計(jì)仿真過程中如果對其實(shí)體建模必然會大大降低計(jì)算效率,增加計(jì)算內(nèi)存資源,現(xiàn)有的計(jì)算機(jī)性能無法滿足實(shí)際工程設(shè)計(jì)需要。因此,一般而言在實(shí)際天線罩工程設(shè)計(jì)過程中,首先提取蜂窩材料的等效介電常數(shù),把周期性的蜂窩結(jié)構(gòu)等效為一種均勻介質(zhì)。蜂窩格孔的結(jié)構(gòu)參數(shù)決定著對蜂窩的力學(xué)、熱學(xué)、電磁性能,研究介質(zhì)蜂窩材料格孔參數(shù)與蜂窩等效介電常數(shù)的關(guān)系對蜂窩材料的設(shè)計(jì)具有重要的意義。

傳統(tǒng)的蜂窩設(shè)計(jì)(包括其他類似的多孔結(jié)構(gòu)人工合成材料,如多孔氮化硅等)一般采用經(jīng)驗(yàn)公式的方法來預(yù)估蜂窩的介電常數(shù)[4-5],然后通過測試來最終確定該材料的實(shí)際復(fù)介電常數(shù)值。這種方法相對簡單,不是嚴(yán)格的理論解,存在較大誤差。隨著電磁數(shù)值計(jì)算理論的發(fā)展,時(shí)域有限差分法、有限元法、準(zhǔn)靜態(tài)法[6-8]等都可應(yīng)用于人工材料等效介電常數(shù)的預(yù)估,這類方法計(jì)算精度較高,但這些算法相對復(fù)雜難以短時(shí)間內(nèi)掌握。采用成熟的仿真軟件如ANSYS公司的HFSS、CST公司的CST微波工作室以及EMSS公司的FEKO等,可以克服上述缺點(diǎn)[9-10]。文獻(xiàn)[9]中基于ANSYS公司的EMG軟件采用半自由空間法分析了蜂窩的等效介電常數(shù),半自由空間的介電常數(shù)計(jì)算公式為一超越方程,從而給復(fù)介電常數(shù)計(jì)算帶來不便。文獻(xiàn)[11]采用強(qiáng)擾動理論對蜂窩吸波材料的等效復(fù)介電常數(shù)進(jìn)行了分析但是忽略了蜂窩桿間的耦合效應(yīng)。文獻(xiàn)[12]采用均質(zhì)化方法對蜂窩吸波材料等效介電常數(shù)進(jìn)行分析,難以反映具體結(jié)構(gòu)參數(shù)對材料造成的影響。本文借助ANSYS公司的有限元電磁分析工具HFSS對蜂窩的介電常數(shù)解析分析。此外,采用自由空間仿真的方法來提取蜂窩材料的等效介電常數(shù),避免了自由空間測試過程中由于背景電平、材料邊緣繞射帶來的測試誤差。

本文其余內(nèi)容安排如下:第2節(jié)介紹自由空間法介電常數(shù)測試?yán)碚?第3節(jié)給出蜂窩結(jié)構(gòu)的仿真流程,第4節(jié)采用自由空間法介電常數(shù)測試方法,根據(jù)仿真結(jié)果給出不同蜂窩結(jié)構(gòu)參數(shù)對蜂窩等效介電常數(shù)的影響。

2 自由空間法介電常數(shù)測試?yán)碚揫13]

在自由空間中,假設(shè)材料的復(fù)介電常數(shù)為

如圖1所示,假設(shè)垂直入射的線極化波的反射和傳輸系數(shù)分別為S11和S21,則有

其中,Γ和T分別為介質(zhì)材料在與空氣交界面上的傳輸反射系數(shù)。

其中:

求解上面

其中:

正負(fù)號選取由|Γ|＜1確定。

則

圖1 介質(zhì)材料示意圖Fig.1 The geometry of dielectric

3 蜂窩結(jié)構(gòu)的仿真

蜂窩材料為一種周期性人工介質(zhì)結(jié)構(gòu),如圖2所示,需要采用周期性邊界條件進(jìn)行仿真分析。目前主流的三維電磁仿真軟件如HFSS、CST、FEKO等都支持周期性邊界條件分析。本文采用HFSS有限元電磁分析軟件進(jìn)行仿真,對蜂窩的六邊形結(jié)構(gòu)進(jìn)行分析可知其周期性單元,如圖3所示。假設(shè)蜂窩格孔厚度為t,邊長為a,則其元胞周期邊長為3 a、夾角為60°的平行四邊形。

圖2 蜂窩的實(shí)際結(jié)構(gòu)Fig.2 The real dielectric honeycomb structure

圖3 蜂窩的元胞Fig.3 The unit cell of honeycomb

在仿真軟件中設(shè)置入射波為垂直入射,入射參考面為蜂窩上下入射表面,則可以仿真計(jì)算出各頻點(diǎn)的散射矩陣參數(shù)S11和S21。

4 計(jì)算實(shí)例與方法驗(yàn)證

為驗(yàn)證方法的正確性,本文對實(shí)際應(yīng)用的蜂窩結(jié)構(gòu)等效介電常數(shù)進(jìn)行了計(jì)算。芳綸紙的介電常數(shù)為ε=4(1-j0.03),蜂窩格孔a=2.75 mm,格孔厚度t=0.08 mm,蜂窩介質(zhì)厚度d=2 mm。蜂窩周期如圖4所示,則通過仿真其S參數(shù)如圖5和圖6所示,采用第2節(jié)給出的計(jì)算公式則可求得蜂窩的等效復(fù)介電常數(shù)如圖7～10所示。

