微带耦合器的中英文对照翻译

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微带耦合器的中英文对照翻译

Design and Analysis of Wideband Nonuniform Branch Line Coupler

and Its Application in a Wideband Butler Matrix

Yuli K. Ningsih,1,2 M. Asvial,1 and E. T. Rahardjo

Antenna Propagation and Microwave Research Group (AMRG),

Department of Electrical Engineering, Universitas Indonesia, New

Campus UI, West Java, Depok 16424, Indonesia Department of Electrical

Engineering, Trisakti University, Kyai Tapa, Grogol, West Jakarta 11440,

Indonesia

Received 10 August 2011; Accepted 2 December 2011

Academic Editor: Tayeb A. Denwdny

Copyright ? 2012 Yuli K. Ningsih et al. This is an open access article

distributed under the Creative Commons Attribution License, which

permits unrestricted use, distribution, and reproduction in any medium,

provided the original work is properly cited.

Abstract

This paper presents a novel wideband nonuniform branch line

coupler. An exponential impedance taper is inserted, at the series arms

of the branch line coupler, to enhance the bandwidth. The behavior of

the nonuniform coupler was mathematically analyzed, and its design of

scattering matrix was derived. For a return loss better than 10?dB, it

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achieved 61.1% bandwidth centered at 9GHz. Measured coupling

magnitudes and phase exhibit good dispersive characteristic. For the 1dB

magnitude difference and phase error within 3°, it achieved 22.2%

bandwidth centered at 9GHz. Furthermore, the novel branch line coupler

was implemented for a wideband crossover. Crossover was constructed

by cascading two wideband nonuniform branch line couplers. These

components were employed to design a wideband Butler Matrix working

at 9.4GHz. The measurement results show that the reflection coefficient

between the output ports is better than 18dB across 8.0GHz–9.6GHz,

and the overall phase error is less than 7.

1. Introduction

Recently, a switched-beam antenna system has been widely used in

numerous applications, such as in mobile communication system,

satellite system, and modern multifunction radar. This is due to the

ability of the switched-beam antenna to decrease the interference and

to improve the quality of transmission and also to increase gain and

diversity.

The switched-beam system consists of a multibeam switching

network and antenna array. The principle of a switched-beam is based

on feeding a signal into an array of antenna with equal power and phase

difference. Different structures of multibeam switching networks have

been proposed, such as the Blass Matrix, the Nolen Matrix, the Rotman

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Lens, and the Butler Matrix .

One of the most widely known multibeam switching networks with

a linear antenna is the Butler Matrix. Indeed, it seems to be the most

attractive option due to its design simplicity and low power loss .

In general, the Butler Matrix is an N × N passive feeding network,

composed of branch line coupler, crossover, and phase shifter. The

bandwidth of the Butler Matrix is greatly dependent on the performance

of the components. However, the Butler Matrix has a narrow bandwidth

characteristic due to branch line coupler and crossover has a limited

bandwidth. As there is an increased demand to provide high data

throughput , it is essential that the Butler Matrix has to operate over a

wide frequency band when used for angle diversity. Therefore, many

papers have reported for the bandwidth enhancement of branch line

coupler . In reference , design and realization of branch line coupler on

multilayer microstrip structure was reported. These designs can achieve

a wideband characteristic. However, the disadvantages of these designs

are large in dimension and bulk.

Reference introduces a compact coupler in an N-section

tandem-connected structure. The design resulted in a wide bandwidth.

Another design, two elliptically shaped microstrip lines which are

broadside coupled through an elliptically shaped slot, was employed in .

This design was used in a UWB coupler with high return loss and

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isolation. However, these designs require a more complex

manufacturing.

In this paper, nonuniform branch line coupler using exponential

impedance taper is proposed which can enhance bandwidth and can be

implemented for Butler Matrix, as shown in Figure

1. Moreover, it is a simple design without needs of using multilayer

technology. This will lead in cost reduction and in design simplification.

Figure 1:Geometry structure of a new nonuniform branch line

coupler design with exponential impedance taper at the series arm.

To design the new branch line coupler, firstly, the series arm’s

impedance is modified. The shunt arm remains unchanged. Reduced of

the width of the transmission line at this arm is desired by modifying the

series arm. Next, by exponential impedance taper at the series arm, a

good match over a high frequency can be achieved.

