度随着收发天线间距离的平方而減少 ; 换言之, 隔离度将随着距离增加以 20dB/decade 的速率变化, 这符合球面波的衰减特征 暂忽略天线增益, 相比 (1) 及 (3), 两种隔离都是随着天线间距作对数的衰减, 但 (1 ) 却 40dB/decade 的速率下降, 这一般不符合自由空间中电

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1 天线垂直隔离度 伍裕江叶海欧高卓锋曾骏 ( 广东通宇通讯设备有限公司, 广东省中山市 ) 摘要 : 针对广泛应用于移动蜂窝网络干扰分析中的天线垂直隔离度公式, 利用解析的偶极子天线公式及其计算结果, 指出了该公式应用的局限性, 并给出了新的经验公式 ; 以偶极子天线为例, 验证了新公式的有效性 本文所提出的经验公式对移动工程建设有很好的参考价值 关键词 : 基站天线, 垂直隔离, 互阻抗 On the vertical isolation of two antenna WU Yujiang, YE Haiou, GAO Zhuofeng, ZENG Jun (Tongyu Communication Equipment Co., Ltd., Zhongshan Guangdong ) Abstract: In view of the widely used vertical isolation formula of two antennas, a new empirical formula is proposed in this paper. It is proved by the explicit mutual impedance formulation of two dipole antennas. This new formula has important reference value to the interference analysis in mobile networks. Keywords: Base station antenna, Vertical isolation, mutual impedance 1 引言 移动通信的干扰分析及基站天线的安装规划过程中, 往往需要求解两基站天线间的隔离度, 从而推算出天线间的最小间隔及最优布局 其具体原理是基于被干扰接收机的灵敏度恶化余量, 计算出干扰信号的电平强度, 然后和发射机发射的干扰信号强度比较, 得到隔离度门限的要求, 最后换算为天线的空间间隔距离 由于垂直隔离具有更高的隔离度, 故在多副基站天线共塔安装中得到较多应用 当得到天线隔离度, 来反推天线的最小垂直间隔时, 需要适当的工程经验公式 现有垂直隔离分析中, 以下经验公式 [1][2] : 被得到广泛采用 Iv (db) = 28 40*lg( s ) (1) 其中 s 为两天线端对端的垂直距离, 具体含义如图 1 所示, 为工作波长 该公式是基于自由空间下的经验公式, 但隔离度却以 40dB/decade 的速率变化, 这种速率一般应发生于存在反射物或障碍物下的多径环境 [3], 在自由空间情况下很难对这种衰落特 1188 性作出合理解释 虽然该经验公式已被广泛应用, 但并没有看到相关的任何推导, 故有必要对此作深入的讨论 本文将首先通过理想偶极子的解析公式, 推导出天线垂直隔离度的精确计算公式 ; 然后通过计算结果指出原公式 (1) 的不合理性, 并给出新的经验公式 ; 最后作进一步的讨论 2 理论分析 自由空间中, 两根水平相隔天线的隔离度, 可采用基于远场的 Friis 公式计算, 即 [3] : 2 GG t r I = (2) (4 π ) d 其中 d 为两天线的水平间隔,G t 及 G r 分别为发射天线与接收天线增益 若采用对数形式, 可得 I(dB) = 22 20*lg( d ) + G (db) + G r (db) (3) 上述的自由空间公式显示, 收发天线间的隔离 t

