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Progress In Electromagnetics Research, PIER 98, 1–13, 2009
A WIDEBAND HALF OVAL PATCH ANTENNA FOR BREAST IMAGING J. Yu ? , M. Yuan, and Q. H. Liu Department of Electrical and Computer Engineering Duke University Durham, NC 27708, USA Abstract—A simple half oval patch antenna is proposed for the active breast cancer imaging over a wide bandwidth. The antenna consists of a half oval and a trapezium, with a total length 15.1 mm and is fed by a coaxial cable. The antenna performance is simulated and measured as immersed in a dielectric matching medium. Measurement and simulation results show that it can obtain a return loss less than ?10 dB from 2.7 to 5 GHz. The scattered ?eld detection capability is also studied by simulations of two opposite placed antennas and a full antenna array on a cubic chamber. 1. INTRODUCTION Breast cancer is the most common cancer in women, but fortunately early detection and treatment can signi?cantly improve the survival rate. Ultrasound, mammography and magnetic resonance imaging (MRI) are currently used clinically for breast cancer diagnosis [1]. However, these techniques have many limitations, such as high rate of missed detections, ionizing radiation (mamography), too expensive to be widely available, and so on. Compared with conventional mammography, microwave imaging of breast tumors is a nonionizing, potentially low-cost, comfortable and safe alternative [2]. The high contrast of the dielectric property between the malignant tumor and the normal breast tissue should manifest itself in terms of lower numbers of missed detections and false positives [3, 4]. The microwave breast tumor detection also has the potential to be both sensitive and speci?c, to detect small tumors, and to be less expensive than methods such as MRI.
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Corresponding author: M. Yuan (mengqing.yuan@https://www.wendangku.net/doc/1c10482490.html,). Also with National Key Laboratory of EMC, Wuhan, Hubei 430064, China.

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Theoretical analysis and numerical simulation results have shown that microwave imaging for breast cancer is feasible [5–13], but during practical fabrication of imaging systems, there are many practical problems [14]. One of the biggest challenges of constructing a microwave breast cancer imaging system is the sensor design. Various types of antennas have been proposed by research groups involved in breast cancer detection applications [15–20]. For example, [16] proposed and fabricated a compact stair-shaped dielectric resonator antenna (DRA) for microwave breast cancer detection. A quarterwavelength choke was incorporated to reduce the ?nite ground plane size. [17] studied and compared the detection capabilities of two co-polarized and cross-polarized antenna arrays consisting of two slot, CPW fed antennas for the purpose of ultra-wideband breast cancer detection. [18] proposed an antenna for radar-based breast imaging, which detects tumors by observing variations in microwave signals re?ected from the tumors as the antenna location changes. Di?erent breast cancer detection methods need di?erent antennas. Most antennas proposed recently are applied to the time-domainbased detection method, capable of detecting the location of tumor, but not targeted for the reconstruction of the whole breast dielectric distributions. Here we proposed a prototype of 3D imaging system, which uses a small 100 × 100 × 100 mm3 cubic chamber integrated with patch antenna arrays [21, 22] as the sensor. One chamber can contain one breast immersed in a matching dielectric medium. And the antenna array located on four vertical walls of the chamber can sweep and acquire 3D scattered ?eld data in a relatively short time. For a breast imaging system, the antenna should be compact, lightweight and suitable for directly touching the breast. [21, 22] proposed a kind of bowtie patch antenna for imaging at 2.75 GHz. However, broadband antennas are preferable to increase the possibility of detecting tumors over a large range of sizes. So an operating bandwidth of 2.7–5 GHz is the objective of this work. This paper presents a simple half oval patch antenna that can operate over the necessary wide bandwidth for this application. The half oval patch antenna presented here has been proposed to radiate directly into a dielectric medium (matching medium). As described in subsequent sections, the initial antenna design and performance optimization were carried out by simulations with HFSS and Wavenology EM. And the performance of proposed antenna is validated by measurement. For further integration and scattered ?eld calculation, we will study and compare the coupling of the antenna array and determine the smallest spacings for reducing interferences

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among antennas. The detection capability of the antenna array will be discussed by simulations of di?erent positions in a matching dielectric medium. 2. ANTENNA DESIGN 2.1. Half Oval Patch Antenna Structure According to the imaging system requirement as discussed in [21, 22], the antennas will be mounted on four vertical panels of a cubic chamber. Each panels has the same number of antennas. To obtain the data for reconstruction of the breast dielectric distribution, the antennas are switched electronically between source and receiver one by one. In each scan process, only one antenna is used as the source and the others act as receivers. We choose an oval antenna as our initial structure, then change it to half oval for reducing its size. Because the antenna size is too small to omit the coaxial connector in simulation, we proposed an trapezium for connecting the coaxial cable connector and the half oval antenna arm, which can keep the antenna in the same size but with better return loss performance. This design uses a 100 × 100 mm2 FR4 substrate (1.6 mm thickness). The ground plane is placed right behind the substrate and covers the whole substrate. The antenna is fed by a coaxial line. Because each antenna is as small as 15.1 mm, the coaxial cable connector should be considered as part of the antenna design. The dimensions and structure are shown in Fig. 1. The inner conductor of the coaxial cable connector (SMB 50 Ohm connector) is modeled as a cylinder 1.27 mm in diameter. And the dielectric insulator in the connector is Te?on. The outer diameter of the cable is 4.2 mm and is connected with the ground plane. In our model, the thickness of the shell is 1 mm, which is not shown in the ?gure. The fabricated antenna prototype is made of copper. The thickness of patch is 0.16 mm for both simulation model and real antenna. 2.2. Antenna Performance During the breast cancer detection and imaging, a matching medium should be applied to surround the breast to reduce the scattering from the breast skin. The relative permittivity (εr ) of tumor varies from 40 to 60, and normal breast tissue varies from 9 to 25 [23–26]. From the past experimental experiences [21], we choose acetone as the matching medium, whose relative permittivity is εr = 21.8 and conductivity is σ = 0.17 S/m. Acetone is easy to obtain for the system prototype development.