2. Mathematical Analysis of Nonuniform Branch Line Coupler

The proposed nonuniform branch line coupler use λ/4 branches

with impedance of 50Ω at the shunt arms and use the exponential

impedance taper at the series arms, as shown in Figure

1. Since branch line coupler has a symmetric structure, the

even-odd mode theory can be employed to analyze the nonuniform

characteristics. The four ports can be simplified to a two-port problem in

which the even and odd mode signals are fed to two collinear inputs [22].

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Figure 2 shows the schematic of circuit the nonuniform branch line

coupiers.

Figure 2:Circuit of the nonuniform branch line coupler.

The circuit of Figure 2 can be decomposed into the superposition of

an even-mode excitation and an odd-mode excitation is shown in Figures

and .

Figure 3:Decomposition of the nonuniform branch line coupler into

even and odd modes of excitation.

The ABCD matrices of each mode can be expressed following . In

the case of nonuniform branch line coupler, the matrices for the even

and odd modes become:

A branch line coupler has been designed based on the theory of

small reflection, by the continuously tapered line with exponential

tapers , as indicated in Figure 1, where

which determines the constant as:

Useful conversions for two-port network parameters for the even

and odd modes of S11 and S21 can be defined as follows :

where

Since the amplitude of the incident waves for these two ports are

±1/2, the amplitudes of the emerging wave at each port of the

nonuniform branch line coupler can be expressed as

Parameters even and odd modes of S11 nonuniform branch line

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coupler can be expressed as and as follows:

An ideal branch line coupler is designed

to have zero reflection power and splits the input power in port 1

(P1) into equal powers in port 3 (P3) and port 4 (P4). Considering to , a

number of properties of the ideal branch line coupler maybe deduced

from the symmetry and unitary properties of its scattering matrix. If the

series and shunt arm are one-quarter wavelength, by using , resulted in

S11 = 0.

As both the even and odd modes of S11 are 0, the values of S11 and

S21 are also 0. The magnitude of the signal at the coupled port is then

the same as that of the input port.

Calculating and under the same , the even and odd modes of

S21 nonuniform branch line coupler will be expressed as follows in

Based on ,S11 can be expressed as follows Following ,

S41 nonuniform branch line coupler can be calculating as follows

From this result, both S31 and S41 nonuniform branch line couplers

have equal magnitudes of ?3dB. Therefore, due to symmetry property,

we also have thatS11=S22=S33=S44=0,S13=S31，S14=S41，S21=S34, and .

Therefore, the nonuniform branch line coupler has the following

scattering matrix in

3. Fabrication and Measurement Result of Wideband Nonuniform

Branch Line Coupler

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To verify the equation, the nonuniform branch line coupler was

implemented and its -parameter was measured. It was integrated on TLY

substrate, which has a thickness of 1.57mm. Figure 4 shows a

photograph of a wideband nonuniform branch line coupler. Each branch

at the series arm comprises an exponentially tapered microstrip line

which transforms the impedance from ohms to ohms. This

impedance transformation has been designed across a discrete step

length mm.

Figure 4:Photograph of a proposed nonuniform branch line coupler.

Figure 5 shows the measured result frequency response of the

novel nonuniform branch line coupler. For a return loss and isolation

better than 10dB, it has a bandwidth of about 61.1%; it extends from 7

to 12.5GHz. In this bandwidth, the coupling ratio varies between 2.6?dB

up to 5.1dB. If the coupling ratio is supposed approximately 3 ± 1dB, the

bandwidth of about 22.2% centered at 9GHz.

Figure 5:Measurement result for nonuniform branch line coupler.

As expected, the phase difference between port 3 (P3) and port 4

(P4) is 90°. At 9?GHz, the phases of and are 85.54° and 171°,

respectively. These values differ from ideal value by

4.54°. The average phase error or phase unbalance between two

branch line coupler outputs is about 3°. But even the phase varies with

frequency; the phase difference is almost constant and very close to

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ideal value of 90° as shown in Figure 6.

Figure 6:Phase characteristic of nonuniform branch line coupler.

4. Design and Fabrication of the Wideband Butler Matrix

Figure 7 shows the basic schematic of the Butler Matrix .

