Shortened 3D Corner Reflector Antenna
Dragoslav Dobri?i?, YU1AW
缩短型3D角反射器天线
Abstract
概要
In this text two 3D corner reflector antenna modifications are described.
本文描述对3D角反射器天线的两处修改。
The first modification is regarding the input impedance decrease from about 72 ohms of the original antenna, to about 50 ohms, which made possible supplying with usual coaxial cables of 50 ohms impedance. This is achieved by adding a passive element to the existing active element. This decreased impedance while retaining antenna’s gain and its radiation diagram.
第一处修改是把原天线的输入阻抗从大约72欧姆降低到大约50欧姆，这样就能够和我们平常使用的50欧姆同轴电缆匹配了。这个修改是依靠在有源振子的基础上增加了一个无源振子实现的。
The second modification is regarding the alteration of the shape of the antenna by removing one piece of the bottom reflector surface. The result of this is smaller and more compact antenna with smaller resistance to the wind and accumulation of the snow, with very small change of radiation diagram and gain decrease of about 0.25 dB.
第二项修改是去掉天线底面反射体的一部分，其结果是天线更小更紧凑了，降低了风阻，减少了落雪的堆积。而方向图和增益只降低了很小的0.25dB。 The practical solution of the construction of Shortened 3D Corner Reflector Antenna for 2.4 GHz is given at the end of the text.
本文最后给出缩短型角反射器天线的实际结构。
Introduction
引言
The original design of 3D Corner Reflector Antenna was for the first time described in:
IEEE Transactions on Antennas and Propagation, July, 1974. "Three-Dimensional Corner Reflector Array" by Naoki Inagaki (pp. 580-582).
3D角反射器天线最初发表在：电气和电子工程师协会会刊《天线和传播》，1974年7月号，Naoki Inagaki 先生的文章“三维角反射器阵列天线”第580-582页。
The precise and explicit results of computer analysis and simulation were reported in July 2003. by L.B. Cebik W4RNL in the article: “The 3-D Corner Reflector” (https://www.doczj.com/doc/8d17855585.html,/vhf/3c.html).
精确的计算机模拟报告由L.B. Cebik W4RNL先生发布在2003年7月的文章：“3D角形反射器”(https://www.doczj.com/doc/8d17855585.html,/vhf/3c.html) 。
Fig. 1. Original 3D Corner Reflector Antenna.
图1：最初的3D角反射器天线
The antenna consists of three square reflector surfaces placed among each other perpendicularly to form half of the cube, and with the active element in the form of monopole at one of them, as shown in figure 1. This structure concentrates electromagnetic energy in relatively narrow beam, whose direction of maximum radiation is in the line with the large diagonal of the cube, which begins in the apex, i.e.under angle of 45 degrees between the beam and all three reflector surfaces.
天线由3个矩形平面反射器直立围成半个立方体，有源振子（单极天线）安装在其中一个反射器上，如图1所示。这种结构使电磁能量汇聚为狭窄的波束，最大辐射方向在从顶点开始的立方体最长的对角线上，也就是说，波束和3个反射面之间的夹角是45度。
The reflector surfaces’ dimensions are not critical. With the enlargement of the surfaces, antenna gain also increases, at first considerably and later on less and less.
反射面的尺寸不是最关键的。扩大反射面，天线的增益也会增加，开始时增加的较多，然后就越来越少了。
Our analyses revealed that the practical maximum of the gain is achieved before we expected so far.
我们的分析显示，实际上最大增益远远高于我们的预期。
The optimal dimension is about 2.8 wavelengths. Further dimension enlargement leads to more and more insignificant increase of the gain of the antenna, and for 3-3.5 wavelengths the practical gain maximum is achieved. Further enlargement of reflector surfaces has no meaning, because it does not lead to the gain increase, as shown in the figure 2.
最佳尺寸大约是2.8个波长，更大的尺寸对于增益来说就越来越没有价值了，到3-3.5个波长时，增益就达到极限了。反射板尺寸再大也没有意义了，不会带来增益的增长，见图2。
Fig. 2. Original 3D Corner Reflector Antenna gain with 0.8 to 4 wavelengths
reflectors length.
