Finite-Difference Time-Domain Analysis of Integrated Ceramic Ball Grid Array Package Antenna for
FDTD算法概述
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• 基本计算步骤
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时域有限差分法二维
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时域有限差分法二维1. 引言时域有限差分法(Finite Difference Time Domain, FDTD)是一种常用的数值计算方法,用于求解电磁场在时域中的传播和辐射问题。
本文将以二维情况为例,深入探讨时域有限差分法的原理和应用。
通过本文的介绍和解读,您将更全面地理解这一方法,并能够灵活应用于相关领域。
2. 时域有限差分法简介2.1 原理概述时域有限差分法是一种迭代求解偏微分方程的方法,通过将时域和空间离散化,将连续问题转化为离散问题。
在二维情况下,假设空间网格分辨率为Δx和Δy,时间步长为Δt。
根据电磁场的麦克斯韦方程组,可以利用中心差分公式进行离散化计算,得到求解方程组的更新方程。
2.2 空间离散化对于二维情况,空间离散化可以采用正交网格或非正交网格。
常见的正交网格包括方形格点、Yee网格等,而非正交网格则具有更灵活的形态。
根据需要和应用场景,选择合适的离散化方法对问题进行求解。
2.3 时间离散化时间离散化主要有显式和隐式两种方法。
显式方法将时间推进方程展开成前一时刻的电场和磁场与当前时刻的源项之间的关系,容易计算但对时间步长有限制;隐式方法则是通过迭代或矩阵计算求解当前时刻的电场和磁场。
3. 时域有限差分法的应用领域时域有限差分法广泛应用于电磁场传播和辐射问题的数值模拟中。
以下是几个典型的应用领域:3.1 辐射问题时域有限差分法可以模拟电磁波在空间中的辐射传播过程。
可以用于分析天线的辐射特性,设计无线通信系统的天线,或者分析电磁波在无线电频段的传播情况。
3.2 波导问题对于波导结构,时域有限差分法可以求解其模式、传输特性等问题。
波导结构广泛应用于光子学器件、微波器件等领域,时域有限差分法为建立数值模型和解析波导特性提供了一种有效的数值计算手段。
3.3 散射问题时域有限差分法在散射问题的数值模拟中也有重要应用。
通过模拟散射体与电磁波的相互作用过程,可以研究和分析散射体的散射特性,例如雷达散射截面的计算、微波散射问题等。
时域有限差分法
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时域有限差分法时域有限差分(FiniteDifferenceinTimeDomain,称FDTD)法是一种广泛应用于电磁场仿真的数值计算方法,它以离散时间步长来描述电磁场的变化,可以准确模拟空间内电磁场随时间变化的波动特性。
在时域有限差分仿真中,以Maxwell方程描述电磁场的运动,将时域的空间变化转换为表示时间的一维网格,用有限差分技术对Maxwell 方程组及其边界条件进行求解,可以得到空间中电磁场的离散值的解,从而达到仿真电磁场变化的目的。
FDTD仿真技术的最早应用出现在1960年代。
由于它的有效性和快速灵活性,FDTD仿真技术得到了快速发展,在电磁场仿真中得到了普遍应用。
FDTD仿真技术具有以下优点:1.基本实现简单,编程简单,计算效率高;2.可以准确仿真各种复杂电磁环境中电磁波传播的特性,如介质内各种参数随时间变化;3.不仅可以仿真欧姆模型,还可以用于局部质点模型的仿真;4.容易添加吸收边界,有效地抑制反射和折射现象;5.可以定制计算区域,灵活处理各种复杂的边界条件;6.计算中可以容易地加入激励和探测源;7.可以同时计算多个激励源和探测源,完成多源多探测器的仿真;8.可以方便地仿真非线性电磁材料的特性;9.单片机控制的实时仿真可以实时进行激励和探测调制;10.可以方便地模拟分布式电磁系统。
时域有限差分仿真技术的基本原理是采用有限差分法,沿时间轴以离散的步长,用一维数组离散地表示各点的电场态,并以此实现电磁场系统的时间域模拟。
FDTD法在时间域上使用一维离散网格,将Maxwell方程组及其边界条件分解,分别应用一阶导数近似公式(如中心差分公式)求解,按照计算元(grid point)在时空域中的局部特性,分别设定电磁场源、介质参数和边界条件,利用时域有限差分公式迭代求解Maxwell方程,可以得到边界条件和激励源允许的范围内的空间中的电磁场的离散值的解,从而达到仿真电磁场变化的目的。
借助时域有限差分法可以实现对天线、微波传输线、无线局域网、雷达、全波器件等电磁系统的仿真,其结果可以用于设计、性能预测、状态诊断、运行维护、电磁干扰抑制等诸多应用领域。
光子晶体能带fdtd
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光子晶体能带fdtd
时域有限差分法(Finite-Difference Time-Domain,FDTD)是一种用于求解电磁场问题的数值方法。
它在光子晶体能带计算中具有重要的应用。
光子晶体是一种周期性结构,其周期性排列的介电常数可以对光的传播产生调控作用。
通过改变光子晶体的结构参数,可以实现对光的频率和传播方向的控制,从而产生光子能带结构。
在使用 FDTD 方法计算光子晶体能带时,我们将光子晶体的结构在空间和时间上进行离散化,将电磁场表示为离散的场分量。
通过迭代求解麦克斯韦方程组,我们可以获得电磁场在空间和时间上的演化。
FDTD 方法的优点包括计算效率高、易于实现、适用于复杂结构等。
它可以有效地处理光子晶体中的周期性结构和边界条件,并且可以提供关于能带结构、能带隙、传输特性等重要信息。
然而,FDTD 方法也存在一些局限性,例如在处理高折射率对比度和长波长情况时可能会遇到数值不稳定和精度问题。
此外,FDTD 方法对于大型光子晶体结构的计算可能会消耗大量的计算资源。
总的来说,FDTD 方法是一种常用的数值技术,用于研究光子晶体的能带结构和光学特性。
它在光子晶体设计、光电子器件模拟和光学波导等领域具有广泛的应用。
随着计算技术的不断发展,FDTD 方法也在不断改进和优化,以满足更复杂的光子晶体研究需求。
fdtd激光泵浦能量密度
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fdtd激光泵浦能量密度
FDTD (Finite-Difference Time-Domain) 是一种计算电磁波行为
的数值方法,它使用网格化的空间和时间步长来模拟电磁波的传播。
激光泵浦能量密度是指激光泵浦光束在单位面积上的能量分布密度。
在FDTD模拟中,激光泵浦能量密度可以通过以下步骤计算:
1. 在仿真区域中定义一个合适的单位面积区域,以便于计算能量密度。
通常这个区域选择为激光泵浦光束在空间中的照射区域。
2. 将激光泵浦光束的能量进行离散化,将其分成若干个小体积元,并计算每个小体积元上的能量。
3. 对于每个小体积元,计算其包含的能量,并除以单位面积得到能量密度。
这可以通过测量或计算小体积元内的光强度来实现。
4. 将能量密度结果可视化,以了解激光泵浦能量在空间中的分布情况。
需要注意的是,FDTD方法是对电磁波的时域行为进行模拟的,而能量密度通常是在稳态或近稳态下进行计算的。
因此,在FDTD模拟中,通常要考虑激光泵浦光束的脉冲宽度、重复频
率和持续时间等参数的影响,并考虑平均化处理来获得更准确的能量密度结果。
时域有限差分
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时域有限差分时域有限差分(FiniteDifferenceinTimeDomain,简称FDTD)是一种基于有限差分方法的数值模拟技术,用于求解电磁场的时域行为。
它在电磁学仿真建模中有着重要的作用,广泛应用于电磁屏蔽、电磁兼容、发射器设计、天线特性测试、雷达和无线通信等诸多领域。
本文将从介绍FDTD的历史背景、基本思想及特点出发,重点讨论它的基本框架及其基本算法,并以此来深入剖析它的优势及应用场景,以期激发更多的研究者更好的应用FDTD去解决实际的问题。
一、FDTD的历史背景时域有限差分法始于20世纪50年代,其有名的开创者是美国科学家Yee在1966年提出的。
至此,它比传统时域分析方法(如横波模型)具有更强的计算能力,有利于模拟电磁场以及其他物理场。
经过Yee的提出,FDTD的理论基础也在不断的完善,其在电磁仿真领域的应用也更加普及,它的算法也得到了不断的改进和优化,有利于优化电磁仿真技术,并使它更容易被应用在电磁学仿真中。
二、FDTD基本思想及特点时域有限差分法基于有限差分法,用于求解电磁场的时域行为。
它采用基于欧拉方程(Maxwell-Faraday)的电磁场表示,将欧拉方程空间和时间解分,从而简化时域求解中的计算工作。
在做时域积分的时候,它采用的是一种求近似解的方法。
根据反文本定理,这种求近似解的方法能够准确地表示电磁场的时变行为,从而正确地描述电磁场在空间和时间上的变化规律。
在求解电磁场的时候,它把分析的小单元划分成不同的网格,每个网格为一个小空间,把大量的电磁场计算转换成了大量的有限差分的计算,从而极大地简化了电磁场的模拟,节约了计算时间。
另外,FDTD还具有计算简单、模拟效率高、模拟准确等优点,因此在电磁学仿真中非常受到重视。
三、FDTD的基本框架及其基本算法FDTD的基本框架由应变和电场两个部分构成,两个部分相互协作,用来计算空间上电磁场的变化过程,以及对应的时间变化过程。
其基本算法由三个步骤构成:(1)横电场更新,先从欧拉方程计算横电场;(2)纵电场更新,再从欧拉方程计算纵电场;(3)应变更新,最后从欧拉方程计算应变。
FDTD介绍解析
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FDTD介绍解析FDTD(Finite-Difference Time-Domain)是一种时域有限差分方法,用于求解电磁波在介质中传播的问题。
它是一种直接的数值求解方法,通过离散化时空域,将电磁波的偏微分方程转化为差分方程,利用时间步进的方式进行数值计算,从而得到电磁波在空间中的传播情况。
FDTD方法最早由美国伊利诺伊大学的Kane S. Yee于1966年提出,是时域有限差分方法中最为广泛应用的一种。
它的优点是简单易实现,计算效率高,适用于各种不规则场景和介质。
因此,在电磁学、光学、天线、无线通信等领域中得到了广泛应用。
FDTD方法的基本思想是将时空域离散化,将电磁场的偏微分方程转换为差分方程。
在FDTD方法中,空间域被划分为一个有限的网格,时间域被划分为离散的时间步长。
通过迭代计算,根据已知的初值条件和边界条件,在每个时间步长内更新场量的数值。
FDTD方法主要包括以下几个关键步骤:1.空间网格的划分:将求解区域按照一定精度进行离散,通常采用矩形网格,也可以根据具体问题选择其他形式的网格。