Crossover also known as 0dB couplers is a four-port device and must

provide for a very good matching and isolation, while the transmitted

signal should not be affected. In order to achieve wideband

characteristic crossover, this paper proposes the cascade of two

nonuniform branch line couplers.

Figure 7:Basic schematic of the Butler Matrix .

Figure 8 shows the microstrip layout of the optimized crossover. The

crossover has a frequency bandwidth of 1.3GHz with VSWR = 2, which is

about 22.2% of its centre frequency at 9?GHz. Thus, it is clear from these

results that a nonuniform crossover fulfills most of the required

specifications, as shown in Figure 9.

Figure 8:Photograph of microstrip nonuniform crossover.

Figure 9:Measurement result for nonuniform crossover.

Figure 10 shows the layout of the proposed wideband Butler Matrix.

This matrix uses wideband nonuniform branch line coupler, wideband

nonuniform crossover, and phase-shift transmission lines.

Figure 10:Final layout of the proposed wideband Butler Matrix .

The wideband Butler Matrix was measured using Network Analyzer.

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Figure 11 shows the

simulation and measurement results of insertion loss when a signal

was fed into port 1, port 2, port 3, and port 4, respectively. The insertion

loss are varies between 5dB up to 10dB. For the ideal Butler matrix, it

should be better than 6dB. Imperfection of fabrication could contribute

to reduction of the insertion loss.

Figure 11:Insertion loss of the proposed Butler Matrix when

different ports are fed. The simulated and measured results of the return

loss at each port of the widedend Butler Matrix is shown in Figure 12.

For a return loss better than 10dB, it has a bandwidth about

17% centered at 9.4GHz.

Figure 12:Return loss of the proposed Butler Matrix when different

ports are fed.

Figure 13 shows the phase difference of measured results when a

signal was fed into port 1, port 2, port 3, and port 4, respectively. The

overall phase error was less than 7°. There are several possible reasons

for this phase error. A lot of bends in high frequency can produce phase

error. Moreover, the imperfection of soldering, etching, alignment, and

fastening also could contribute to deviation of the phase error.

Figure 13:Phase difference of the proposed Butler Matrix when

different ports are fed. Table 1 shows that each input port was resulted a

specific linear phase at the output ports. The phase differences each

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between the output ports are of the same value. The phase difference

can generate a different beam ( θ). If port 1 (P1) is excited, the phase

difference was 45°, the direction of generated beam ( θ) will be 14.4° for

1L. It is summarized in Table 1.

Table 1:Output phase difference and estimated direction of

generated beam.

5. Conclusion

A novel nonuniform branch line coupler has been employed to

achieve a wideband characteristic by exponential impedance taper

technique. It is a simple design without needs of using multilayer

technology and this will lead to cost reduction and design simplification.

The scattering matrix of the nonuniform branch line coupler was derived

and it was proved that the nonuniform branch line coupler has equal

magnitude of ?3dB. Moreover, the novel nonuniform branch line coupler

has been employed to achieve a wideband 0dB crossover. Furthermore,

these components have been implemented in the Butler Matrix and that

achieves wideband characteristics.

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宽带非均匀支线耦合器及其应用在宽带巴特勒矩阵的设计与分

析

协作院校：印尼大学新校区电机工程学系天线传播和微波研究小

组（AMRG）。 学校院系；印尼雅加达西部大学，电机

工程学系。

时间： 2011年8月10日-2011年12月2日

学术编辑：Dnney

摘要

本文是对一种新的宽带不均匀分支线耦合器的分析设计。通过在

分支线耦合器中插入指数衰减电阻，以提高带宽。并对非均匀耦合器

进行数学分析，推导出其散射矩阵。此次设计的耦合器中心频率为

9GHz，带宽大于61.1%，回波损耗优于10分贝。 测量耦合程度和相

位具有良好的色散特性。对于1dB的幅度差和相位误差不大于3 时 ，

以9GHz为中心频率，带宽范围达到22.2%。 此外，新的分支线耦合

器还实现了宽带交叉，构建了交叉级联的不均匀分支线耦合器。 并

把这些组件用在9.4 GHz的宽带巴特勒矩阵中。 测量结果表明，在输

出端口的反射系数比在8.0 GHz-9.6GHz 之间18dB的要好很多，整体

的相位误差小于 7 。

1. 介绍

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最近，开关波束天线系统已被广泛使用在许多应用，例如，在移