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Figure 1. Top and side views of a half oval patch antenna. (Unit: mm).
Figure 2. Return loss simulation and measurement results for the antenna in Fig. 1.
We assume that the normal breast tissue is perfectly matched with the medium. So above the patch antenna is matching medium, while it is the air under the PEC ground plane. With these design considerations, the prototype antenna shown in Fig. 1 is simulated by both HFSS and Wavenology EM. We we measured the |S11 | parameter in acetone by an Agilent E8362B PNA series network analyzer. The simulated and measured return loss results from 2 to 5 GHz in Fig. 2 show good agreement. Both commercial software simulation results and measurement results indicate that the proposed half oval patch antenna satis?es the basic performance requirements, and the length is as short as 15.1 mm. The re?ection is less than ?10 dB within 2.7– 5 GHz. 2.3. Array Design An imaging system with a chamber size 100 × 100 × 100 mm3 was proposed to ?t regular breast size [21]. One prototype of the chamber is shown in Fig. 3 and Fig. 4. The vertical spacing between two adjacent antennas is de?ned as Dv , while the horizontal spacing is noted as Dh . In this prototype, each plane has a 3 × 3 antenna array. And the ground covers the 4 side and bottom panels to isolate the noise from the environment. The antennas in each array has the same vertical and horizontal spacings. How to arrange the antennas on each plane and how to choose Dv and Dh will be discussed below.

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Dh Breast Tissue
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Figure 3. (a) Side view of the imaging chamber. (b) Each face of the imaging chamber with 3 × 3 antennas.
Figure 4. 3D view of the chamber with an array of 36 antennas. 3. ANTENNA COUPLING ANALYSIS The antennas will be integrated into a 3-D array on the four vertical walls of the cubic chamber. Usually, the more antennas the wall contains, the more imaging data can be obtained from each scan, but the undesirable coupling may be stronger and the array becomes more expensive. So the spacings of the antenna array are also discussed in the paper. The couplings between the co-polarized horizontal and vertical array elements are represented by |S21 |.

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Figure 5. Coupling versus the horizontal distance of two parallel antennas.
Figure 6. Coupling versus the vertical distance of two parallel antennas.
The antennas will be parallel mounted on each of the four side panels. Here, we studied the vertical (Dv ) and horizontal (Dh ) spacings for any two half oval patch antennas on the same plane as Fig. 3(b) shows. The simulation is under the assumption that there are only two antennas on a 100 mm ×100 mm substrate (ground covers the whole substrate). According to the study of [17], we choose ?20 dB as the coupling requirement in the imaging frequency band of 2.7 to 5 GHz. From the simulation results shown in Fig. 5 and Fig. 6, we can see that to meet the requirement of isolation less than ?20 dB, the smallest Dh is 5 mm, while smallest Dv is 17 mm. As a preliminary study of this kind of imaging system, these results are only for the reference of further antenna array design. 4. ANTENNA DETECTION CAPABILITY For breast cancer imaging application, the antenna should be able to detect weak signals and identify small tumors, and high quality signals received will bene?t the imaging. So we place two half oval patch antennas on the opposite sides in Fig. 7 to determine the detection capability of the antennas. The space between two antennas is also ?lled with a homogenous dielectric material (breast tissue surrounded by matching medium, and skin is omitted here). We assume that the tumor is spherical, and located at the center point between two antennas (deepest place under skin for detection) as in Fig. 7. The relative permittivity of the tumor is εr = 50, and conductivity is σ = 9 S/m [19].

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inc Figure 8. Simulated |S11 | and inc | results for the con?guration |S21 in Fig. 7.
The scattered ?eld of the tumor is calculated by subtracting the incident ?eld (background ?eld) from the total ?eld. Here the incident ?eld means the electromagnetic ?eld generated by one antenna radiation in dielectric medium when there is no tumor, while the total ?led is the corresponding ?eld when a tumor exists. So the S21 parameter, which depends on signal transmission and reception, can inc be used to represent the detection capability. If S21 is the incident S tot parameter when there is no tumor inside the breast, S21 is the total ?eld S parameter when there is a tumor inside breast, the scatter S sct parameter S21 is sct tot inc S21 = S21 ? S21 (1) If no tumor exists, the antenna will only receive the background signals from the other. |S11 | and |S21 | in this condition are shown in Fig. 8 (|S22 | = |S11 | and |S12 | = |S21 | for the symmetric structure). |S11 | still satis?es the requirements of the system, i.e., |S11 | ≤ ?10 dB between 2.7 and 5 GHz. 4.1. Case 1: Detection of a 10-mm Tumor at the Origin Here, we connect the center points of two coaxial cable connectors of two opposite antennas, and de?ne the center point of this line as origin (Fig. 7). First simulation case is assuming the 10-mm tumor (radius r = 5 mm) is located at the origin (x = 0 mm, y = 0 mm, z = 0 mm) as in Fig. 7. The horizontal distances (along z direction) between the tumor and both antennas are 50 mm. Simulation results are shown in Fig. 9. The background ?eld,