2. 时间步长的确定:根据Courant-Friedrichs-Lewy(CFL)条件,确定时间步长,保证波的传播速度不超过网格尺寸的倒数。
较小的时间步长可以提高求解的精度,但会增加计算量。
3.电场和磁场的更新:通过差分方程更新电场和磁场的数值。
根据麦克斯韦方程组,可以得到电场和磁场的更新公式。
其中,电场的更新公式涉及磁场的数值,磁场的更新公式涉及电场的数值。
4.边界条件的处理:为了模拟无限大的介质,需要对边界进行特殊处理。
常见的边界条件有吸收边界条件和周期性边界条件等。
吸收边界条件可以避免反射和波的传播超出边界,周期性边界条件可以模拟波的周期性传播。
5.辅助量的计算:在求解过程中,可以根据需要计算一些辅助量,如场强、功率流密度等。
这些辅助量可以用于分析电磁波传播的特性和效果。
FDTD方法的应用非常广泛。
在电磁学中,可以用于计算二维或三维空间中的电磁场分布、辐射特性、散射特性等。
电磁波时域有限差分方法
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电磁波时域有限差分方法
电磁波时域有限差分法(Finite-Difference Time-Domain Method, FDTD)是一种求解电磁学问题的常用数值方法。
它由Yee在1966年首次提出,可用于求解复杂三维电磁场交互作用的问题,如,电磁波、磁致传导、微波加热、能量传输、电磁辐射等。
相比其它数值方法,FDTD方法求解算例更为精确,具有以下特点:
1. TDTD方法是在时域上,而非在频域中,因此可以方便地处理暂态和复杂变化的电磁场。
2. FDTD方法可以通过改变差分格式和计算网格或计算量来获得更加精确的结果。
3. FDTD方法可以数值模拟出任何电磁场的行为,并且可以得到高质量的结果,而且不受物理规律的限制。
4. 可以自动识别模型中的隐藏材料特性,并增强模型的实用性。
5. FDTD方法可以结合有限体积法(FVM)和有限元法(FEM),提高模型的精度,并减少工作量。
6. 较少的内存要求,使FDTD方法更适用于工程应用。
FDTD方法在处理复杂电磁场时,有时会导致计算窗口大小,以及时间分辨率的降低,因此,要想获得较为准确的结果,就要采取足够的计算网格,以及足够高的时间分辨率。
fdtd方法
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fdtd方法FDTD方法是一种用于计算电磁波在空间中传播行为的数值方法,是Ma某well方程组的数值求解方法之一。
FDTD(Finite-Difference Time-Domain)方法的基本思想是将Ma某well方程组离散化为差分方程组,并通过迭代求解差分方程组来得到电磁场分布的数值解。
该方法的主要优点是简单易懂、计算效率高、适用于各种场强分布以及各种边界条件。
FDTD方法的基本步骤如下:1.离散化空间:将空间划分为网格点,每个网格点上存储电磁场和介质参数等信息。
2.离散化时间:将时间划分为离散的步长,每个时间步长都进行电磁场的更新。
3. 计算电场:根据Ma某well方程中的Faraday定律,利用差分方法更新电场分布。
4. 计算磁场:根据Ma某well方程中的Ampere定律,利用差分方法更新磁场分布。
5.计算介质响应:根据电磁场分布和介质参数,计算介质响应,如电流密度、电荷密度等。
6.更新边界条件:根据边界条件,更新边界处的电场和磁场。
7.循环迭代:重复以上步骤,直到达到预设的仿真时间或满足停止条件。
FDTD方法的应用范围广泛,可以用于模拟、设计和优化各种电磁器件和系统,如天线、微波管、波导、光纤等。
由于FDTD方法具有较高的计算精度和稳定性,已经成为计算电磁学领域中最重要的数值方法之一。
虽然FDTD方法具有很多优点,但也存在一些限制。
首先,FDTD方法的计算精度受到网格尺寸和时间步长的限制,因此需要进行适当的参数选择和网格优化。
其次,FDTD方法对于复杂几何体和材料较难处理,需要采用更复杂的技术来解决这些问题,如非结构网格、截断技术等。
最后,FDTD方法在计算大型系统时,计算量较大,需要使用高性能计算机进行计算。
总之,FDTD方法是一种有效的电磁场数值计算方法,具有简单易懂、计算效率高的优点,在电磁学领域中有着广泛的应用。
随着计算机技术的不断发展,FDTD方法将会得到更广泛的应用和进一步的改进。
FDTD时域有限差分法
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对时间离散:
(2)
FDTD基本原理(续)
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为了满足(1)式空间精度的要求,并满足(2)式,Yee 把空间任一网格上的E和H的六个分量,如下图放置:
Yee把E 和H 在时间长相差半个步长计算(为了满足精度的要求)。
FDTD基本原理(续)
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根据这一原则可以写出六个差分方程:
每个网格点上的各场分量的新值依赖于该点在前一时间步长时刻 的值,即该点周围的邻近点上另一场量在早半个时间步长时的值。 因此任一时刻可一次算出一个点,并行算法可计算出多个点。通 过这些运算可以交替算出电场磁场在各个时间步的值。
C:为光速,自由空间中: c
数值色散
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• 产生原因
–FDTD网格中,会导致数字波模在网格中发生改变,这种改 变是由于计算网格本身引起的,而非物理因素,所以必须 考虑
• 适当选取时间步长,空间步长,传播方向,可以得到 理想情况
–3-D方形网格:取波沿对角线传播 (数值稳定的极限状态),可得理想色散关系。 –2-D方形网格:也是沿对角线传播, (也是数值稳定的极限状态) –1-D网格 (数值稳定的极限状态)
参考文献
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• 电磁波时域有限差分方法(第二版),葛德彪, 闫玉波,西安电子科技大学出版社 • 工程电磁场数值计算,倪光正
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练习要求:
fdtd圆偏振光极化反射率
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FDTD圆偏振光极化反射率FDTD(Finite-Difference Time-Domain)方法是一种常用的计算电磁场的数值求解方法,能够模拟波的传播和反射现象。
本文将讨论在FDTD方法中,对于圆偏振光的极化反射率的计算和分析。
正文1. 概述光的偏振是指光波振动方向的特性,其中圆偏振光的振动方向在平面垂直于光传播方向上旋转。
在材料的界面上,当圆偏振光遇到反射时,一部分光会被反射回去,形成反射光。
圆偏振光的极化反射率就是指反射光与入射光强度之比。
2. FDTD方法FDTD方法是一种常用的计算电磁场的数值计算方法,它基于Maxwell方程组,通过将空间离散化和时间步长进行离散化,可以模拟电磁波在材料中的传播和反射现象。
在FDTD方法中,我们可以通过改变入射光的偏振状态,模拟不同偏振状态下的反射现象,进而计算圆偏振光的极化反射率。
3. 圆偏振光的极化反射率计算在FDTD方法中,首先需要建立一个包含材料界面的模拟空间,并设置合适的入射光源。
然后,通过调整入射光的波长、入射角和偏振状态,可以模拟不同情况下的反射现象。
在计算过程中,我们可以通过设置一个检测器,记录反射光和入射光的强度。
通过计算反射光与入射光的强度之比,即可得到圆偏振光的极化反射率。
4. 极化反射率分析通过计算不同偏振状态下的极化反射率,可以得到材料对不同偏振光的反射特性。
进一步分析不同入射角、波长和材料特性对极化反射率的影响,可以深入了解光在材料界面上的行为。
同时,通过与实验结果进行对比,可以验证FDTD方法的准确性和可靠性。
这对于研究光在材料中的传播和反射现象,以及光学器件的设计和优化具有重要意义。
【文档结尾】: 结尾本文简要介绍了FDTD方法在计算圆偏振光极化反射率中的应用。
通过该方法,我们可以模拟不同偏振状态下的反射现象,并计算出相应的极化反射率。
这对于深入了解光在材料界面上的行为以及优化光学器件具有重要意义。
亚波长光栅FDTD模拟
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亚波长光栅FDTD模拟
亚波长光栅是一种具有周期性结构的光学器件,其周期小于光的波长。
FDTD (Finite-Difference Time-Domain)方法是一种数值计算方法,用于求解电磁波在时域中的传播和相互作用问题。
在亚波长光栅FDTD模拟中,我们可以使用FDTD方法来模拟光在亚波长光栅中的传播和衍射现象。
亚波长光栅FDTD模拟的步骤如下:
1. 网格划分:将亚波长光栅区域划分为网格,通常使用正交网格进行划分。
网格的大小应该足够小,以满足亚波长光栅的周期性结构。
2. 初始化:将亚波长光栅的初始条件设置为适当的数值。
这包括设置光源的位置、频率和波形,以及设置亚波长光栅的材料参数。
3. 更新电场:使用FDTD方法更新电场的数值。
这可以通过Maxwell方程组的离散化形式来实现。
通常使用时域的电场更新方程,如Yee算法。
4. 更新磁场:使用FDTD方法更新磁场的数值。
这也可以通过Maxwell方程组的离散化形式来实现。
通常使用时域的磁场更新方程,如Yee算法。
5. 计算光的传播和衍射:根据电场和磁场的数值,计算光在亚波长光栅中的传播和衍射现象。
这可以通过计算光的功率谱、衍射图样等来实现。
6. 迭代计算:重复步骤3到步骤5,直到达到预定的计算精度或计算时间。
亚波长光栅FDTD模拟可以帮助我们理解光在亚波长光栅中的行为,并优化光栅的设计和性能。
这种模拟方法适用于各种亚波长光栅结构,包括表面等离子体光栅、光子晶体光栅等。
时域有限差分法fdtd算法
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时域有限差分法(Finite-Difference Time-Domain,FDTD)是一种用于对计算电动力学建模的数值分析技术,为相关的微分方程组寻找近似解。
时域有限差分法是由K.S.Yee在1966年发表的一篇论文建立起来的,后被称为Yee网格空间离散法。
本质原理是将随时间变化的Maxwell旋度方程更改为离散差分形式,将连续的空间分成有限的网格进行计算。
网格数量越多,计算结果更加精准,但是计算量也呈指数倍数增长,计算所需时间越长。
计算过程主要是在给定的时间点求解空间体积中的电场矢量分量,然后在下一个时刻计算相同空间体积中的磁场矢量分量,并在此结果上进行下一次的循环运算。
在空间和时域上分别不断进行循环计算,最终得到比较精准的瞬态或稳态电磁场结果。
FDTD使用说明文档
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FDTD使用说明文档FDTD(Finite-Difference Time-Domain)是一种计算电磁波动方程的数值模拟方法。