图2：0.8至4个波长原版3D角反射器天线的增益
Reflector surfaces can be made of full material, such as aluminum, copper or brass tin. At lower frequencies they can be made of metal wire grid, whose density must be determined in the way that the opening, measured parallel with the polarization plane, i.e. with the active element plane, has to be less than 0.1 wavelengths.
反射面可以用铝、铜或黄铜板材制成，在低频段，也可以用金属线栅网，其密度取决于孔眼，而孔眼根据有源振子的极化面确定，必须小于0.1个波长。 The thing that makes this antenna outstanding are its unique simplicity and design that is very tolerant to the errors in dimensions, which guarantees great reproducibility of practical results and the possibility of its use, along with recalculating its dimensions, at frequencies from couple of tens of MHz to several GHz.
制作这种天线的最大优点就是少见的简单和尺寸误差的宽容度。这使它具有巨大的再生性，从数十MHz到几个GHz的宽阔频段，只要重新计算它的尺寸，都可以使用。
Another good quality of this antenna is that it has excellent side lobe suppression, which makes it a very good choice when the noise and interference from the signals from other directions have to be pushed out as much as possible.
这种天线的再一个优点就是它有非常好的旁瓣抑制，当必须尽可能排除其它方向的杂波干扰时，这种天线是一个非常好的选择。
Fig. 3. Original antenna input impedance change with change of active element DR
length in wavelengths.
图3：通过改变有源振子DR的波长长度改变原天线的输入阻抗
Fig. 4. Original antenna input matching with change of active element DR length
in wavelengths.
图4：改变有源振子DR的波长长度时原天线的输入匹配
The only disadvantage of the original version of this antenna is its input impedance. Regarding its position between three orthogonal planes, the input impedance of the active monopole changes with its position and length. In the same time, with these changes, the gain of the antenna also changes.
原天线唯一的缺陷就是输入阻抗问题。
与此有关的是它在3个直角平面的位置，有源振子的输入阻抗会因其位置和长度的变化而改变。同样，随着这些改变，天线的增益也随之改变。
Fig. 5. Original antenna gain and side lobes suppression with change of active
element DR length in wavelengths.
图5：有源振子的波长长度改变时原天线增益和旁瓣抑制
The change of the input impedance and 50 ohms matching of the original antenna with the change of the length of the active monopole is shown in the figure 3 and 4.
改变原天线有源振子的波长长度而改变输入阻抗与50欧姆匹配，见图3和4.
The gain maximum is reached with the position of the active element at about x=0.6 and y=0.6 wavelengths measured from apex, and with the optimal length of DR=0.75 wavelengths measured from the reflector surface. In that case, input impedance is about 72 ohms when the antenna is in resonance, which leads to minimal SWR of about 1.4 for matching on 50 ohms. This SWR is acceptable at lower frequencies where the losses in cables are small, but at UHF and SHF band it becomes unacceptable, because the losses in cables due to SWR are considerable. The alternative is supplying the antenna with 75 ohms cable, which decreases the losses,
有源振子在X=0.6、Y=0.6波长（从顶点开始）的位置时，增益达到最佳。从反射体表面开始测量，有源振子的最佳长度DR=0.75个波长。这种情况下，当天线谐振时，其输入阻抗约为72欧姆，这就导致在和50欧姆匹配时其最小驻波比大约为1.4。这个驻波比在低频段还可以接受（此时电缆损耗较小），但是在UHF 和SHF 频段则不能令人满意，因为随着驻波比的增大电缆的损耗也会加大。我们可以选择75欧姆电缆给天线馈电，把损降到最小。但问题是，TX/RX （发送/接收）设备工作时都需要50欧姆阻抗才能与之匹配，
but the problem of adequate matching to TX/RX devices intended for working with the 50 ohms impedance remains.
The change of the gain of the original 3D corner antenna with the reflector of 2 wavelengths, depending on the length of the active element DR expressed in wavelengths, is shown in figure 5.
原3D 角反射器天线用2个波长的反射板（其长度和有源振子DR 一样用波长表示）时增益的变化见图5.
The working band width of the original antenna, i.e. the change of the input
impedance with the change of the working frequency in the band from -10% to +10% of the resonant frequency, is shown in figure 6.