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Figure 9. |S21 | for the background ?eld, incident ?eld and scattered ?eld when a 10-mm tumor is located at the origin.
Figure 10. |S21 | for the scattered ?eld when a 10-mm tumor is located at (0, 0, 0) mm and (10, 0, 0) mm.
inc which is plotted by solid line, represents |S21 |. The dotted line is tot |). The di?erence between these two lines are hard total ?eld (|S21 to see by eyes. So we subtract them according to Equation (1), and sct plot the magnitude of the subtraction results (|S21 |) by dashed line. According to the experiences of [21, 22], the imaging system can detect sct and reconstruct the dielectric distribution of the object when |S21 | sct | ranges from ?65 dB to higher than ?75 dB. Here, the simulated |S21 ?47 dB. So the antenna is suitable for the system to detect the tumors bigger than 10 mm in diameter.
4.2. Case 2: Detection of a 10-mm Tumor at (10, 0, 0) mm The origin is the deepest position in breast for antenna to detect (horizontally). However, there may be tumors located near the chest, for example at (10, 0, 0) mm. Simulation results are plotted in Fig. 10 by dotted line for a 10sct mm tumor at (10, 0, 0) mm. |S21 | for this tumor ranges from ?56 dB to ?45 dB. The position change of the tumor is detectable by the change sct of this |S21 |. 4.3. Case 3: Detection of a 10-mm tumor at (40, 0, 0) mm In this case, the tumor is located closer to the chest (the open end of chamber) at (40, 0, 0) mm. Simulation results are plotted in Fig. 10 sct by solid line. |S21 | for this tumor ranges from ?52 dB to ?80 dB. Scattered ?eld of some frequencies are lower than ?80 dB. But most

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frequencies are detectable. And when antennas are mounted on the imaging chamber and build array, the performance will be better as discussed in the following Section 5.
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Figure 11. Return losses of 6 representative antennas in chamber.
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Figure 12. Incident ?eld of 6 pairs of representative antennas in the imaging chamber.
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Figure 13. Scattered ?eld results of antenna 20 and 23 as receivers, antenna 14 as transmitter on imaging chamber when a 10-mm tumor is located at origin and (10, 0, 0) mm.
Figure 14. Scattered ?eld results of antenna 20 and 23 as receivers, antenna 14 as transmitter on imaging chamber when a 10-mm tumor is located at origin and (40, 0, 0) mm.

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5. ANTENNAS ON CHAMBER Antenna array design is another challenge for the imaging system. We modeled a simple prototype as Fig. 4 to validate the antennas performance when they are mounted on an imaging chamber. By the results of Section 3, vertical spacing of the antennas Dv is set to 17 mm. Although 5 mm horizontal spacing is enough for ?20 dB isolation, we set Dh = 20 mm as a preliminary study of the antenna performance in chamber. The array is symmetric, so six antennas (center column and left column in Fig. 3(b)) are enough to represent the performance of all antennas. We choose antennas 1, 2, 13, 14, 25 and 26 as sources in the array shown in Fig. 4. The return losses of these antennas are shown in Fig. 11. At the frequencies higher than 3.5 GHz, the return losses are slightly higher than ?10 dB for part of the 6 representative antennas. Although antenna performance is slightly a?ected by the chamber, the antennas are still suitable for the imaging system. Figure 12 plots the coupling of 6 pairs of antennas to their counterparts on the opposite side of the chamber. For example, antennas 1 and 9 are the antennas located in the upper left corner of two parallel walls of the chamber; the coupling result is shown as |S9,1 | in Fig. 12; |S33,25 | is for the pair located in the bottom corner of the chamber. The antennas are numbered in Fig. 4. These coupling results are simulated under the hypothesis that there is no tumor in the breast. So the results are the incident ?eld. The magnitude of these incident ?elds are similar to the results simulated by two opposite antennas in Section 3. Here we de?ne the center point of the chamber as the origin; the x direction is pointed to the open face of the imaging chamber, and the y and z directions are pointed to two adjacent vertical walls. Similar to Section 3, we simulated and calculated the scattered ?eld of a 10-mm tumor at three di?erent positions, namely at the origin, (10, 0, 0) mm, and (40, 0, 0) mm. Fig. 13 and Fig. 14 show the di?erent scattered ?eld results at antenna 20 and 23 when antenna 14 is radiating. We can observe that the most scattered ?eld is over ?75 dB. This level of scattered ?eld has been shown to enable imaging in a homogeneous ?uid [8], although much more work needs to be done to allow imaging in a real breast tissue. 6. CONCLUSION A simple half oval patch antenna is proposed for breast cancer imaging. Both simulation and measurement results show that the return loss of

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the proposed antenna is less than ?10 dB from 2.7 to 5 GHz. In a cubic imaging chamber, the antennas are mounted on four vertical walls. The couplings of two co-polarized antennas placed horizontally and vertically are studied for the antenna array design. And the detection capability of the antenna is simulated by two opposite antennas with 100 mm distance. The space between two antennas is ?lled with dielectric medium, which simply represents a model of breast immersed in perfect matching medium omitting the skin. Simulation results show that the antenna can detect the signal variation caused by a 10-mm tumor at di?erent positions. According to the co-polarized coupling results, we modeled a chamber with 3×3×3 antenna array. Simulation results prove that the proposed antenna is applicable to the breast cancer imaging system. Ongoing work is being conducted to build appropriate antenna array, integrate them in the chamber, and perform experiments to validate the feasibility of the imaging system we proposed. REFERENCES 1. Fear, E. C., S. C. Hagness, and P. M. Meaney, “Enhancing breast tumor detection with near-?eld imaging,” IEEE Microwave Mag., Vol. 3, No. 1, 48–56, 2002. 2. Fear, E. C. and M. A. Stuchly, “Microwave detection of breast cancer,” IEEE Trans. Microwave Theory Tech., Vol. 48, No. 11, 1854–1863, 2000. 3. Liu, Q. H., Z. Q. Zhang, T. Wang, G. Ybarra, L. W. Nolte, J. A. Bryan, and W. T. Joines, “Active microwave imaging I: 2-D forward and inverse scattering methods,” IEEE Trans. Microwave Theory Tech., Vol. 50, No. 1, 123–133, 2002. 4. Fear, E. C., P. M. Meaney, and M. A. Stuchly, “Microwaves for breast cancer detection,” IEEE Potentials, Vol. 22, No. 1, 12–18, 2003. 5. Bindu, G., S. J. Abraham, A. Lonappan, V. Thomas, C. K. Aanandan, and K. T. Mathew, “Active microwave imaging for breast cancer detection,” Progress In Electromagnetics Research, PIER 58, 149–169, 2006. 6. Zhang, H., S. Y. Tan, and H. S. Tan, “A novel method for microwave breast cancer detection,” Progress In Electromagnetics Research, PIER 83, 413–434, 2008. 7. Zhang, Z. Q., Q. H. Liu, C. Xiao, E. Ward, G. Ybarra, and W. T. Joines, “Microwave breast imaging: 3-D forward scattering