它通过将空间和时间离散化,将整个问题转化为了差分方程的求解。
FDTD方法适用于计算二维和三维空间中的电磁波的传播和辐射问题,广泛应用于大气物理、电磁学、光学和电磁兼容等领域。
下面是FDTD的使用说明文档,包括基本原理、步骤和参数设置等。
一、基本原理:FDTD方法基于麦克斯韦方程组,将空间和时间划分为网格进行离散化,通过差分形式的麦克斯韦方程进行求解。
具体步骤如下:1.空间离散化:将计算区域划分为网格,每个网格点上都有电场和磁场分量。
2.时间离散化:使用时间步长Δt,将时间进行离散化。
3.更新电场:根据麦克斯韦方程组的电场更新公式,根据磁场的值更新电场的值。
4.更新磁场:根据麦克斯韦方程组的磁场更新公式,根据电场的值更新磁场的值。
5.边界条件:设置适当的边界条件,如吸收边界条件、周期性边界条件等。
6.重复步骤3-5,直到模拟结束。
二、步骤:使用FDTD方法进行模拟一般可分为以下步骤:1.设定计算区域的大小和网格划分,根据模拟需求确定网格节点数和间距。
2.初始化电场和磁场,设置初始场分布。
3.根据模拟需求设置时间步长Δt,以及计算的总时间或模拟步数。
4.迭代更新电场和磁场,按照FDTD的原理进行计算。
5.设置边界条件和吸收边界条件,确保计算区域的边界不会对计算结果产生影响。
6.输出结果,根据需求选择输出电场、磁场以及网格中其他物理量的数值。
7.模拟结束。
三、参数设置:在使用FDTD方法进行模拟时,一些重要的参数需要进行合理的设置,以保证模拟结果的准确性和稳定性:1.网格分辨率:根据模拟的需求和计算资源,设置合适的网格划分和节点数,以充分捕捉到目标问题的细节。
2.时间步长:时间步长Δt决定了模拟的时间分辨率,需要根据模拟的频率范围和计算精度要求设置。
3.边界条件:选择适当的边界条件,可以是吸收边界条件、周期性边界条件等,以避免计算区域的边界对计算结果的影响。
fdtd单个粒子散射光谱
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fdtd单个粒子散射光谱
FDTD(Finite-Difference Time-Domain)是一种计算有限差分时域的方法,用于解决物理波在介质中的传播问题。
利用FDTD方法可以计算单个粒子散射光谱,使用其中波在不同尺寸和形状的粒子间传播的传播和折射模型。
FDTD最初仅用于电磁学,但是其算法也很快被用于处理其他物理数据,例如,声学波、热传导等。
物体对射线的散射是将来自它们的射线以及其他介质之间的波传播的动态效果的映射。
FDTD可以实现这个目标,通过模拟介质中物体的时域行为,计算物体和介质之间改变的动量及其响应的各种动态波传播信息,得到粒子的散射光谱。
FDTD的算法的核心思想是在时空维度上分解空间,并对每一个时间和空间点进行模拟。
这样,在这个空间中,粒子此时此刻引发的信号及其随时间变化及输出信号在空间上进行建模。
通过FDTD模拟可以实现Kirchhoff相干散射,从而计算单个粒子散射光谱。
此外,它还能模拟有色的散射,考虑物体的反射系数、衰减系数、折射率及几何特性等参数。
综上所述,FDTD算法是一种有效的计算单个粒子散射光谱的方法,它可以模拟介质中物体的时域行为,并考虑物体具体参数和几何特性,从而得到粒子的散射光谱。
时域有限差分方法
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时域有限差分方法时域有限差分方法(Finite Difference Method in Time Domain,简称FDTD)是一种常用的求解偏微分方程的数值方法,适用于时间和空间均匀离散的情况。
FDTD方法通过将偏微分方程转化为差分方程,将时间和空间离散化为网格点,利用差分算子对网格点进行逼近,从而得到离散形式的方程,最终通过迭代求解差分方程从而得到数值解。
在FDTD方法中,时间和空间的离散化是方法的关键。
对于时间,通常将其分割为若干个时间步长,假设每个时间步长为Δt。
对于空间,通常将其分割为若干个网格点,假设每个网格点之间的距离为Δx。
在这里,需要注意时间步长和网格点之间的距离需要满足一定的稳定性条件,以保证数值解的稳定性。
常见的稳定性条件是CFL(Courant-Friedrich-Levy)条件,即Δt/Δx小于等于某一常数。
在时间和空间离散化后,对偏微分方程中的导数部分进行差分逼近。
例如,对于一维波动方程∂²u/∂t²= c²∂²u/∂x²,其中u表示波函数,c表示波速。
可以通过近似表示为差分方程:u(i,n+1) = 2(1 - r²)u(i,n) - u(i,n-1) + r²(u(i+1,n) + u(i-1,n))其中n表示时间步数,i表示空间网格点,u(i,n)表示波函数在网格点(i,n)处的值,r = cΔt/Δx表示稳定性条件,常称为Courant系数。
这里的差分方程即为FDTD 方法的核心方程之一。
通过迭代使用这个差分方程,可以求解出波函数在任意时间和空间位置的数值解。
FDTD方法在电磁场、声学、地震学等领域有广泛的应用。
例如,在电磁场模拟中,可以利用FDTD方法求解关于电场和磁场的Maxwell方程组,通过数值模拟电磁波在空间中的传播、反射、折射等现象。
在声学领域,FDTD方法可以用于模拟声波在空间中的传播、散射、吸收等现象,对于模拟声学器件的性能具有重要意义。
fdtd 耦合直波导弯曲波导
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fdtd 耦合直波导弯曲波导
FDTD(Finite-Difference Time-Domain)是一种电磁场数值计算方法,常用于模拟电磁波在复杂结构中的传播和辐射。
直波导和弯曲波导的耦合问题可以通过FDTD方法进行求解。
在FDTD方法中,将空间划分为网格,在每个时间步长和空间位置上更新电磁场的数值。
对于直波导,可以在网格中定义适当的介质属性和边界条件,通过FDTD方法模拟电磁波在直波导中的传播。
对于弯曲波导的耦合问题,可以将直波导和弯曲波导分别进行建模,然后通过适当的耦合边界条件或相应的耦合元件进行模拟。
具体步骤包括:
1. 网格划分:将直波导和弯曲波导区域进行网格划分,可以根据需要选择不同的网格尺寸和密度。
2. 边界条件:设置适当的边界条件,如吸收边界条件或周期性边界条件,以确保电磁波在边界处的正确反射和透射。
3. 材料参数:对于直波导和弯曲波导中的介质,设置相应的材料参数,如介电常数和导电率。
4. 激励源:在适当的位置设置激励源,可以是电场源或磁场源,用于激发电磁波。
5. 时间步进:按照FDTD方法的更新公式,在每个时间步长和空间位置上更新电磁场的数值。
6. 耦合处理:对于直波导和弯曲波导的耦合问题,可以通过耦合边界条件或耦合元件进行模拟,将两者之间的电磁能量传递和耦合
考虑进去。
7. 结果分析:根据模拟结果进行电磁场分析,如电场分布、传输特性等。
需要注意的是,FDTD方法是一种数值方法,模拟结果受到网格尺寸、时间步长、边界条件等参数的影响。
在实际应用中,需要根据具体情况进行参数选择和验证,以获得准确的模拟结果。
时域有限差分法的六阶形式
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时域有限差分法的六阶形式
时域有限差分法(Finite-Difference Time-Domain, FDTD)是一种用于模拟电磁波在时间和空间中的传播行为的数值方法。
在FDTD中,电磁场的各个分量在离散的时间和空间网格上进行差分近似。
通常,FDTD的基础是二阶精度的,这意味着它使用电场和磁场分量的一阶时间导数和二阶空间导数来近似麦克斯韦方程。
然而,为了获得更高的精度,可以开发更高阶的FDTD方案,例如六阶FDTD。
六阶FDTD方案意味着在时间和空间上的导数近似将使用更高阶的差分公式。
这通常涉及更复杂的差分系数和更多的邻近网格点,以更精确地逼近连续函数的导数。
对于六阶FDTD方案的具体形式,它通常涉及电场和磁场分量的六阶空间导数和四阶时间导数。
这些高阶导数需要更复杂的差分系数和更多的网格点来计算。
由于六阶FDTD方案的具体实现可能因研究者和应用的不同而有所差异,因此没有通用的标准形式。
通常,这些方案是通过研究高阶差分公式和数值稳定性条件来开发的,并且可能涉及复杂的数学推导和计算机编程实现。
如果您需要具体的六阶FDTD方案,我建议您查阅相关的研究文献或教科书,以了解特定应用或问题中使用的具体方法和公式。
这些文献通常会提供详细的数学推导、算法实现和数值实验,以验证所提出的高阶FDTD方案的有效性和准确性。
fdtd计算光纤本征模
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fdtd计算光纤本征模
FDTD(Finite-Difference Time-Domain)方法是一种数值计算方法,用于求解电磁波的传播和相互作用问题。
它是一种基于时域的方法,将时域Maxwell方程组转化为差分方程组,并通过迭代求解来获得波的传播和相互作用的信息。
对于光纤的本征模计算,可以使用FDTD方法来模拟光在光纤中的传播和衍射。
具体步骤如下:
1. 建立光纤的结构模型:确定光纤的截面形状和材料参数,并将其转化为空间离散的网格结构。
2. 初始化电磁场分布:在网格中初始化电磁场的分布,通常可以选择一个高斯波包或正弦波作为激励源。
3. 更新电磁场:根据FDTD的差分方程组,分别更新电场和磁场在每个时间步长和空间位置上的数值。
4. 计算本征模:通过模拟一段时间后,观察电场和磁场在光纤中的传播情况,可以得到各种不同频率的模式,其中一些模式对应于光纤的本征模。
在具体计算中,需要考虑光纤中的色散效应、吸收效应以及光纤中的非线性效应等因素,以更准确地计算光纤的本征模。
另外,还可以通过改变光纤的几何形状、材料参数等来模拟不同类型的光纤和本征模。
需要注意的是,FDTD方法是一种数值方法,计算结果可能与实际情况存在一定的误差。
因此,在进行实际应用时,需要结合实验结果进行验证和修正。
同时,为了提高计算效率,可以采用优化技术,如剖分网格、使用并行计算等方法。
fdtd计算动量空间角度分辨反射谱
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fdtd计算动量空间角度分辨反射谱
FDTD(Finite-Difference Time-Domain)计算动量空间角度分辨反射谱是一种用于测量物体表面反射特性的技术。
它可以用来测量物体表面的反射率,以及物体表面反射的角度分辨率。
FDTD计算动量空间角度分辨反射谱的原理是,通过模拟物体表面的反射特性,来计算物体表面反射的角度分辨率。
FDTD计算动量空间角度分辨反射谱的过程是,首先,使用FDTD技术模拟物体表面的反射特性,然后,根据模拟的结果,计算物体表面反射的角度分辨率。
最后,根据计算的结果,得出物体表面反射的角度分辨率。
FDTD计算动量空间角度分辨反射谱的优点是,它可以模拟物体表面的反射特性,从而计算出物体表面反射的角度分辨率,这样可以更准确地测量物体表面的反射率。