改变原天线的工作频率，偏离谐振频率-10%到+10%时，输入阻抗的变化见图
6.
Fig. 6. 3D Corner Reflector Antenna input impedance change with change of
working frequency +/- 10% from resonance.
图6：改变工作频率（偏离谐振频率）+/-10%时3D 角反射器天线输入阻抗的变
化。
Modification of the input impedance of the antenna
改变天线的输入阻抗
At first glance it was clear that it would be good if we could adjust this exceptional antenna in that way, from 72 to about 50 ohms, in order to match it to 50 ohms coaxial cable.
毋庸置疑，如果我们把天线从75欧姆调整到50欧姆，会和50欧姆的同轴电缆达到很好的匹配。
The first thing that could be considered was adding one passive element whose impact on the active element would be adjusted in the way to decrease the input impedance to 50 ohms. This attempt, of course, included maximal conservation of the existing good properties of the antenna.
第一件事就是增加一个无源振子来影响有源振子，使输入阻抗降低到50欧姆。当然，这个尝试必须最大限度地保持天线现有的优良属性。
For that job the best available programs for analysis needed to be used, because most of the programs for antenna analysis show the lowest accuracy in calculating input impedance. In addition, this is the case of so called aperture (surface) antenna that works mainly by using the laws of geometric optics, so it was needed to choose good program in simulating the aperture antennas. The famous professional program for simulating antennas NEC-2 was chosen with its derivative 4nec2, whose author is Arie Voors.
完成这项工作需要最好的分析程序，因为大多数应用于天线系统的程序，在计算输入阻抗时都显得太不精确了。另外，这种情况在口径（面）天线大都遵循几何光学的规则。那么，需要选择模拟口径天线的好程序。我们选中了著名的模拟天线专业程序NEC-2的派生版本4NEC2，其作者是Arie Voors。
After completing analyses for several different position and element length variants, finally, one solution relieved: the solution with additional parasitic element DI which would be positioned in front of the active element, similarly as the first director in Yagi antennas. Of course, it is only the analogy, because resolving the problem of the input impedance of this antenna is just similar to the solutions in Yagi antennas.
接着就是分析几种不同位置和不同振子长度的情况，最后，找到一个解决办法：增加一个二次辐射振子DI，放置在有源振子的前面，类似八木天线的第一个导向器。当然，也是唯一的类似，因为解决这种天线的输入阻抗问题，与八木天线的解决办法非常相似。
By putting the additional passive element and adjusting its length and distance from the active element, almost ideal matching of 50 ohms was achieved.
增加无源振子并调节它的长度，调节它和有源振子的距离，得到了近乎理想的50欧姆匹配。
Model testing and simulation results
样品测试和模拟结果
Before the final determination of the positions and the lengths of the elements, we needed to verify the accuracy of the model used to simulate the antennas.
在最后确定振子的位置和长度之前，我们需要证实曾经仿真过的样品天线的精确性。
L.B.Cebik’s simulation, described in the mentioned article, for original antenna with reflector of 2 wavelengths and monopole of 0.75 wavelengths at position x=0.6 and y=0.6 wavelengths, has gain of 16.19 dBi with input impedance of 71+j7 ohms.
L.B.Cebik先生的仿真，在前面提到的文章中描述过，原天线用2波长反射器和0.75波长的单极天线，在X=0.6波长Y=0.6波长的位置输入阻抗71＋j 7ohm 时增益为16.9dBi。
Fig. 7. Vertical diagram of original and modified 3D Corner Reflector Antene
with 2 wavelengths reflector length.
图7：2波长反射器长度时原天线（蓝色线）和改进后（红色线）的3D角反射
器天线的垂直方向图
Fig. 8. Horizontal diagram of original and modified 3D Corner Reflector
Antene with 2 wavelengths reflector length.
图8：2波长反射器长度时原天线（蓝色线）和改进后的（红色线）3D角反射器
天线的水平方向图
Our simulation for the same antenna exhibited almost identical results of 16.2 dBi with impedance of 69.2+j8.5 ohms! In this way, we compared and tested the accuracy of our model and the simulation in relation to the professional version of the NEC-4 program.
我们对同样天线的仿真显示，大部分结果同样是16.2dBi（阻抗是69.2+j 8.5 ohm）。用这样的方法，我们比较和测试了样品天线的精确性，是用NEC-4专业程序仿真的。
After the verification of the model and the accuracy of the simulation, we simulated modified antenna of 2 wavelengths with additional passive element for impedance adjustment. The gain of modified antenna was 16.46 dBi with input impedance of 49.7+j1.1 ohms, with a slight change of the vertical radiation diagram. The vertical and horizontal radiation diagrams of the original and the modified antennas are shown side by side in figures 7 and 8. As shown in the figure, horizontal radiation diagram remained practically intact. Modified antenna exhibited slightly higher gain in relation
to the unmodified, which is the result of the decrease of the radiation resistance of the antenna from 72 to 50 ohms and effect of added passive element.
在验证和模拟了样品天线的精确性之后，我们仿真了增加了调整阻抗的无源振子的2波长天线。改进的天线在输入阻抗49.7+j1.1欧姆时增益为16.46dBi，垂直方向图有微小的改变。原天线和改进的天线的水平和垂直方向图见图7和8。数字显示，水平方向图几乎保持不变。改进后的天线比改进前的增益稍有增高。这是增加了无源振子使天线阻抗从72降低到50欧姆导致的结果。
Fig. 9. Modified antenna input matching change with change of passive element DI length and constant length of active element DR=0.75 wavelengths.
图9：改变无源振子DI的长度（保持有源振子DR=0.75波长）引起天线输入阻
抗的变化
Fig. 10. Modified antenna gain and side lobe suppression with change of passive element DI length and constant length of active element DR=0.75 wavelengths.图10：改变无源振子DI的长度（保持有源振子DR=0.75波长）天线的增益和
旁瓣抑制
Fig. 11. Modified antenna gain and side lobe suppression with change of active element DR length and constant length of passive element DI=0.65 wavelengths. 图11：改变有源振子DR的长度（保持无源振子DI=0.65波长）天线的增益和
旁瓣抑制
Fig. 12. Modified antenna input impedance change with change of passive element DI length and constant length of active element DR=0.75 wavelengths.
图12：改变无源振子DI的长度（保持有源振子DR=0.75波长）引起天线输入
阻抗的变化
The changes of input impedance and gain of the antenna with only the change of the length of either the passive or the active element, while the other retains the length at which it gave the best results, are given in figures 9, 10, 11 and 12.
改变天线的输入阻抗和增益，只需改变有源和无源振子两者之中任何一个（另一个保持原长度）即可取得最好的结果。见图9、10、11和12。
Fig. 13. Input matching and bandwidth of original antenna with 75 ohms feed.
图13：75欧姆的原天线的输入匹配和带宽
Fig. 14. Input matching and bandwidth of modified antenna with 50 ohms feed.
图14：50欧姆的改进型天线的输入匹配和带宽
It became clear that, for the best performances of the antenna, the length of the active element, even after addition of the passive element, should remain unchanged in regard to the original antenna.
这就很清楚了，天线的最大优点是（对于原天线来说）：有源振子的长度可以保持不变（即使增加了无源振子）。
Fig. 15. Modified 3D Corner Reflector Antenna input impedance change with change of working frequency +/- 10% from resonance.
图15：改进型3D角反射器天线的输入阻抗变化（工作频率对谐振频率改变
+/-10%时）
With this modification, due to decreasing of the radiation resistance of the antenna, we expected slight decrease of the width of the frequency working band of the antenna, which was also analyzed. Achieved values of matching with changing frequencies are given in the figure 13. for unmodified (75ohms) and in the figure 14 for modified (50 ohms) antenna.
辐射电阻的降低带来的这些变化，我们预计会使天线的工作带宽有轻微的减少。图13给出了未更改的（75欧姆）天线、图14给出改进型（50欧姆）天线因改变工作频率引起的带宽和输入匹配的变化。
We also analyzed the changing of the gain of the antenna with the increase of the length of the reflector surfaces, in order to compare it to the original antenna and to determine the optimal reflector dimensions for achieving the gain maximum. The result of this analysis is given in figure 16.