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18. Yun, X., E. C. Fear, and R. H. Johnston, “Compact antenna for radar-based breast cancer detection,” IEEE Trans. Antennas Propag., Vol. 53, No. 8, 2374–2380, 2005. 19. Nilavalan, R., I. J. Craddock, A. Preece, J. Leendertz, and R. Benjamin, “Wideband microstrip patch antenna design for breast cancer tumour detection,” IET Microw. Antennas Propag., Vol. 1, No. 2, 277–281, 2007. 20. Bond, E. J., X. Li, S. C. Hagness, and B. D. Van Veen, “Microwave imaging via space-time beamforming for early detection of breast cancer,” IEEE Trans. Antennas Propag., Vol. 51, No. 8, 1690–705, 2003. 21. Yuan, M., C. Yu, J. P. Stang, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, “Experiments and simulations of an antenna array for biomedical microwave imaging applications,” URSI Meeting, San Diego, CA, July 2008. 22. Stang, J. P., W. T. Joines, Q. H. Liu, R. T. George, G. A. Ybarra, M. Yuan, and I. Leonhardt, “A tapered microstrip patch antenna array for use in breast cancer screening via 3D active microwave imaging,” APS-URSI Meeting, Charleston, SC, June 2009. 23. Jossinet, J. and M. Schmitt, “A review of parameters for the bioelectrical characterization of breast tissue,” Ann. N. Y. Acad Sci., Vol. 873, 30–41, 1999. 24. Woten, D. A., J. Lusth, and M. El-Shenawee, “Interpreting arti?cial neural networks for microwave detection of breast cancer,” IEEE Microwave Wireless Compon. Lett., Vol. 17, No. 12, 825–827, 2007. 25. Lazebnik, M., L. McCartney, D. Popovic, C. B. Watkins, M. J. Lindstrom, J. Harter, S. Sewall, A. Magliocco, J. H. Booske, M. Okoniewski, and S. C. Hagness, “A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries,” Phys. Med. Biol., Vol. 52, 2637–2656, 2007. 26. Lazebnik, M., D. Popovic, L. McCartney, C. B. Watkins, M. J. Lindstrom, J. Harter, S. Sewall, T. Ogilvie, A. Magliocco, T. M. Breslin, W. Temple, D. Mew, J. H. Booske, M. Okoniewski, and S. C. Hagness, “A large-scale study of the ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries,” Phys. Med. Biol., Vol. 52, 6093–6115, 2007.

天线线列阵方向图

阵列方向图及MATLAB 仿真 1、线阵的方向图 2 ()22cos(cos )R φψπφ=+- MATLAB 程序如下（2元）： clear; a=0:0.1:2*pi; y=sqrt(2+2*cos(pi-pi*cos(a))); polar(a,y); 图形如下：若阵元间距为半波长的M 个阵元的输出用方向向量权重11(,,)M j j M g e g e φφ???加以组合的话，阵列的方向图为 [(1)cos()]1()m M j m m m R g e ψπφφ--==∑ MATLAB 程序如下（10个阵元）： clear; f=3e10; lamda=(3e8)/f;

beta=2.*pi/lamda; n=10; t=0:0.01:2*pi; d=lamda/4; W=beta.*d.*cos(t); z1=((n/2).*W)-n/2*beta* d; z2=((1/2).*W)-1/2*beta* d; F1=sin(z1)./(n.*sin(z2));i K1=abs(F1) ; polar(t,K1); 方向图如下： 2、圆阵方向图程序如下： clc; clear all； close all; M = 16; % 行阵元数 k = 0.8090; % k = r/lambda DOA_theta = 90; % 方位角 DOA_fi = 0; % 俯仰角 % 形成方位角为theta，俯仰角位fi的波束的权值m = [0 : M-1];

w = exp(-j*2*pi*k*cos(2*pi*m'/M-DOA_theta*pi/180)*cos(DOA_fi*pi/180)); % w = exp(-j*2*pi*k*(cos(2*pi*m'/M)*cos(DOA_theta*pi/180)*cos(DOA_fi*pi/180)+sin(2*pi*m'/M)*si n(DOA_fi*pi/180))); % 竖直放置 % w = chebwin(M, 20) .* w; % 行加切比雪夫权 % 绘制水平面放置的均匀圆阵的方向图 theta = linspace(0,180,360); fi = linspace(0,90,180); for i_theta = 1 : length(theta) for i_fi = 1 : length(fi) a = exp(-j*2*pi*k*cos(2*pi*m'/M-theta(i_theta)*pi/180)*cos(fi(i_fi)*pi/180)); %a=exp(-j*2*pi*k*(cos(2*pi*m'/M)*cos(theta(i_theta)*pi/180)*cos(fi(i_fi)*pi/180)+sin(2*pi*m'/ M)*sin(fi(i_fi)*pi/180))); % 竖直放置 Y(i_theta,i_fi) = w'*a; end end Y= abs(Y); Y = Y/max(max(Y)); Y = 20*log10(Y); % Y = (Y+20) .* ((Y+20)>0) - 20; % 切图 Z = Y + 20; Z = Z .* (Z > 0); Y = Z - 20; figure; mesh(fi, theta, Y); view([66, 33]); title('水平放置时的均匀圆阵方向图'); % title('竖面放置时的均匀圆阵方向图'); % 竖直放置 axis([0 90 0 180 -20 0]); xlabel('俯仰角/(\circ)'); ylabel('方位角/(\circ)'); zlabel('P/dB'); figure; contour(fi, theta, Y); 方向图如下：