此外,FDTD计算动量空间角度分辨反射谱的计算速度也很快,可以在短时间内完成计算。
总之,FDTD计算动量空间角度分辨反射谱是一种有效的测量物体表面反射特性的技术,它可以模拟物体表面的反射特性,从而计算出物体表面反射的角度分辨率,并且计算速度也很快。
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Finite-Difference Time-Domain Analysis of Integrated Ceramic Ball Grid Array Package Antennafor Highly Integrated Wireless TransceiversY .P.ZhangAbstract—This paper presents a study of the integration of an antenna in a ceramic ball grid array package for highly integrated wireless transceivers.The study has been carried out on an111166mm 2small microstrip antenna in a thin 48-ball ceramic ball grid array package with the finite-difference time-do-main (FDTD)method in C band.The impedance and radiation characteristics of the antenna are examined.More importantly,the loading effects of the complementary metal–oxide–semicon-ductor (CMOS)chip and bond wires on the performance of the antenna are investigated.It is found that the loading generally increases the impedance bandwidth but decreases the radiation efficiency of the antenna.To minimize detrimental loading,the shield of the antenna from the CMOS chip is considered.A new design has been realized.The new antenna achieves impedance bandwidth of 4.65%,radiation efficiency of 63%,and gain of 5.6dBi at 5.52GHz.Index Terms—Ceramic ball grid array package technology,highly integrated wireless transceivers,microstrip antennas,the finite-difference time-domain (FDTD)method.I.I NTRODUCTIONBASIC wireless transceiver components consist of an antenna,a radio,and a baseband controller/processor.The antenna is deliberately separated from the radio because it has independent properties that affect the wireless transceiver as a whole.Traditionally,antennas for portable wireless trans-ceivers are based around either a retractable whip monopole or an encapsulated helix because of their simple structures and high radiation efficiencies.However,since neither the monopole nor the helical antenna can be neatly integrated with the rest of a wireless transceiver,as a result,the wireless transceiver appears bulky.Furthermore,being external to the wireless transceiver,damage to the antenna also explains a high proportion of wireless transceiver failures [1].Currently,antennas for portable wireless transceivers are mainly derived from a planar inverted-F radiator.As the planar inverted-F antenna (PIFA)can be fully embedded into the body of the wireless transceiver,thus it can offer to the wireless transceiver with reduced maintenance and improved aesthetic appearance [2].More recently,driven by growing pressure to further lowerManuscript received September 20,2001;revised January 29,2003.This work was supported in part by the National Science Foundation of China under Grant 69972030.The author is with the School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore,Singapore 639798(e-mail:eypzhang@.sg).Digital Object Identifier 10.1109/TAP.2004.823889cost and shrink physical volume,various chip antennas have been developed for portable wireless transceivers [3]–[7].A one-wavelength loop chip antenna from the thick film processhas the sizeof.The chip antenna grounded on a big copper plate was measured.The results show that this chip antenna resonates at 1.765GHz and has impedance bandwidth of 1.02%and gain of 4.79dBi [4].A multilayer chip antenna from the low temperature ceramictechnology has thevolume.The chip antenna mounted on a laptop personal computer was tested.The results reveal that this chip antenna has impedance bandwidth of more than 4.1%and gain comparable to the conventional resonance mode dipole antenna at 2.45GHz [6].All these chip antennas employ the dielectric loading techniques to miniaturize their sizes.The dielectric materials are often ceramics with high permittivity [8].The radio was largely discrete and now is usually imple-mented as a multichip module with gallium arsenide (GaAs)for the power amplifier and perhaps for the low-noise amplifier and bipolar or BiCMOS for the mixer and intermediate frequency (IF)functions.The baseband controller/processor was realized with general-purpose complementary metal–oxide–semi-conductor (CMOS)integrated circuits and is now always implemented with special-purpose CMOS integrated circuits.Considering the overwhelming dominance of CMOS in the electronics industry and the steady improvement in the radio frequency (RF)performance of CMOS,there is much in-terest today in the integration of the radio with the baseband controller/processor into a single CMOS chip.For example,single-chip wireless transceivers have been fabricated in0.25-at 1.8GHz for DCS-1800wireless communications and at 2.45GHz for Bluetooth applications [9],[10].Advancesin deep submicron CMOS will also make single-chip CMOS wireless transceivers at 5–6GHz band feasible [11],[12].Single-chip solutions have employed the zero-or low-IF archi-tectures for the wireless transceivers.As such,the difficulty of the integration of different high-Q analog bandpass filters for image frequency rejection and for channel selection has been circumvented.However,not all integration difficulties can be overcome or avoided by the proper selection of the transceiver architectures.There are the antenna filter for spurious emission suppression and the antenna itself for efficient radiation.They are independent of the architectures for wireless transceivers and appear currently impossible to be combined into a single silicon chip with the size of several square millimeters.Con-sequently,they are left external to the single silicon chip (or0018-926X/04$20.00©2004IEEEFig.1.Integrated ceramic ball grid array package antenna (ICPA):(a)3-D view of laminated layers,(b)geometry of radiator layer,(c)geometry of bottom layer,and (d)bare chip attachment and bond wires.chips)in virtually all solutions of highly integrated wireless systems.Single-chip wireless transceivers in their bare forms are susceptible to the effects of mechanical stress,environmental change,and electrostatic discharge.Therefore,they are pack-aged with ceramic materials.A ceramic package that can carry a single-chip wireless transceiver has a typical volume around 200mm .The larger ceramic package offers an alternative solution and enough estate to integrate the antenna filter and the antenna.In fact,the integration of the antenna filter,balun,and switch into the ceramic package has been realized recently [13]–[15].However,little work has been done to integrate an antenna into the ceramic package [16].The integration of the antenna into the ceramic package is a radically different approach as compared with chip antenna solutions.It is indeed a rather novel topic and is worthwhile being investigated.For this purpose,we have carried out a study onansmall microstrip antenna in a thin 48-ball ceramic ball grid array package with the finite-difference time-domain (FDTD)method in C band.We call the antenna implemented in this manner the integrated circuit package antenna simply (ICPA).We describe the details of the ICPA in Section II and the FDTD analysis in Section III.The performance of the ICPA with and without the CMOS chip loading is presented in Section IV .Finally the conclusions are summarized in Section V .II.ICPASurface mounted packages are suitable to carry single-chip wireless transceivers.For example,small-outline module ce-ramic land grid array (MCLGA),micro lead frame (MLF),and lead quad flat pack (LQFP)packages have been utilized to carry single-chip wireless transceivers [15],[17],[18].Ceramic ball grid array (CBGA)packages have recently become the packageZHANG:FDTD ANALYSIS OF INTEGRATED CERAMIC BALL GRID ARRAY437Fig.2.Feed of ICPA forsimulations.Fig.3.ICPA return loss versus frequency.of choice to carry single-chip wireless transceivers because of their excellent RF performance [19],[20].Fig.1(a)shows a custom designed 48-ball thin CBGA package.The CBGA package consists of four cofired lam-inated ceramic layers,with a bare chip cavity formed by the third layer.There are two buried metallization layers in the construction.The lower buried layer provides the metallization for the chip cavity base and the signal traces,while the upper buried layer provides the metallization for the radiating element.The CBGA package has the dimensionsof.The package ceramic material istypical alumina with dielectric constant of 9.7and loss tangent of 0.0002at 5GHz.The fabrication of this custom CBGA is compatible with the standard CBGA technology but with a slight increase in the cost due to the additional ceramic and metal layers.This cost increase can,in fact,be diluted by the added function and the save in the board space and the assembly cost in the next-level package.Fig.1(b)shows the geometry of the radiator layer.It is seen that the radiating element takes the basic form of a microstrip patch on a high permittivity substrate.The microstrip patch of size 11mm 11.66mm is fed through a microstrip line 4mm 0.67mm.The microstrip line resides on the substrate of ef-fective thickness 1.34mm and dielectric constant 9.7.The mi-crostrip line width was chosen to be 0.67mm to have a line characteristic impedance close to50.Fig.1(c)shows the de-tails of the bottom layer.As shown,there are 48signal traces.The outer ends of all 48signal traces will be connected to48Fig. 4.ICPA input impedance versus frequency:(a)resistance and (b)reactance.solder balls through 48vias,while the inner ends of 45signal traces will be connected to the bare chip through 45bond wires.There are three signal traces directly linked to the grounded chip cavity