2 度随着收发天线间距离的平方而減少 ; 换言之, 隔离度将随着距离增加以 20dB/decade 的速率变化, 这符合球面波的衰减特征 暂忽略天线增益, 相比 (1) 及 (3), 两种隔离都是随着天线间距作对数的衰减, 但 (1 ) 却 40dB/decade 的速率下降, 这一般不符合自由空间中电磁波扩散所造成的衰减特性 为了验证原经验公式 (1) 的准确性, 这里将采用两根等长度的理想偶极子天线为收发天线 选用理想偶极子的原因是由于其有解析的互阻抗公式, 从而可得到精确的隔离度, 从而验证公式 (1) 的准确性 文献 [4] 给出了当天线长度 L= n/2, 其中 n 为奇数下的互阻抗公式 : R21 = 15cos βh[ [ 2Ci2βh+ Ci2 β( h L) h L + Ci2 β ( h+ L) ln( ) 15sin β h 2 + h [ 2Si2βh Si2 β( h L) Si2 β( h+ L) ](4) X 21 = 15cos βh[ 2Si2βh Si2 β( h L) Si2 β( h+ L) + 15sin βh[ 2Ci2βh h L Ci2 β( h L) Ci2 ( h L) ln( ) β + 2 h (5) 其中 β 为相速,h s 与 L 参数如图 1 所示,Ci 及 Si 分别为正弦积分及余弦积分函数 [4] 求出 R 21 及 X 21 后, 即可得互阻抗为 : Z = R + jx (6) 结合天线自阻抗的计算 [4], 即可得到互阻抗矩阵 : Z11 Z12 Z = Z21 Z (7) 22 以下计算中, 假定两根天线为相同的天线, 并以理想的负载, 即自阻抗的共轭作匹配, 则 S 参数矩阵可求解为 [5] : 1 S= ( Z+ Z I) ( Z Z I ) (8) 其中上标 * 表示共轭计算,I 为 2 2 的单位矩阵 通过 (8) 式即可求出隔离度 S 21 图 1 两垂直相隔天线的示意图 3 新的经验公式及计算结果分析 根据第 2 节的理论推导, 本节将给出各种长度下的隔离度结果 由于基站天线的垂直孔径一般都在 15 个波长以内, 故以下计算只考虑 n 从 1 变化到 15 的情况 根据第 2 节的理论计算, 通过大量的结果分析, 我们提出了新的垂直隔离度经验公式, 如下 : 33 20lg( ) (40 )lg( s n + n ), n 5 Iv = 14 + (40 n)lg( s ), 15> n> 5 (9) 上式在 n 小于 5 时, 前面的常数项需要根据 n 作修正 这是由于垂直隔离计算中, 间隔距离采用了如图 1 所示的端对端距离 隔离度随着距离变化的速率修正为 (40-n)dB/decade, 显示出随着天线尺寸的增大, 衰减特性将逐步趋向球面波的衰减特性, 这是由于随天线尺寸的加大, 其副瓣也随之增多, 从而增大了端射方向的辐射 图 2 给出了采用原经验公式 (1), 理论公式 (8) 以及本文所提出的经验公式 (9), 分别计算 n 为 1 7 及 13 的结果 可以看出, 原公式 (1) 仅当天线尺寸较小时才符合理论结果, 而随着天线尺寸的增大, 误差将变得越来越大 而新的经验公式 (9) 则在各种尺寸下都显示出很好的拟合结果 1189

3 图 2 分别应用公式 (1) (8) 以及 (9) 计算得到的垂直面隔离度, 其中实线是采用公式 (8) 结果, 其与采用公式 (9) 得到的结果很吻合 4 进一步的讨论 由于两长度为 /2 奇数倍的理想偶极子天线存在解析的互阻抗公式, 从而可精确求出垂直隔离度, 故本文采用该天线对广泛应用的垂直隔离度经验公 式 (1) 作验证, 并基于该模型下的计算结果提出新的经验公式 (9) 但对于实际的基站天线, 其隔离度的计算将复杂得多 : 首先, 基站天线一般在垂直方向组阵, 在整个垂直组阵的方向上, 其电流分布与相同长度下的偶极子电流分布有较大差别 ; 其次, 现有基站天线多为 ±45 度的双极化天线, 这将会明显增大端射方向的辐射, 从而降低垂直隔离 ; 第三, 基站定向天线总存在反射板, 也一定程度上增大端射方向的孔径, 从而降低隔离度 尽管如此, 本文的结论还是有着重要的参考意义 : 首先, 通过严格的理论分析, 指出了原公式 (1) 中的 40 db/decade 衰减斜率不合理 ; 其次, 通过严格的计算, 指出了该斜率与天线的尺寸相关, 而且将随着尺寸的增大, 以及端射强度的增大, 将趋向于球面波的衰减特性 下一步, 我们将通过仿真以及各种测试, 给出典型的基站天线隔离度结果, 从而试图给出更符合物理图像的经验公式 参考文献 [1] Qualcomm incorporated. Interference Analysis and Guidelines for Coexistence. The 3rd Meeting of the APT Wireless Forum, 2006 [2] 陈行, 马璐, WCDMA/GSM 共址时的干扰及其隔离度分析, 移动通信, 2006 年 11 期 : [3] T.S. Rappaport, Wireless Communications Principles and Practice, Prentice Hall, 2001 [4] 约翰. 克劳斯等著, 章文勋译. 天线 ( 第三版 ). 北京 : 电子工业出版社, [5] D.M. Pozar 著, 张肇仪等译, 微波工程 ( 第三版 ), 北京 : 电子工业出版社,