阵列天线方向图的初步研究

通信信号处理实验报告 ——阵列天线方向图的初步研究 11级通信（研）刘晓娟一、实验原理： 1、智能天线的基本概念：智能天线是一种阵列天线，它通过调节各阵元信号的加权幅度和相位来改变阵列的方向图形状，即自适应或以预制方式控制波束幅度、指向和零点位置，使波束总是指向期望方向，而零点指向干扰方向，实现波束随着用户走，从而提高天线的增益，节省发射功率。智能天线系统主要由①天线阵列部分；②模/数或数/模转换部分；③波束形成网络部分组成。本次实验着重讨论天线阵列部分。 2、智能天线的工作原理：智能天线的基本思想是：天线以多个高增益的动态窄波束分别跟踪多个期望信号，来自窄波束以外的信号被抑制。 3、方向图的概念：以入射角为横坐标，对应的智能天线输出增益为纵坐标所作的图称为方向图，智能天线的方向图有主瓣、副瓣等，相比其他天线的方向图，智能天线通常有较窄的主瓣，较灵活的主、副瓣大小、位置关系，和较大的天线增益。与固定天线相比最大的区别是：不同的全职通常对应不同的方向图，我们可以通过改变权值来选择合适的方向图，即天线模式。方向图一般分为两类：一类是静态方向图，即不考虑信号的方向，由阵列的输出直接相加得到；另一类是带指向的方向，这类方向图需要考虑信号的指向，通过控制加权相位来实现。二、实验目的： 1、设计一个均匀线阵，给出λ（波长），N （天线个数），d （阵元间距），画出方向图曲线，计算3dB 带宽。 2、通过控制变量法讨论λ，N ，d 对方向图曲线的影响。 3、分析旁瓣相对主瓣衰减的程度(即幅度比)。三、实验内容： 1、公式推导与整理：权矢量12(,,......)T N ωωωω=，本实验旨在讨论静态方向图，所以此处选择 ω=(1,1,......1)T 。信号源矢量(1)()[1,,...]j j N T a e e ββθ---=，2sin d πβθλ = ，幅度方向图函数()()H F a θωθ== (1)1 sin 2sin 2N j n n N e β β β--== ∑=sin(sin /)sin(sin /)n d n d πθλπθλ。

基于HFSS的4_24微带阵列天线的研究与设计_惠鹏飞

第26卷第5期齐齐哈尔大学学报 Vol.26,No.5 2010年9月 Journal of Qiqihar University Sep.,2010 基于HFSS 的4×24微带阵列天线的研究与设计惠鹏飞，夏颖，周喜权，陶佰睿，苗凤娟（齐齐哈尔大学通信与电子工程学院，黑龙江齐齐哈尔 161006）摘要：微带阵列天线的馈电方式有微带线馈电和同轴馈电两种方式，本文利用HFSS软件对微带阵列天线进行了研究，分析了两种馈电方式的传输损耗及其对天线方向图的影响，利用模块化的设计方法实现了一种基于同轴线馈电结构的多元矩形微带阵列天线。在HFSS仿真设计环境里对天线进行了物理建模，该微带阵列天线的方向图特性良好，工程上实现比较方便。关键词：微带阵列天线；模块化设计；HFSS 仿真；物理建模；方向图中图分类号：TN820.1 文献标识码：A 文章编号：1007-984X(2010)05-0009-04 随着无线电技术的发展，微带天线在许多领域得到了越来越广泛的应用，主要应用场合包括：卫星通信、多普勒雷达及其它制式雷达、导弹遥测系统、复杂天线中的馈电单元等[1] 。微带天线通常采用天线阵列的形式，由馈电网络控制对天线子阵的激励幅度和相位，以获得高增益、强方向性等特点。微带阵列天线的馈电方式主要有微带线馈电和同轴线馈电方式两种。利用微带线馈电时，馈线与微带贴片是共面的，因此可以方便地光刻，但缺点是损耗较大，在高效率的天馈系统里的应用受到较大限制[2]。本文首先对微带馈电网络产生的损耗进行了详细分析，利用HFSS 软件设计了2×4结构的微带子阵，采用同轴馈电的方式，利用模块化设计方法和方向图叠加原理最终实现了4×24矩形微带阵列天线，仿真设计结果表明，该大型矩形微带阵列天线的各项指标参数良好，设计思想得到了很好的验证。 1 微带阵列及馈电网络损耗分析 1.1 微带阵列理论微带天线单元的增益较小，一般单个贴片单元的辐射增益只有6～8 dB，为了实现远距离传输和获得更大的增益，尤其是对天线的方向性要求比较苛刻的场合，常采用由微带辐射单元组成的微带阵列天线，如果对增益要求较高，可采用大型微带阵列天线结构[3]。首先分析平面微带阵列天线的激励电流与电场分布情况，无论是线天线还是面天线，其辐射源都是高频电流源，天线系统将高频电流源的能量转换成电磁波的形式发射出去，讨论电流源的辐射场是分析天线的基础。假设由若干相同的微带天线元组成的平面阵结构，建立三维坐标系分析阵列天线的场量分布情况。以阵列的中心为坐标原点，天线在x 轴方向和y 轴方向的单元编号分别用m 和n 表示。以原点天线单元为相位参考点，为了简化分析，假设阵列中各单元间互耦影响可以忽略不计，各单元激励电流为 j()e xs ys m n mn I ψψ?+，天线阵在远区的辐射总场(,)E θ?为 ()(,)(,)E f S θ?θ?θ??,= 式中，(,)f θ?为阵元的方向性函数，(,)S θ?为平面阵的阵方向性函数。平面阵因子是两个线阵因子的乘积，可以利用线阵方向性分析的结论来分析平面阵列的方向性。 1.2 馈电网络及损耗分析天线只有承载高频电流才能有电磁波辐射，馈线指将高频交流电能从电路的某一段传送到另一段所用的设备，对天线的馈电包括对单元天线的馈电和阵列天线的馈电两种形式。当利用传输线对阵列结构进行收稿日期：2010-06-06 基金项目：齐齐哈尔市科技局工业攻关项目（GYGG-09011-2）作者简介：惠鹏飞（1980-）,男，辽宁凌源人，讲师，硕士，主要从事雷达极化信息处理的研究，weibo505@https://www.wendangku.net/doc/1c10482490.html,。

