On the development of a new coplanar transmission line based on gap waveguide

2025-05-02 0 0 1.55MB 17 页 10玖币

侵权投诉

C. BIURRUN-QUEL et al.: ON THE DEVELOPMENT OF A NEW COPLANAR TRANSMISISON LINE BASED ON GAP WAVEGUIDE.





Carlos Biurrun-Quel, Student Member, IEEE, Jorge Teniente and Carlos del-Río, Senior Member, IEEE

Abstract— A combination of gap waveguide technology and the

traditional coplanar waveguide is studied in detail and

demonstrated experimentally for the first time. This novel

metamaterial transmission line is presented in three different

configurations and offers a broadband operation, low loss, and low

dispersion characteristics. Analytical expressions for its

characteristic impedance and effective permittivity are provided

and validated by Finite Element Method simulations. The loss and

dispersion of the line are analyzed with an Eigenmode solver. The

proposed line prevents the propagation of substrate modes in the

band of operation at the same time it reduces the dielectric loss in

the line due to a higher concentration of the E-field over the air.

Moreover, its coplanar layout facilitates the integration of active

components. As such, it is considered to constitute a potential key

element in the development of more efficient, millimeter wave

systems.

Index Terms—CPW, electromagnetic band gap, gap waveguide,

metamaterial, millimeter wave and terahertz components and

technologies, on-wafer measurements, periodic structures, planar

transmission lines, sub-millimeter, transmission line theory.

I. I. INTRODUCTION

ICROWAVE engineers have been constantly

pursuing the development of new alternatives for

propagating the electromagnetic fields in the most

advantageous manner for diverse, specific target scenarios. This

everlasting goal is fostered by a continuous demand for

progress due to the emergence of new applications and services,

which may present more stringent requirements that might not

be satisfied by the current technologies. In addition, the

microwave and mmWave parts of the spectrum are increasingly

being filled, which encourages the pursuit for expansion

towards higher, less populated frequency bands. As a result of

this development, a plethora of available technologies have

been proposed during the last century, with the advent of planar

transmission lines [1], [2] and hollow, metallic waveguides, but

specially over the last two decades, with the development of

Substrate Integrated Waveguides [3] and Gap Waveguide

technology with all its different configurations [4][7].

Depending on the targeted application and frequency band,

one may find different challenging aspects when designing a

This work was funded by the FPU Program (FPU18/00013) and PID2019-

109984RB-C43  FRONT-MiliRAD, from the Spanish Ministry of Science and

Innovation (Corresponding author: C. Biurrun-Quel).

C. Biurrun-Quel is with the Antenna Group, Department of Electrical,

Electronic and Communications, and the Institute of Smart Cities, Public

University of Navarra, Pamplona, 31006 Spain. (e-mail:

carlos.biurrun@unavarra.es).

microwave/mmWave circuit in planar technology. For instance,

whereas hollow metallic waveguides present the lowest

attenuations for mmWave frequencies, a planar technology

(typically, coplanar waveguides, CPW) is required for

integrating active devices such as oscillators, (photo)diodes or

transistors. One challenging issue concerning these planar

technologies involve the propagation of substrate modes,

especially when the substrate presents a back metallization

(typically required for mechanical support). These modes incur

in additional loss and become more important when increasing

the frequency of operation. This is mainly because the number

of propagated substrates modes increases with the electrical

thickness of the substrate [8], which imposes a limitation, since

the thickness of commercially available substrates is

constrained by mechanical aspects (found either during their

fabrication or just due to an unfeasible handling).

One way to prevent substrate modes is the inclusion of

metallic vias along the perimeter of the line. This solution,

however, is not applicable to every material. For instance, some

polymers are difficult to drill without compromising the

mechanical stability (drilling holes make the surrounding parts

of the substrate brittle). Other substrates broadly employed in

microelectronics (such as Silicon  Si  or Indium Phosphide 

InP) require complex chemical processes to etch these holes,

increasing the overall costs. Furthermore, the higher the

frequency of operation, the lower the required via separation

and size, which challenges the state-of-the-art CNC machining

techniques. On top of that, these via holes require inner-wall

metallization, a step that might not be feasible for very small

via dimensions, or that may just increase the costs substantially.