为了（通过对比原天线）确定改进型天线的最佳反射面尺寸，获得最大增益。我们同样分析了因反射面长度改变引起的增益变化。
Fig.16. Modified 3D Corner Reflector Antenna gain with 0.8 to 4 wavelengths
reflectors length.
图16：反射器长度0.8至4波长时改进型角反射器天线的增益
Shape modification
外形的更改
Computer simulations revealed that part of the bottom reflector surface which is the most distant from active and passive element very little influences focusing electromagnetic energy and formation of radiation diagram. That gave us the idea to try to modify the shape of the antenna by cutting the half of the bottom reflector surface. By doing this, we achieved much more compact and half shorter antenna. The analysis of the influence of this intervention revealed that performances of the antenna remained unchanged.
计算机模拟显示，底部反射面距离有源和无源振子最远的那部分，对于电磁能量的汇聚影响很小，这使我们产生了改变天线形状——切除底部反射面一半的想法。于是，我们得到了短了一半的紧凑的天线。分析报告显示，天线的性能没有改变。
The decrease of the overall length of the antenna to the half without any serious consequences indicates that the other two reflector surfaces actually play the main role in focusing electromagnetic energy and formation of very directional radiation diagram with excellent side lobes suppression in both planes.
天线缩短了一半而没有造成任何严重后果，说明另外两面反射面在汇聚电磁能量、构成非常优秀的旁瓣抑制的定向方向图中，实际承担了主要角色。
The bottom reflector surface has more impact on the formation of the radiation diagram only between apex and active and passive element and closely around them. The influence decreases with distance from elements towards periphery of the bottom reflector surface.
底部反射面对方向图构成的影响，仅限于顶点、有源振子、无源振子之间。其作用从振子到底部反射板边缘逐渐减小。
As a logic step in further improving and increasing the gain of the antenna was to elongate both vertical planes to the overall length of 3 wavelengths and in that way to achieve practical maximum of the antenna gain. This modification also increased the distance between passive element and the outer edge of the bottom reflector surface, because of the increase of the diagonal of the reflector surface itself. The removal of the half of the bottom reflector at the antennas with reflectors of 3 wavelengths has less influence on the diagram than at the antennas with smaller reflector, and that’s because of the fixed positions of the active and passive element regardless of the length of the reflector.
要进一步改善和增加天线的增益，可以延长每一个垂直反射面直到3个波长，以此获得最大的增益。这次修改也增加了无源振子到底部反射面边沿的距离（因为底部反射面的对角线本身增长了）。把（反射面为3个波长的）天线的底面反射面切掉一半，对方向图影响较小（相对于小反射面的天线来说），这是因为固定了有源和无源振子的位置，就无须更多考虑反射面的长度。
This kind of antenna was submitted to the detailed computer analysis and comparison with previous versions. Without any doubt, achieved performances were superior and with half shorter and more compact antenna the maximum of practical gain was achieved.
这种天线依据了对先前版本进行计算机详细分析和对照的结果。毫无疑问，这个半短、紧凑、有最大增益的天线，其功能也同样优秀。
The difference in the shape of the diagram and gain between shortened and full antenna with 3 wavelengths reflector are shown in figures 17 and 18.
3波长反射器的缩短型天线和完整天线的不同的方向图和增益见图17和18。
Fig. 17. Vertical diagram and gain of shortened and full antenna.
图17：缩短（红线）和完整（蓝线）天线的垂直方向图和增益
Fig. 18. Horizontal diagram and gain of shortened and full antenna.
图18：缩短（红线）和完整（蓝线）天线的水平方向图和增益
Small change in position of the main beam and suppression of the side lobes in vertical diagram and even small narrowing of the horizontal diagram reveal that because of the absence of the half of the bottom surface destructive changes in behavior and parameters of the antenna did not occur. The input impedance remained unchanged and gain decreased for about 0.25 dB due to decrease of the aperture of the antenna.
水平方向图中主波束的小小改变和旁瓣抑制以及垂直方向图的小小缩窄，说明虽然底部反射面缺失了一半，天线的性能和参数没有发生破坏性的改变。输入阻抗保持不变，增益则因为天线口径面的减小而降低了0.25dB。
The results of the computer simulations are used for building experimental specimen of the antenna which were then used for laboratory measurements and testing.