(重要)阵列天线

(完整版)射频微带阵列天线设计毕业设计

射频微带阵列天线设计摘要微带天线是一种具有体积小、重量轻、剖面低、易于载体共形、易于与微波集成电路一起集成等诸多优点的天线形式，目前已在无线通信、遥感、雷达等诸多领域得到了广泛应用。同时研究也发现由于微带天线其自身结构特点，存在一些缺点，例如频带窄、增益低、方向性差等。通常将若干单个微带天线单元按照一定规律排列起来组成微带阵列天线，来增强天线的方向性，提高天线的增益。本文在学习微带天线和天线阵的原理和基本理论，加以分析，利用Ansoft 公司的高频电磁场仿真软件HFSS，设计了中心频率在10GHz的4元均匀直线微带阵列，优化和调整了相关参数，然后分别对单个阵元和天线阵进行仿真，对仿真结果进行分析，对比两者在相关参数的差异。最后得到的研究结果表明，微带天线阵列相较于单个微带天线，由于阵元间存在互耦效应以及存在馈电网络的影响，微带阵列天线的回波损耗要大于单个阵元。但是天线阵列增益明显大于单个微带天线，且阵列天线比单个阵元具有更好的方向性。

关键词：微带天线微带阵列天线方向性增益 HFSS仿真 Design of Radio-Frequency Microstrip Array Antenna ABSTRACT Microstrip antenna is a kind of antenna form with many advantages like,small size, light weight, low profile, easy-to-carrier conformal, easy integration with many other of microwave integrated circuits and so on. Now microstrip array wildly applied in the filed of wireless

阵列天线分析与综合

阵列天线分析与综合前言任何无线电设备都需要用到天线。天线的基本功能是能量转换和电磁波的定向辐射或接收。天线的性能直接影响到无线电设备的使用。现代无线电设备，不管是通讯、雷达、导航、微波着陆、干扰和抗干扰等系统的应用中，越来越多地采用阵列天线。阵列天线是根据电磁波在空间相互干涉的原理，把具有相同结构、相同尺寸的某种基本天线按一定规律排列在一起组成的。如果按直线排列，就构成直线阵；如果排列在一个平面内，就为平面阵。平面阵又分矩形平面阵、圆形平面阵等；还可以排列在飞行体表面以形成共形阵。在无线电系统中为了提高工作性能，如提高增益，增强方向性，往往需要天线将能量集中于一个非常狭窄的空间辐射出去。例如精密跟踪雷达天线，要求其主瓣宽度只有1/3度；接收天体辐射的射电天文望远镜的天线，其主瓣宽度只有1/30度。天线辐射能量的集中程度如此之高，采用单个的振子天线、喇叭天线等，甚至反射面天线或卡塞格伦天线是不能胜任的，必须采用阵列天线。对一些雷达设备、飞机着陆系统等，其天线要求辐射能量集中程度不是很高，其主瓣宽度也只有几度，虽然采用一副天线就能完成任务，但是为了提高天线增益和辐射效率，降低副瓣电平，形成赋形波束和多波束等，往往也需要采用阵列天线。在雷达应用中，其天线即需要有尖锐的辐射波束又希望有较宽的覆盖范围，则需要波束扫描，若采用机械扫描则反应时间较慢，必须采用电扫描，如相控扫描，因此就需要采用相控阵天线。在多功能雷达系统中，既需要在俯仰面进行波束扫描，又需要改变相位展宽波束，还需要仅改变相位进行波束赋形，实现这些功能的天线系统只有相控阵天线才能完成。随着各项技术的发展，天线馈电网络与单元天线进行一体化设计成为可能，高集成度的T/R组件的成本越来越低，使得在阵列天线中的越来越广泛的采用，阵列天线实现低副瓣和极低副瓣越来越容易，功能越来越强。等等。综上所述，采用阵列天线的原因大致有如下几点：