In an attempt to overcome these limitations, we presented in

2021 the conceptualization of a new planar transmission line

that combined CPWs with the basic theory of Gap Waveguides

[9]. This line, depicted in Fig. 1 (i), consists of a coplanar

waveguide on a dielectric substrate supported on top of an

artificial magnetic conductor (AMC), which prevents the

propagation of the EM fields inside the substrate below the

conductors. This conceptualization resulted from a natural

correspondence between the traditional transmission lines and

J. Teniente is with the Antenna Group, Department of Electrical, Electronic

and Communications, and the Institute of Smart Cities, Public University of

Navarra, Pamplona, 31006 Spain. (e-mail: jorge.teniente@unavarra.es).

C. del-Río is with the Antenna Group, Department of Electrical, Electronic

and Communications, and the Institute of Smart Cities, Public University of

Navarra, Pamplona, 31006 Spain. (e-mail: carlos@unavarra.es).

Color versions of one or more of the figures in this article are available

online at http://ieeexplore.ieee.org

C. BIURRUN-QUEL et al.: ON THE DEVELOPMENT OF A NEW COPLANAR TRANSMISISON LINE BASED ON GAP WAVEGUIDE.

their gap waveguide counterparts, shown in Fig. 1. The main

      C 

(GapCPW) is that propagation inside the substrate underneath

the coplanar grounds is prevented due to the virtual stopband

created by the PEC/PMC parallel plates. That previous work

also addressed an additional modification to the proposed line,

which consisted of including a metallic encapsulation on top of

the line (Fig. 1 (j)). However, this encapsulation may excite

cavity/parallel-plate modes between the top metallic

encapsulation and the coplanar grounds. For this reason, an

enclosed encapsulation was also proposed and coined as

, Fig. 1 (k), in

clear resemblance to the inverted microstrip gap waveguide [5],

[7], [10]. This encapsulation serves three main purposes. First,

it connects both lateral grounds, preventing the propagation of

the typically undesired slotline odd mode. Secondly, it allows

the EM fields to couple to this metallic encapsulation and to

propagate over the air. Thirdly, it provides an

electromagnetically compatible encapsulation to isolate and

package the circuits, while preventing cavity modes.

The present work aims to shed light onto these new

transmission lines by providing some design rules and

expressions for calculating their impedance, as well as useful

insight into their simulation with commercial software

packages. Moreover, experimental validation of these new

types of transmission lines is also provided for the first time.

The remainder of this manuscript is structured as follows:

Section II reviews the theory and principle of operation behind

the concept of Gap Coplanar Waveguides. Accurate

expressions for the effective permittivity and characteristic

impedance are then provided in Section III, obtained by means

of Conformal Mapping. The values computed with these

expressions will be then compared to the impedance calculated

by Finite Element Method (FEM). Section IV continues

providing useful insight into the design and simulation of these

lines, addressing their simulation with an Eigenmode solver.

Fig. 1. Summary of the typical transmission lines and waveguide-(k) are the ones proposed. E-field lines of the

dominant mode are also plotted for each case. Blank spaces are considered air/vacuum.

  

  

   



 



 

  

  









C. BIURRUN-QUEL et al.: ON THE DEVELOPMENT OF A NEW COPLANAR TRANSMISISON LINE BASED ON GAP WAVEGUIDE.

The analysis is continued in Section V, where a comprehensive

study of the loss in the lines is presented. It must be noted that,

throughout this work, the commercial software ANSYS

Electromagnetics Desktop (traditionally known as HFSS) [11]

has been employed. Nevertheless, any other simulator packages

should be suitable for designing and simulating these

transmission lines accurately. The first experimental validation

of the GapCPW is then presented and discussed

comprehensively in Section VI. Last, the paper is concluded by

discussing the potential applications of the new Gap Coplanar

Waveguides and by sketching some interesting lines of research

to be addressed in the future.

II. THE CONCEPT OF GAP COPLANAR WAVEGUIDES

As previously introduced, the operation principle of every

variation of the Gap Coplanar Waveguide (GapCPW) relies on

the inclusion of a Perfect Magnetic Conductor (AMC/PMC)

below the substrate. Considering both lateral grounds of the

CPW to extend infinitely (or far enough) along the axis

perpendicular to propagation, a PEC/PMC parallel plates region

is created inside the substrate. Following the principles of Gap

Waveguide theory [12], if the gap separating both plates is

lower than a quarter of a wavelength, propagation inside the

parallel plates will not be allowed. In this case the gap, defined

by the thickness of the dielectric substrate (hs) must fulfil (1),

r 0 is the

free-space wavelength.