4 易迪拓培训 专注于微波 射频 天线设计人才的培养网址 : 如何学习天线设计 天线设计理论晦涩高深, 让许多工程师望而却步, 然而实际工程或实际工作中在设计天线时却很少用到这些高深晦涩的理论 实际上, 我们只需要懂得最基本的天线和射频基础知识, 借助于 HFSS CST 软件或者测试仪器就可以设计出工作性能良好的各类天线 易迪拓培训 ( 专注于微波射频和天线设计人才的培养, 推出了一系列天线设计培训视频课程 我们的视频培训课程, 化繁为简, 直观易学, 可以帮助您快速学习掌握天线设计的真谛, 让天线设计不再难 HFSS 天线设计培训课程套装套装包含 6 门视频课程和 1 本图书, 课程从基础讲起, 内容由浅入深, 理论介绍和实际操作讲解相结合, 全面系统的讲解了 HFSS 天线设计的全过程 是国内最全面 最专业的 HFSS 天线设计课程, 可以帮助你快速学习掌握如何使用 HFSS 软件进行天线设计, 让天线设计不再难 课程网址 : CST 天线设计视频培训课程套装套装包含 5 门视频培训课程, 由经验丰富的专家授课, 旨在帮助您从零开始, 全面系统地学习掌握 CST 微波工作室的功能应用和使用 CST 微波工作室进行天线设计实际过程和具体操作 视频课程, 边操作边讲解, 直观易学 ; 购买套装同时赠送 3 个月在线答疑, 帮您解答学习中遇到的问题, 让您学习无忧 详情浏览 : MHz NFC/RFID 线圈天线设计培训课程套装套装包含 4 门视频培训课程, 培训将 13.56MHz 线圈天线设计原理和仿真设计实践相结合, 全面系统地讲解了 13.56MHz 线圈天线的工作原理 设计方法 设计考量以及使用 HFSS 和 CST 仿真分析线圈天线的具体操作, 同时还介绍了 13.56MHz 线圈天线匹配电路的设计和调试 通过该套课程的学习, 可以帮助您快速学习掌握 13.56MHz 线圈天线及其匹配电路的原理 设计和调试 详情浏览 :

5 ` 专注于微波 射频 天线设计人才的培养易迪拓培训网址 : 关于易迪拓培训 : 易迪拓培训 ( 由数名来自于研发第一线的资深工程师发起成立, 一直致力和专注于微波 射频 天线设计研发人才的培养 ; 后于 2006 年整合合并微波 EDA 网 ( 现已发展成为国内最大的微波射频和天线设计人才培养基地, 成功推出多套微波射频以及天线设计经典培训课程和 ADS HFSS 等专业软件使用培训课程, 广受客户好评 ; 并先后与人民邮电出版社 电子工业出版社合作出版了多本专业图书, 帮助数万名工程师提升了专业技术能力 客户遍布中兴通讯 研通高频 埃威航电 国人通信等多家国内知名公司, 以及台湾工业技术研究院 永业科技 全一电子等多家台湾地区企业 我们的课程优势 : 成立于 2004 年,10 多年丰富的行业经验 一直专注于微波射频和天线设计工程师的培养, 更了解该行业对人才的要求 视频课程 既能达到了现场培训的效果, 又能免除您舟车劳顿的辛苦, 学习工作两不误 经验丰富的一线资深工程师主讲, 结合实际工程案例, 直观 实用 易学 联系我们 : 易迪拓培训官网 : 微波 EDA 网 : 官方淘宝店 :

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