5G阵列天线设计

5G阵列天线设计 5G——第五代无线通信技术，作为全球性的暴热话题已经是不争的事实。如众多专家所述，该技术将带来更低时延、更快速率的数据通信，并将导致互联设备的爆发式增长。 5G网络的更大带宽需求，要求必须彻底重新设计天线阵列，从单元到阵列，到馈电网络，到全模型验证和应用场景评估，都需要做完善的精细化仿真和优化设计。通过ANSYS HFSS的帮助，只需八个步骤，就能轻松完成5G天线阵列的设计和综合验证。更方便的是，HFSS还能帮助工程师优化各项天线性能指标，如：增益— 最强的信号辐射方向。波束控制— 能够将信号辐射控制在某个方向上。回波损耗— 从天线反射回来的回波能量。旁瓣电平— 不需要的信号辐射方向。设计流程结束后，获得的阵列天线聚焦增益更高、回波损耗及旁瓣电平最低，而且方向可控制。第1步：通过HFSS天线工具箱（ATK）找到天线单元模板 5G天线阵列设计的第1步是通过HFSS天线工具箱（ATK）找到合适的天线单元模板。该天线单元将定义一个最终用于复制成一系列天线（天线阵列）中的相同部分。

先从天线工具箱（ATK）的库中选择一个天线类型，然后输入工作频率及天线基板属性。数秒后，天线工具箱（ATK）将生成天线单元的初始几何结构。然后，HFSS 还可计算天线单元的增益及回波损耗等指标特性。第2步：将天线单元代入天线阵列有了天线单元后，工程师就可将其代入一个周期阵列中。把单元代入一系列复制设计中，有助于提高增益。在第一步中，天线单元是自行评估的。现在可使用无限大天线阵列的周期单元重复评估这一过程。很容易理解，阵列内其它天线的距离会影响增益、回波损耗、旁瓣回波及波束控制等特性。当然，也可通过调整天线方位来优化这些特性。选定最佳阵列方位后，可通过定义阵因子，将无限大阵列改为理想化的有限大阵列。本例中仿真了一个16x16的正方形天线阵列。第3步：使用域分解方法设计有限大天线阵列

阵列天线方向图的MATLAB实现

阵列天线方向图的MATLAB 实现课程名称：MATLAB程序设计与应用任课教师：周金柱班级：04091202 姓名：黄文平学号：04091158 成绩：

阵列天线方向图的MATLAB 实现摘要：天线的方向性是指电磁场辐射在空间的分布规律，文章以阵列天线的方向性因子F（θ，φ）为主要研究对象来分析均匀和非均匀直线阵天线的方向性。讨论了阵列天线方向图中主射方向和主瓣宽度随各参数变化的特点，借助M ATLAB绘制出天线方向性因子的二维和三维方向图，展示天线辐射场在空间的分布规律，表现辐射方向图的特点。关键词：阵列天线;;方向图；MATLAB 前言：天线是发射和接收电磁波的重要的无线电设备，没有天线也就没有无线电通信。不同用途的天线要求其有不同的方向性，阵列天线以其较强的方向性和较高的增益在工程实际中被广泛应用。因此，对阵列天线方向性分析在天线理论研究中占有重要地位。阵列天线方向性主要由方向性因子F（θ，φ）表征，但F（θ，φ）在远区场是一组复杂的函数，如果对它的认识和分析仅停留在公式中各参数的讨论上，很难理解阵列天线辐射场的空间分布规律[ 1 ]。MATLAB以其卓越的数值计算能力和强大的绘图功能，近年来被广泛应用在天线的分析和设计中。借助MATLAB可以绘制出阵列天线的二维和三维方向图，直观地从方向图中看出主射方向和主瓣宽度随各参数的变化情况，加深对阵列天线辐射场分布规律的理解。 1 均匀直线阵方向图分析若天线阵中各个单元天线的类型和取向均相同，且以相等的间隔d 排列在一条直线上。且各单元天线的电流振幅均为I，相位依次滞后同一数值琢，那么，这种天线阵称为均匀直线式天线阵，如图1 所示[ 2 ]: 均匀直线阵归一化阵因子为[ 3 ]： Fn（θ，φ）是一个周期函数，所以除§= 0 时是阵因子的主瓣最大值外，§= ±2 mπ

线极化微带天线阵列的设计

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ABSTRACT Microstrip, microwave, originated in the middle of the last century, in the end of la st century has launched the research of practical antenna and made the first batch of pra ctical antenna, the microstrip antenna has made breakthrough progress now, no matter in theory or application on the depth and width of further development, this new antenna has been increasingly mature, its application to our daily life, military, science and techn ology are closely related. Compared with the common antenna microstrip antenna with small volume, light weight, the characteristics of thin section, it can be made with missil e and satellite surface phase structure, and suitable for mass production printed circuit te chnology. Therefore, microstrip antenna has been widely used in wireless communicatio n, remote sensing and radar. However, according to the structure of microstrip antenna, t here are still some shortcomings, such as narrow band, low efficiency, low gain and poo r directivity. The way to solve these problems is to arrange a number of antenna element s in a regular arrangement, and make up the antenna array to improve the gain and direc tion of the antenna. Based on the theory of microstrip antenna and basic theory of microstrip antenna ar ray, HFSS is used to analyze the array antenna. The array antenna with the center freque ncy of 5.8GHZ is designed, and the characteristics of the antenna are studied in detail. T he gain of antenna array is obviously larger than that of single microstrip antenna, and t he direction is better. Therefore, the antenna array was used for simulation and the corr elation parameters in the results were compared and analyzed, and the correlation param eters were optimized and adjusted. Simulation of the antenna of the indicators are up to par, the physical processing, and testing in microwave dark room to the related paramete rs of the antenna, and comparing with design index, the simulation results, finally reach ed the design requirements. Keywords: miccrostrip antennas antenna array directivity gain HFSS simulation

元阵列天线方向图及其MATLAB仿真

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式中：ζφθψ+=cos sin kd 均匀直线阵最大值发生在0=ψ 处。由此可以得出这里有两种情况最为重要。 1.边射阵，即最大辐射方向垂直于阵轴方向，此时，在垂直于阵轴的方向上，各元观察点没有波程差，所以各元电流不需要有相位差。 2.端射振，计最大辐射方向在阵轴方向上，此时 0=m ?或π，也就是说阵的各元电流沿阵轴方向依次超前或滞后kd 。 3设计过程本次设计的天线为14元均匀直线阵天线，天线的参数为：d=λ/2，N=14相位滞后的端射振天线。基于MATLAB 可实现天线阵二维方向图和三维方向图的图形分析。 14元端射振天线H 面方向图的源程序为： a=linspace(0,2*pi); b=linspace(0,pi); f=sin((cos(a).*sin(b)-1)*(14/2)*pi)./(sin((cos(a).*sin(b)-1)*pi/2)*14); polar(a,f.*sin(b)); title('14元端射振的H 面方向图，d=/2,相位=滞后'); 得到的仿真结果如图所示： kd m ζ?-=cos 2π ?±=m

5.8GHz通信系统阵列天线设计与校正

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阵列原计划微带天线设计要点

编号：毕业设计(论文)说明书题目：圆极化微带4单元阵列天线学院：专业：学生姓名：学号：指导教师：职称：题目类型：理论研究实验研究工程设计工程技术研究软件开发 2012 年 6 月 5 日摘要

圆极化天线具有一些显著的优点: 任意线极化的来波都可以由圆极化天线收到, 圆极化天线辐射的圆极化波也可以由任意极化的天线收到; 圆极化天线具有旋向正交性, 圆极化波入射到对称目标反射波变为反旋向等。正是由于这些特点使圆极化天线具有较强的抗干扰能力, 已经被广泛地应用于电子侦察和干扰,通信和雷达的极化分集工作和电子对抗等领域。

目录第一章微带天线简介 ............................. 错误!未定义书签。

§1.1微带天线的发展............................. 错误!未定义书签。 §1.2微带天线的定义和结构....................... 错误!未定义书签。 §1.3微带天线的优缺点........................... 错误!未定义书签。 §1.4微带天线的应用 (6) 第二章微带天线的辐射原理与分析方法.............. 错误!未定义书签。 §2.1微带天线的辐射原理......................... 错误!未定义书签。 §2.2微带天线的分析方法......................... 错误!未定义书签。 §2.2.1 传输线模型法 (8) §2.2.2 空腔模型法........................... 错误!未定义书签。 §2.2.3 积分方程法........................... 错误!未定义书签。 §2.3微带天线的馈电方法......................... 错误!未定义书签。第三章圆极化微带天线单元的设计与仿真............ 错误!未定义书签。 §3.1A NSOFT HFSS高频仿真软件的介绍............... 错误!未定义书签。 §3.2微带天线圆极化技术 (14) §3.2.1 圆极化天线的原理..................... 错误!未定义书签。 §3.2.2 圆极化实现技术 (15) 第四章圆极化微带4单元阵列天线的设计与仿真...... 错误!未定义书签。 §4.1圆极化微带天线单元的设计与仿真............. 错误!未定义书签。 §4.1.1圆极化微带天线单元的设计仿真......... 错误!未定义书签。 §4.1.2天线单元轴比的优化................... 错误!未定义书签。 §4.2馈电网络的仿真与设计....................... 错误!未定义书签。 §4.2.1两路微带等功率分配器的设计与仿真..........错误!未定义书签。 §4.2.2连续旋转馈电网络............................错误!未定义书签。 §4.3圆极化阵列天线模型的设计与仿真 ............. 错误!未定义书签。 §4.3.1阵列天线的创建与仿真................错误!未定义书签。 §4.3.2阵列天线的优化设计................错误!未定义书签。第五章结论致谢........................................... 错误!未定义书签。参考文献错误!未定义书签。

5g微带阵列天线讲解

5G微带阵列天线要求：利用介质常数为2.2，厚度为1mm损耗角为0.0009的介质，设计一个工作在5G的4X4的天线阵列。评分标准：良：带宽〈7% 优：带宽〉7%且效率大于60% 1微带辐射贴片尺寸估算设计微带天线的第对于工作频率即为：步是选择合适的介质基板，假设介质的介电常数为&r， f的矩形微带天线，可以用下式设计出高效率辐射贴片的宽度W，式中，C 波长，即为：是光速，辐射贴片的长度一般取为飞/2 ；这里e是介质内的导波考虑到边缘缩短效应后，实际上的辐射单元长度L应为: L—C-2 丄 2 f ?. ；e 式中，计算，即为: ；e是有效介电常数，厶L是等效辐射缝隙长度。它们可以分别用下式 1 E r +1 E r —1 h -5 ；e (1 12 ) 2 2 2 w .丄"412h(；e。①⑶川 °264 ) ? —0.258)(w/h+0.8) 2.单元的仿真由所给要求以及上述公式计算得辐射贴片的长度L=19.15mm,W=23.72mm采用非辐射边馈电方式，模型如图1所示：

图1单元模型此种馈电方式，可以通过移动馈电的位置获得阻抗匹配，设馈电点距离上宽边的偏移量为dx,经仿真得到当dx=4mm P寸，阻抗匹配最好。另外，之前计算出的尺寸得到的谐振点略有偏移，经过仿真优化后贴片尺寸变为L=19mm,W=23.72mm仿真结果图如图2,图3所示。 Freq [GHz] 图2 S11参数

图3增益图从图中可以看出谐振点为5GHz计算的相对带宽为2.2%,增益为5.78dB 2. 2 X 2阵列设计设计馈电网络并组阵，模型图如图4所示。图4 2 X2微带天线阵列

王健阵列天线讲义习题

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