 

 (1)

Consequently, the TM and TE modes propagating in

grounded substrates [8] are prevented from propagation. In

addition, the microstrip-like mode, found in conductor-backed

coplanar waveguides (also called grounded CPWs) would also

be prevented by the PEC/PMC parallel plates, since this same

condition is fulfilled below the center conductor of the CPW.

As a result, a purer coplanar fundamental (even) mode can be

propagated. Let us now consider the proposed Gap CPW (Fig.

1 (i)). There are two fundamental, quasi-TEM modes, that can

propagate in the structure, namely the   

, which can be excited

at bends and due to manufacturing inaccuracies or asymmetries,

and which propagation is typically undesired. The most

effective way of preventing it consist of ensuring the electrical

connectivity between the two ground planes at the sides. This

can be done by placing air-bridges or wire-bonds [13], which

increase the complexity of the manufacturing process. As an

alternative to these, we suggested the insertion of a metallic

cover on top of the substrate that includes a micro-machined

channel. This would not only prevent the slotline mode from

propagating, but also solve the forthcoming issue regarding the

encapsulation of the line. The resulting is the so-called Inverted

Gap Coplanar Waveguide, represented in Fig. 1 (k). The term

       -like

component in between the central strip and the metallic cover,

with an increasing influence that is inversely proportional to the

height of the channel (i.e. the lower the channel, the higher

interaction between the central conductor and the cover). It

corresponds to a mirrored version of the microstrip-like

component in grounded CPWs, with the fundamental difference

that this component propagates over the air, thus forecasting a

lower propagation loss, as the dielectric losses are minimized.

III. ANALYTICAL EXPRESSIONS FOR BASIC PARAMETERS

Some of the basic parameters of a transmission line, essential

for any designing stage, are the characteristic impedance of the

line, Z0, and its effective permittivity, εeff. It is then crucial to be

able to obtain accurate analytical expressions for such

parameters. Consequently, and, in a similar way to the first

works analyzing the CPW parameters [14][16], we obtained

these expressions by computing the total capacitance per unit

length of the fundamental mode. This traditional analysis is

based on conformal mapping, a technique that introduces a

series of geometrical transformations to the cross-section of the

structure to be analyzed, so that the resulting geometry is that

of a parallel plates line, where the distance between the plates

defines the capacitance. Since the purpose of this section is to

provide some analytical expressions for both the characteristic

impedance and effective permittivity of the line and because the

mapping transformations are already explained and available in

different sources, the transformations will not be discussed here

in detail. This analysis relies on the assumption that the slots in

the coplanar waveguide are modelled as magnetic walls [17] (E-

field being parallel to the magnetic wall, H-field perpendicular

to it). Here, the conductors are treated as infinitely thin sheets.

In a transmission line, the velocity of propagation, vp, and

characteristic impedance are given by the following well known

expressions (2) and (3), where vp and c0 (velocity of propagation

in free space) are related by the effective permittivity of the

medium and L and C are respectively the inductance [H/m] and

capacitance [F/m] per unit length of the line.

 

 (2)



 (3)

Note that a lossless scenario is considered here. After a small

reformulation, it is possible to obtain an expression for Z0

depending exclusively on the capacitance:

 (4)

Here, Ca is the total capacitance per unit length that the line

would have when all dielectric materials are replaced by

vacuum and is related to C by the effective permittivity of the

medium.

  (5)

These expressions can be used in any generalized case of a

transmission line and will be used to provide accurate formulas

for the quasi-TEM, even modes of the lines depicted in Fig. 1

(i) to (k). As it will be seen in the following subsections, the

procedure followed allows to divide the studied region in

smaller, homogeneous regions and calculate their partial

C. BIURRUN-QUEL et al.: ON THE DEVELOPMENT OF A NEW COPLANAR TRANSMISISON LINE BASED ON GAP WAVEGUIDE.

capacitances

A. (Encapsulated) Gap Coplanar Waveguide

The cross-section analyzed in this section is depicted in Fig.