计算机仿真结果用来制作样品天线，然后用样品天线用来进行尺寸和试用的实验。
The measured values of input matching and gain of the antennas very well corresponded to computer predictions.
此天线的输入阻抗和增益的测定值完全符合计算机的预估。
Conclusion
结论
From all stated above, we can conclude that on the basis of the obtained results of the computer simulations and laboratory measurements we confirmed the possibility of
decreasing the radiation resistance of the antenna by adding passive element near the active monopole. This gave very good results regarding the value of obtained input impedance of the antenna, width of the frequency working band, the shape of the diagram and gain of the antenna.
综上所述，我们可以得出结论，基于计算机仿真结果和实验数据，我们确信，采用在有源振子附近增加无源振子的方法降低天线的辐射阻抗是可行的。天线的输入阻抗、天线的工作带宽、增益和方向图的形状，都获得非常圆满的结果。Also, we confirmed the possibility of significant shortage of the length of the antenna with negligible change of gain, input impedance and diagram shape of the antenna. In this way we achieved smaller and more compact antenna while retaining good characteristics of the original antenna.
同样，我们确信，因天线长度不足而造成的对天线的增益、输入阻抗和方向图形状的影响可以忽略。这样，我们得到了保持了原天线优良品质的小型、紧凑的天线。
Fig. 19. Main beam of antenna.
图19：天线的主波束
In addition to optimization of the input impedance and the shape of the antenna described in this article, we also analyzed the possibility of changing the shape of the reflector surfaces in order to achieve approximately equal width of horizontal and vertical angle of radiation diagram. In this way, it would be possible to use 3D corner reflector antenna as efficient illuminator for parabolic reflectors.
除了在文章中描述的天线形状和输入阻抗的最优化之外，我们还分析了怎样通过改变反射面形状获得大体相等的水平和垂直辐射角度。分析结果显示，用3D角反射器天线做偏馈抛物面天线的馈源，也是完全可能的。
The results obtained in that direction show that, with specially modified shapes of the reflector surfaces, it is possible to achieve optimal angles of radiation diagrams for the use with offset parabolic reflectors. In separate article we will describe one such shaped 3D corner antenna with additionally modified shape of the reflectors for the use with offset antennas.
这个结果也说明，改变反射面的形状，可以获得用于偏馈抛物面天线的最佳辐射角度。在另外的文章中，我们将叙述一个这样改造了反射器形状的3D角反射器偏馈天线。（作者在另一篇文章《3D角反射器天线作为馈源的5.8千兆赫偏馈抛物线天线》完成了这一命题。——译者注）
We also analyzed the possibility of alteration of shape of antenna by changing the angles between the reflector surfaces. The results of the computer simulations for different angles between reflector surfaces are worse from those achieved for angles
of 90 degrees.
我们同样分析了用改变反射面的夹角来改变天线形状的可能。对反射面不同夹角的计算机仿真显示，其结果都比90度夹角糟糕。
The projection of Shortened 3D Corner Reflector Antenna for 2.4 GHz band
用于2.4G频段的缩短型3D角反射器天线的设计方案
As the optimal dimension of reflectors we accepted the value of 3 wavelengths, which is 370 mm at 2.4 GHz. Properly built antenna has gain of about 17.9 dBi, which is a remarkable value considering the simplicity of build. In addition, this value also represents the practical maximum for this type of antenna.
至于反射器最佳尺寸，我们采用3个波长，就是370mm（用于2.4G频段）。实际制作的天线获得17.9dBi的增益。对结构如此简单的天线来说，这是一个不寻常的数值。此外，这也代表了这类天线的最大值。
The results of the simulation
仿真结果
Fig. 20. Shortened 3D Corner Reflector antenna gain with 3 wavelengths reflectors
length.
图20：缩短型3D角反射器天线的增益（反射面的长度为3个波长）
Fig. 21. Vertical diagram of shortened antenna at 2.4 GHz.
图21：2.4G缩短型天线的垂直方向图
Fig. 22. Horizontal diagram of shortened antenna at 2.4 GHz.
图22：2.4G缩短型天线的水平方向图