圖4 HFSS蜂窩周期模型Fig.4 The periodic honeycomb simulation model in HFSS

圖5 2 mm厚蜂窩S11仿真結(jié)果Fig.5 The S11of 2 mm thickness dielectric honeycomb

圖6 2 mm厚蜂窩S21仿真結(jié)果Fig.6 The S21of 2 mm thickness dielectric honeycomb

圖7 蜂窩等效介電常數(shù)Fig.7 The effective relative dielectric constant of honeycomb

圖8 蜂窩等效損耗正切Fig.8 The effective loss tangent of honeycomb

圖9 蜂窩等效磁介電常數(shù)Fig.9 The effective relative magnetic dielectric constant of honeycomb

圖10 蜂窩等效磁損耗正切Fig.10 The effective magnetic loss tangent of honeycomb

為驗(yàn)證方法的正確性,本文將同樣材料即6 mm厚度的蜂窩和采用相應(yīng)計(jì)算得到的等效介電常數(shù)的介質(zhì)平板分別進(jìn)行仿真,平面波入射方向?yàn)榇怪比肷?比較其相應(yīng)S參數(shù),結(jié)果如圖11～14所示。

圖11 S11相位比較Fig.11 The comparison of S11phase

圖12 S11幅度比較Fig.12 The comparison of S11magnitude

圖13 S21相位比較Fig.13 The comparison of S21phase

圖14 S21幅度比較Fig.14 The comparison of S21magnitude

通過比較可見兩者吻合良好,從而驗(yàn)證了本文方法的正確性。

5 結(jié) 論

本文給出了一種通過仿真計(jì)算蜂窩等效介電常數(shù)的方法,通過對等效平板與蜂窩實(shí)體結(jié)構(gòu)的透射反射性能計(jì)算結(jié)果的驗(yàn)證兩者吻合良好,證明了分析結(jié)果的正確性。通過對蜂窩寬帶等效復(fù)介電常數(shù)的計(jì)算表明,在不考慮蜂窩材料色散的情況下,由蜂窩結(jié)構(gòu)引起的色散比較微弱。同時(shí),該介質(zhì)蜂窩材料為非磁性材料。介質(zhì)蜂窩材料是一種人工材料,

通過文中給出的分析步驟可知,要想準(zhǔn)確得到不同蜂窩結(jié)構(gòu)的等效復(fù)介電常數(shù),先決條件是要已知構(gòu)成格孔結(jié)構(gòu)材料的性能參數(shù)。

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ZHANG Yun-xiang was born in Rizhao, Shandong Province,in 1982.He received the M.S.degree from University of Electronic Science and Technology of China in 2008.He is currently working toward the Ph.D.degree.His research concerns antenna and RCS.

Email:yxzhangwuli@163.com

趙志欽(1969—),男,1996年于電子科技大學(xué)獲博士學(xué)位,現(xiàn)為教授、博士生導(dǎo)師,主要研究方向?yàn)樘炀€與電磁散射、信號處理;

Analysis of Dielectric Honeycombs Effective Complex Permittivity Using Free Space Method

ZHANG Yun-xiang1,ZHAO Zhi-qin1,SHI Wei-guang1,WANG Qian2
(1.School of Electronic Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China; 2.The Research Institute for Special Structures of Aeronautical Composite AVIC,Ji′nan 250023,China)

According to the theory of adopting free space method to measure the dielectric permittivity,the commercial electromagnetic simulation software is used to analyze dielectric honeycomb effective complex permittivity.A certain material and geometry dielectric honeycomb effective complex permittivity is calculated.The validity of the idea is demonstrated by comparing the simulation scatting matrix of the real honeycomb and effective dielectric panel board.Good agreement is achieved.The calculation of wide band dielectric honeycomb effective complex permittivity shows that the martial has a little dispersion property,the permittivity is increasing by frequency slowly and the mue is very close to 1,the magnetic tangent delta is close to 0.

dielectric honeycomb;complex permittivity;free space method;periodic boundary

qin was born in 1969.He

the Ph.D.degree from University of Electronic Science and Technology of China in 1996.He is now a professor and also the Ph.D.supervisor.His research concerns antenna and RCS,signal processing.

The National Defense Pre-Research Foundation of China(9140A07010812DZ02081)

TN804;TM201.4

A

1001-893X(2013)11-1518-05

張?jiān)葡?1982-),男,山東日照人,2008年于電子科技大學(xué)獲碩士學(xué)位,現(xiàn)為博士研究生,主要研究方向天線與電磁散射;

10.3969/j.issn.1001-893x.2013.11.021

2013-07-01;

2013-09-25 Received date:2013-07-01;Revised date:2013-09-25

國防預(yù)研基金項(xiàng)目(9140A07010812DZ02081)

**通訊作者:yxzhangwuli@163.com Corresponding author:yxzhangwuli@163.com

史維光(1989-),男,山東鄒城人,電子科技大學(xué)碩士研究生,主要研究方向天線與電磁散射。

SHI Wei-guang was born in Zoucheng,Shandong Province,in 1989.He is now a graduate student.His research concerns antenna and RCS.