base.Fig.1(d)shows the attachment of a bare CMOS chip to the cavity base and the linkage of the CMOS chip to the signal traces through the bond wires.Note that the CMOS chip is adhered to the cavity base.The signal traces and the bond wires are made of copper and gold materials,respectively,to minimize signal transmission loss.The focus on the single CMOS chip is in line with the single-chip solutions of wireless transceivers.How-ever,we believe that the ICPA design would also be appropriate for multichip architectures within the CBGA package.Further-more,the ICPA could also be used with other (or mixed)IC technologies.III.FDTD A NALYSIS D ETAILSPerformance analysis of the ICPA requires a versatile numer-ical tool that can simulate both metallic and dielectric structures.The FDTD method was chosen because of its applicability to such problems [21]–[23].To model the ICPA,the spatial stepsizes,,and have to be properly chosen so that an438IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION,VOL.52,NO.2,FEBRUARY2004Fig.5.ICPA radiation patterns in the E plane:(a)ICPA,(b)ICPA with a large CMOS chip,and (c)ICPA with the large CMOS chip and bond wires.integral number of Yee cells can fit the ICPA.Furthermore,the spatial step sizes should be much less than the smallest guidedwavelength ,for accuracy.In our simulations the spatial stepsizes were chosen tobe0.333mm.Thus,the ICPA was fittedwith cells and also the spatial step sizes were much smaller than the smallest guidedwavelength =from 16.1to 19.3mm,which corresponds to free spacewavelength=from 50to 60mm in C band.A solder ball was approximately representedby cells.The CMOS chip was modeled by a piece of silicon with dielectric constant of 11.9and loss tangent of 0.005at 5GHz.Two CMOS chipsizes were considered.Onewas cells and the otherwascells.The smaller one corresponds to the current CMOS chip sizeofand the larger one to the future CMOS chip sizeof[24],[25].Both vias and bond wires were treated as thin per-fect electric conductors with the same diameter 0.0333mm.A via was 0.67mm long (2spatial step sizes),the shortest bond wire was 3.63mm long (11spatial step sizes),and the longest bond wire was 6.6mm long (20spatial step sizes).To calculate the far-field patterns,the additional free space mesh cells were added to all six sides of the ICPA.The total computational spacewascells.The outer boundary was second order stabilized Liao [26].ZHANG:FDTD ANALYSIS OF INTEGRATED CERAMIC BALL GRID ARRAY439Fig.6.ICPA radiation patterns in the H plane:(a)ICPA,(b)ICPA with a large CMOS chip,and (c)ICPA with the large CMOS chip and bond wires.Fig.2illustrates the feed of the ICPA in our simulations,where a gap oflength was realized along the via and a Gaussian pulse voltage source was inserted in the gap to ener-gize the ICPA.The gap excitation is not practical in real imple-mentations of the ICPA.However,it is able to facilitate sim-ulations.In real implementations of the ICPA,the feed from the chip to the radiating element involves a bondwire,a signal path,and a via.The time step in our simulationswas,which satisfies the Courant stability criterion.TheGaussian pulse width was 32time steps.The source resistance was set to50to reduce the time steps needed for FDTD cal-culations.It was found that 5000time steps were sufficient for our simulations.IV .R ESULTS AND D ISCUSSIONSIn this section,the ICPA performance in terms of the impedance and radiation characteristics is presented.The effects of the CMOS chip and bond wires on the ICPA per-formance are determined and discussed from the antenna viewpoint.A.Impedance CharacteriticsThe resonant frequency of the ICPA is determined by the re-turn loss dip.Fig.3shows the return losses against frequency for the ICPA with and without the loading of the CMOS chip and bond wires.As shown,the resonant frequency of the ICPA440IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION,VOL.52,NO.2,FEBRUARY 2004without the loading of the CMOS chip and bond wires appears at 5.9GHz.It drops to 5.84and 5.7GHz with the loading of the small and large CMOS chips,respectively.The reso-nant frequency of the ICPA further reduces to 5.14GHz with the attachment of bond wires between the CMOS chip and the CBGA package.It is believed that the decrease in the resonant frequency from the loading of the CMOS chip is because the package cavity partially occupied with the CMOS chip increases the effective permittivity of the package or the substrate of the ICPA,as a result,the resonant frequency of the ICPA decreases.We conjecture that further reduction in the resonant frequency from the attachment of bond wires is due to the increase in the equivalent inductance of the ICPA by bond wires.The impedance bandwidth of the ICPA is defined as the difference between the upper and lower frequencies for which the return loss is less than or equal to 10dB.It is found that the impedance bandwidth of the ICPA without the loading of the CMOS chip and bond wires is 275MHz (4.66%).The impedance bandwidth increases to 287MHz (4.91%)and 325MHz (5.7%)with the loading of the small and large CMOS chips,respectively.The increase in the impedance bandwidth of the ICPA from 4.66%to 5.7%due to the CMOS chip loading is expected as the inherent loss of the CMOS chip decreases the quality factor of the ICPA.The effect of bond wires on the impedance bandwidth of the ICPA is rather interesting.It is noted that the absolute impedance bandwidth reduces to 239.5MHz but the relative impedance bandwidth returns to 4.66%,which happens to be the same as the ICPA without any loading.The resistance and reactance of the input impedance versus frequency for the ICPA with and without the loading of the CMOS chip and bond wires are plotted in Fig.4(a)and (b),re-spectively.It is interesting to see that the impedance has peaks in the resistance and swings in the reactance.The resistance is68at 5.9GHz for the ICPA without the CMOS chip,40at 5.7GHz with the large CMOS chip,and27at 5.14GHz with the attachment of bond wires,respectively.The reactance of the ICPA with the CMOS chip exhibit less capacitance as compared with that of the ICPA without the CMOS chip,and the reactance of the ICPA changes from capacitive to inductive with the at-tachment of bond wires over the frequency range from 5.14to 5.9GHz.B.Radiation CharacteristicsThe radiation characteristics of the ICPA were evaluated at re-spective resonant frequencies.The far-field radiation patterns of the ICPA were calculated for the most important planes.Figs.5and 6show the far-field radiation patterns of the ICPA for the copolarization and cross-polarization in the E and H planes,re-spectively.Note that there is little difference between the radi-ation patterns of the ICPA with and without the CMOS chip loading in the E and H planes.The radiation patterns of the ICPA in the E and H planes are,however,greatly changed with the attachment of bond wires.The ICPA with and without the CMOS chip loading are basically microstrip patch antennas of different substrates on the same ground plane.Therefore,they share the same radiation mechanism,that is,the fundamentalelectromagneticmodegenerates the copolarization radia-tion,while the highermodegenerates thecross-polarization Fig.7.New ICPA return loss versusfrequency.Fig.8.New ICPA input impedance versus frequency.radiation.The other modes contribute to either co or cross-po-larization radiation with less significant effect.As a result,itis not surprising that the radiation patterns of the ICPA with and without the CMOS chip loading are similar to those of a conventional microstrip antenna on a small ground plane.The asymmetry in the copolarization patterns and the null shift in the cross-polarization patterns are caused by the signal traces that surround the ground plane of the ICPA.The ICPA with the at-tachment of bond wires can not be regarded as a microstrip patch antenna any longer because the fundamental and higher-order electromagnetic modes under the microstrip patch are greatly altered by the existence of bond wires,and so are the radiation patterns.The induced currents in those bond wires have different amplitudes,phases,and directions.They cause higher cross-po-larization radiation and make it difficult to realize the desirableradiation patterns.The ICPA is linearly polarized.Thecom-ponent dominates in the E plane,whereasthe —component dominates in the H plane.Besides,the radiation is stronger in the upper hemisphere,i.e.,in the direction normal to the ICPA.This feature of the radiation patterns is desirable because it not only helps improve the efficiency of the ICPA but also reduces the human interaction with the single-chip wireless transceiver.ZHANG:FDTD ANALYSIS OF INTEGRATED CERAMIC BALL GRID ARRAY441Fig.9.New ICPA radiation patterns:(a)in the E plane and (b)in the H plane.The gain of an antenna is a critical parameter in wireless net-work design.The high antenna gain is often required to extend the network coverage.It is found that the gain is 6.7dBi for the ICPA without the loading of the CMOS chip and bond wires.The gain drops to 3.6dBi for the ICPA with the CMOS chip loading and it further drops to 4.2dBi for the ICPA with the at-tachment of bond wires.Thus,we can conclude that the loading of the CMOS chip and bond wires severely reduces the gain of the ICPA.The antenna efficiency is the parameter that takes into account the reflection,conduction,and dielectric losses of an antenna.The high antenna efficiency is desired particularly for personal wireless transceiver antennas because the higher the antenna efficiency is,the longer the battery life and the lower the noise figure are.The efficiency for the ICPA without the CMOS chip loading is 74%.The efficiency becomes as low as 35%for the ICPA with the CMOS chip loading.The lower efficiency is because the loading of the CMOS chip introduces the addi-tional dielectric loss and enhances the surface wave excitation.The efficiency of the ICPA deteriorates to 9%with the attach-ment of bond wires.This deterioration is probably due to the larger reflection loss,the bond wire loss,and the electromag-netic mode conversion loss.The attachment of bond wires se-verely disturbs the electromagnetic mode distribution under the microstrip patch and makes the ICPA an ineffective radiator.C.Another DesignFrom the above analysis,it is clear that the loading of the CMOS chip and bond wires affects the performance of the ICPA.On the other hand,this also implies that the ICPA has the potential to interfere with the functionality of the CMOS chip.To minimize these mutual effects,it is necessary to shield the CMOS chip from the ICPA.This can be easily done with an additional metallic layer,which is inserted between the radi-ating element of the ICPA and the CMOS chip.A new designthat has taken the shield into consideration is implemented as follows.The thickness of the CBGA package remains.However,the radiating element of the ICPA is brought to the top surface of the package and reduced to the smaller size of 11mm 8.33mm,and the shield screen is inserted in the middle of the original radiator layer.The shield short-circuited to the chip cavity base functions as the ground plane of the ICPA.The original feeding via was extended to go through a cell-sized cut on the shield screen to excite the ICPA.Fig.7shows the return loss of the new ICPA as a function of frequency.As shown,the resonant frequency occurs at 5.52GHz with the impedance bandwidth of 256.5MHz (4.65%).Fig.8illustrates the input impedance versus frequency for the new ICPA.The far-field radiation patterns of the new ICPA in the E and H planes are illustrated in Fig.9.Once again,they are similar to those of a conventional microstrip antenna on a small ground plane.The gain is 5.6dBi and the radiation efficiency is 63%for the new ICPA.Nevertheless,the achieved efficiency of the new ICPA is indeed acceptable when we consider those efficiency reduction factors such as the high permittivity,the thick package,the lossy CMOS chip,and etc.Furthermore,the ICPA has a much shorter distance to the RF output of the wireless transceiver than a conventional antenna.This implies a smaller transmission loss,which can be translated as an improvement to the ICPA efficiency by a few percent.V .C ONCLUSIONThe integration of an antenna in a ceramic ball grid array package for highly integrated wireless transceivers has been fully studied from the antenna viewpoint in C band.The study has focused on the single chip in CMOS technology but it can be easily extended to multichip architectures in mixed semicon-ductor technologies within the CBGA package.442IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION,VOL.52,NO.2,FEBRUARY2004It has been demonstrated that the performance of the ICPA is affected with the loading of the CMOS chip and bond wires.The CMOS chip loading generally increases the impedance band-width but decreases the efficiency of the ICPA.The prototype ICPA has achieved the impedance bandwidth of4.66%,the ra-diation efficiency of9%,and a gain of 4.2dBi.It has also con-jectured that the prototype ICPA has the potential interference to the functionality of the CMOS chip.A shield has been called for to protect the CMOS chip and to enhance the ICPA perfor-mance.This has resulted in a new ICPA,which has achieved the comparable impedance bandwidth of4.65%,the improved radiation efficiency of63%,and an enhanced gain of5.6dBi. The novel concept of the ICPA has opened up many oppor-tunities for further investigations.First and most importantly, the ICPA should also be studied from the circuit viewpoint to understand the effect of the ICPA on the signal integrity of the single-chip CMOS wireless transceiver.This is believed to be quite challenging work and has received our attention.Second, more efficient printed antenna candidates for the ICPA appli-cation should be developed.Third,various feeding techniques should be comparatively evaluated for optimal excitation of the ICPA.Finally,the codesign tool of the CMOS integrated cir-cuits,the ceramic package,and the antenna should be made available for the successful realization of single-chip wireless transceivers.A CKNOWLEDGMENTThe author would like to thank Mr.C.K.Sim,Mr.W.C. 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