动通信系统，卫星系统，现代化的多功能雷达。 这是由于开关波束

天线的能力，即减少干扰和提高传输质量，也增加增益和多样性。 交

换束系统组成多波束交换矩阵和天线阵列。 交换束原理是在等功率

阵列天线和相位差信号不断发展的基础上建立的。 不同结构的多波

切换矩阵已经被提出，如Blass的矩阵，的诺伦矩阵，的罗特曼镜头，

巴特勒矩阵。 其中最广为人知的多波束开关与线性天线矩阵是巴特

勒矩阵。 事实上，它似乎是最有吸引力的选择，因为其设计简单，

功耗低。

在一般情况下，巴特勒矩阵是一个N×N被动馈电矩阵，其有分

支线耦合器，交叉和相移器组成。 巴特勒矩阵的带宽是大大依赖组

件的性能。 但是，由于分支线耦合器和交叉有一个有限的带宽，巴

特勒矩阵具有窄带宽的特点。

随着提供高数据吞吐量需求的不断增长，当用于角多样性时，巴

特勒矩阵是必不可少的，这主要利用其工作频带很宽的特性。另外，

许多报纸也报道了大量可以增加带宽分支线耦合器。 设计和实现分

支线耦合多层微带结构，可以实现宽带特性。 然而，这些设计的缺

点是在工作量太大。

一些参考文献介绍了串联连接的N节结构的紧凑耦合器。 这些

设计导致很宽的带宽。 在一个设计中，通过一个椭圆形槽，耦合

两个椭圆形的微带线。 这种设计被用在超宽带耦合器，高回波损耗

和隔离。 然而，这些设计都非常复杂。

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在本文中，用指数阻抗锥设计不均匀的分支线耦合器，可以不仅

能提高带宽，还能实现巴特勒矩阵。如图1所示。 另外，由于它是

一个简单的设计，所以没有使用多层技术， 这降低了设计成本和简

化设计步骤。

图1：一个嵌入了指数衰减阻抗的不均匀分支线耦合器的几何结

构。

对于新设计的分支线耦合器，首先，串联支路阻抗被修改， 并

联支路保持不变。 这样实现了通过修改串联支路，来减少传输线的

宽度的目的。 其次，通过串联支路指数衰减阻抗，实现超高频率的

匹配。

2. 非均匀分支线耦合器的数学分析

建议非均匀分支线耦合器在并联支路中使用阻抗为50Ω的 λ/

4的分支线，在串联支路中使用指数衰减阻抗。如图1 。 由于分支

线耦合器具有对称结构，可以用多模式理论来分析其不均匀性。 四

个端口可以简化为一个双端口的问题，其中的奇数模和偶数模信号为

两线的输入。图2为不均匀分支线耦合器的电路原理图。

图2：不均匀分支线耦合电路。

图2电路可以看成是图3（a）和图3（b）中奇数模和偶数模的

叠加

图3：不均匀分支线耦合器分解成奇数和偶数的激励模式。

用ABCD表示各模式。 在不均匀分支线耦合器的中，奇数和偶

数的模式矩阵表示为：

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当反射很小时，分支线耦合器设计像图1所展示的那样；

其中确定常数a为；

其中L为长度，Zo=Z（0）×ZL=Z（L）

二端口网络参数可转换为奇数模和偶数模之和的形式 可以如

下定义：

其中；

由于这两个端口的入射波的幅度为±1/2，在不均匀的分支线耦

合器的每个端口示：

不均匀的分支线耦合器的奇模和偶模可表示如下：

理想的分支线耦合器反射功率为零，在端口1输入的功率(P1)将

转化成相等得两份在端口3和端口4输出。从上面的等式可以看出，

从理想分支线耦合器的对称性可以求出一些其它的性能。 如果串联

和并联臂是四分之一波长，通过使用上面的等式，可求出 S11= 0。

由于S11的奇数和偶数模式都是0，所以S11和S21也为0.耦合

端的信号幅度与输入端的信号幅度相等。非均匀分支线耦合器的S21

的奇数模和偶数模如下；

同样利用上面的等式可求出S31与S41；

从上面的结果可见，非均匀线性耦合器的S31和S41有相等的幅

度，都为3dB。 因此，由对称性，我们可以得到

S11=S22=S33=S44=0,S13=S31，S14=S41，S21=S34.因此，非均匀线性

耦合器的S矩阵如下；

3.宽带不均匀支线耦合器的制造和测量结果

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为了验证方程，不均匀分支线耦合器需要被应用其S参数也需要

被测量。 它被集成在TLY基板上，其厚度为1.57毫米。 图4是一个

宽带不均匀分支线耦合器的照片。串联支路的每个并联支路包括一个

Zo=50Ω和Zl= 50.6Ω指数衰减微带线.

图4：不均匀分支线耦合器的照片。

图5显示了新设计的不均匀分支线耦合器测量结果的频率响应。

它有一个约61.1％从7到12.5 GHz的带宽，以使回波损耗和隔离度

优于10分贝。在这个带宽里，他的耦合度从5.1dB到 2.6 dB不等。 如

果耦合度要求为3±1分贝，那么以9GHz为中心频率的22.2%频

带范围内都满足这个要求。

图5不均匀分支线耦合的测量结果。

理想情况下，3端口和端口4端口之间的相位差为90°。以9GHz

为中心频率，S31和S41的相位分别是85.54°和171°。 这些值与

理想值相差4.54°。平均相位误差或两个分支线耦合器输出之间的相

位不平衡是3°左右。 但是，相位几乎不随频率变化而变化，非常

接近90°的理想值，如图6所示。

图6：不均匀分支线耦合器的相位特征。

4。 宽带巴特勒矩阵的设计与制作

图7显示的是巴特勒矩阵基本原理。 0 dB耦合器是一个四端口

的设备，当传输的信号不被外界干扰时，它将提供非常好的匹配与隔

离特性。为了实现宽带特性交叉，本文提出了两种不均匀分支线耦合

器的级联方法。

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图7：4×4巴特勒矩阵基本原理。

图8展示的是优化交叉后的不均匀分支线耦合器。 有一个VSWR

为2的交叉耦合器，其频带宽度为

1.3GHz的，为其中心频率的22.2%。 因此，这些结果表明，非

均匀交叉大部分符合要求，如图9所示。

图8：微带非均匀交叉耦合器的照片。

图9：非均匀交叉耦合器测量。

图10是宽带巴特勒矩阵的布局。 这个矩阵使用宽带不均分支线

耦合器，宽带非均匀交叉，传输线相移。

图10：宽带巴特勒矩阵的最终布局. 。

用网络分析仪测量宽带巴特勒矩阵。 图11显示了当一个信号被

送入端口1，端口2，端口3和端口4时，插入损耗的模拟与测量结

果。其插入损耗在5分贝至10分贝内变化。对于理想的巴特勒矩阵，

它应该大于6dB。之所以这样是有助于减少插入损耗。

图11：从不同的端口输入时，巴特勒矩阵的插入损耗。

巴特勒矩阵每个端口的宽带回波损耗模拟与实测结果 如图12

所示。当回波损耗优于10dB时，它有中心频率为9.4GHz的范围约

17%的带宽。

图12：不同的端口输入时，巴特勒矩阵的回波损耗。

图13显示了当一个信号分别被送入端口1，端口2，端口3和端

口4时，测量结果得出别。 整体相位误差小于7°。 产生相位误差

的原因有很多，如， 其他高频干扰产生相位误差。 此外，焊接，蚀

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刻，对齐，并紧固的缺陷，也能产生相位误差。。

图13：不同的端口输入时，巴特勒矩阵的相位差。

表格1显示不同端口输入时，输出端口的线性相位。每个输出端

口有相同的相位差值。 相位差可以产生 θ，如果端口1（P1）输入，

则相位差为45°，产生的θ的方向将是14.4°。各端口θ总结在表1 。

表1：输出相位差估计产生的波束( θ）方向。

5. Conclusion结论

本次设计一种新的非均匀分支线耦合器。它通过嵌入指数衰减电

阻，来实现宽带特性。这是一个简单的设计，它没有使用多层技术，

这大大降低了设计成本并简化了设计。通过对不均匀分支线耦合器散

射矩阵的推导，证明了非均匀分支线耦合器具有相等的幅度，且均为

-3dB。 此外，不均匀分支线耦

合器也已实现了0dB宽带交叉。而且，这些元件已运用与巴特勒

矩阵，实现了宽带。

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