2 (a). A PEC plane is situated at a distance h1 from the substrate,

representing a possible encapsulation. This scenario is

applicable to both Fig. 1 (i) and (j), with the particularity that in

Fig. 1 (i) the distance h1  The remaining design parameters

depicted correspond to substrate height (hs), slot width (s), and

the width of the central conductor (w).

The proposed line resembles that of Fig. 1 (c) in [17], where

a Broadside-Coupled CPW was analyzed. The authors made

use of its symmetry to obtain analytical expressions for the

impedances of both its even and odd modes considering a PEC

(odd) and PMC (even) boundaries. As a result, the expressions

found in [17] for the characteristic impedance of the even mode

represent an equivalent scenario to the one presented in this

section and hence will be reproduced next (Eq. 8 and 9), in

compliance with the nomenclature chosen for our paper.

The line is analyzed by distinguishing two regions, each one

with a different permittivity. Namely, Region 1 includes the part

over the substrate, with relative permittivity of 1, whereas

Region 2 concerns the substrate in between the CPW

metallization and the PMC ground plane, with relative

permittivity εri. The partial capacitances C1,GapCPW and C2,GapCPW

are calculated and added together to obtain the total capacitance

of the line per unit length, CGapCPW. Overall, the partial

capacitance of each region is calculated by:

  

 (6)

   (7)

Where εri is the permittivity of each region and the terms K(k)

and K(k) are respectively the complete elliptic integral of the

first kind with modulus ki and its complement, with the

relationship ki = [1-ki2]1/2. These modules result from the

conformal mapping transformations, to which the reader is

referred to [18] for a more detailed mathematical description.

As provided in [17], the expressions for these modules are:





 (8)





 (9)

The total capacitance can be obtained by introducing (8) and

(9), respectively, in (6) and then applying (7). Unlike in

previous works, the computational challenge involving elliptic

integrals is already overcome by an average CPU, so the

approximations given in [19] for this purpose are no longer

necessary. The characteristic impedance and effective

permittivity are then computed by applying (4) and (5), where

Ca is obtained with Eq. 6 and 7, considering εr as unity. Please

note that the absence of a top PEC plate implies that h1., in

which case (8) would be reduced to (10). The complementary

assumption of hs would not be consistent with the

fundamental constraint already given in (1) and thus will not be

analyzed.





 (10)

B. Inverted Gap Coplanar Waveguide

The cross-section analyzed in this section is depicted in Fig.

2 (b). In this case, a finite-width (wc) metallized shielding is

added on top, defining a channel of height wh. The remaining

parameters depicted are the same as those in Fig. 2 (a).

Following the same procedure, the structure can be divided in

two regions. Region 1 includes the shielded vacuum/air

channel, whereas Region 2 is delimited to the substrate area. It

is seen that Region 2 in both GapCPW and IGCPW are the

same. Thus, it can be concluded that the partial capacitances

will also be the same C2,GapCPW = C2,IGCPW. The remaining task

at this point is to obtain the expression for the partial

capacitance in the shielded channel, C1,IGCPW.

The author of [20] (Chapter 6.3) develops the conformal

mapping method required for calculating the partial capacitance

of the so-     f a

microstrip or coplanar waveguide on top of a dielectric thin film

suspended over a shielded microcavity. This microcavity is

        and

therefore we can employ the same expressions:

 

 (11)

 





 (12)

 

 (13)







 (14)

Please note that the notation β and γ has been kept as in [20]

and do not have a direct relationship with the phase nor the

Fig. 2. Geometry of the proposed lines. (a) Gap Coplanar Waveguide

(GapCPW) with a possible top encapsulation. (b) Inverted Gap Coplanar

Waveguide (IGCPW). Conductor thickness, t, is neglected in the analysis.

























文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

1C.BIURRUN-QUELetal.:ONTHEDEVELOPMENTOFANEWCOPLANARTRANSMISISONLINEBASEDONGAPWAVEGUIDE.*OntheDevelopmentofaNewCoplanarTransmissionLineBasedonGapWaveguideCarlosBiurrun-Quel,StudentMember,IEEE,JorgeTenienteandCarlosdel-Río,SeniorMember,IEEEAbstract—Acombinationofgapwaveguidetechnologyandthetraditional...

展开>> 收起<<

On the development of a new coplanar transmission line based on gap waveguide.pdf

共17页,预览4页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

On the development of a new coplanar transmission line based on gap waveguide

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: