MWCNT驱动的高效微带谐振器设计与特性研究

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本文档主要探讨了"基于多壁碳纳米管(Multiwalled Carbon Nanotube, MWCNT)的高性能微带谐振器"的研究成果，发表在2014年11月的《IEEE Transactions on Nanotechnology》第13卷第6期上。作者们，包括Yi Huang、Lin-Sheng Wu (IEEE会员)、Min Tang (IEEE会员)和Jun-Fa Mao (IEEE Fellow)，共同贡献了一篇深度分析。首先，论文提出了一种半波长的MWCNT微带谐振器设计，并利用半导体传输线模型(Multi-conductor Transmission-Line, MTL)和等效单导体模型(Effective Single Conductor, ESC)对其进行理论预测。MTL模型提供了对谐振频率和品质因数(Q-factor)的精确计算，它不仅能够准确估算共振频率，而且对于Q值的估计也相当精确。然而，尽管ESC模型能大致捕捉到共振频率，但其计算出的Q值精度相对较低。为了实现特定的共振频率，作者强调了根据MTL模型获得的曲线进行几何尺寸选择的重要性。这意味着设计师可以根据实际需求调整谐振器的参数，以达到理想的工作性能。此外，论文还深入研究了MWCNT谐振器的特性，特别是其共振频率与温度的关系，即谐振频率对温度的依赖性。这表明MWCNT作为材料在温度变化下的稳定性能是其高性能的关键因素之一。通过一系列的仿真和实验结果，作者展示了基于MWCNT的谐振器具有显著的优势，包括高Q值、优良的频率响应和潜在的高温稳定性，这些特性使其在微电子、无线通信、传感器和量子计算等领域具有广阔的应用前景。因此，这篇研究不仅深化了我们对碳纳米管在微纳尺度电路中的理解，还为开发高性能、小型化以及能够在极端条件下工作的设备提供了新的可能性。

1240 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 13, NO. 6, NOVEMBER 2014

High-Performance Resonator Based on Multiwalled

Carbon Nanotube (MWCNT)

Yi Huang, Lin-Sheng Wu, Member, IEEE, Min Tang, Member, IEEE, and Jun-Fa Mao, Fellow, IEEE

Abstract—A half-wavelength multiwalled carbon nanotube

(MWCNT) microstrip resonator is proposed and analyzed in

this paper. Its resonant frequency, as well as the correspond-

ing unloaded Q-factors, is predicted by using the multiconductor

transmission-line (MTL) model and the equivalent single conduc-

tor (ESC) model. The MTL model provides an accurate solution for

both the resonant frequency and Q-factors. Although the resonant

frequency can be captured approximately with the ESC model, the

calculated Q-factors are with low accuracy. By properly selecting

the geometric dimensions according to the curves obtained with

the MTL model, MWCNT resonators can be designed easily for

a speciﬁc resonant frequency. Further, the radius-dependent char-

acteristic of temperature drift of the resonator is explored. The

superior performance and potential applications of the MWCNT

resonator are illustrated by numerical results.

Index Terms—Half-wavelength resonator, multiwalled carbon

nanotube (MWCNT), resonant frequency, temperature drift, un-

loaded Q-factor.

I. INTRODUCTION

ARBON nanotubes (CNTs) have excellent mechanical,

thermal, chemical, and electrical properties, which have

been demonstrated by much research since their discovery in

1991 [1]–[4]. Depending on the charity, CNTs can behave

as metallic or semiconducting materials. The semiconducting

CNTs are usually applied in ﬁeld effect transistors (FETs), while

the metallic CNTs are considered to have signiﬁcant potentials

in the interconnection due to their high conductivity and large

current handling capability [5]–[10]. In high-frequency applica-

tions, since the skin effect in CNTs is different from that in free

electron systems, the CNTs have much better conductive per-

formance in comparison with conventional metals. Therefore,

CNTs can potentially be applied for microwave and millimeter-

wave passive components and circuits, such as resonators and

ﬁlters [11]–[13].

In [11], a gigahertz resonator based on a single-walled carbon

nanotube (SWCNT) is presented. Compared with SWCNTs,

multiwalled carbon nanotubes (MWCNTs) are more suitable to

Manuscript received December 2, 2013; revised May 13, 2014; accepted

September 4, 2014. Date of publication September 17, 2014; date of current

version November 6, 2014. This work was supported by the National Science

Foundation of China under Grants 61331004 and 61234001. The review of this

paper was arranged by Associated Editor L. Dong.

The authors are with the Key Laboratory of Ministry of Education of

Design and Electromagnetic Compatibility of High-Speed Electronic Sys-

tems, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail:

huangyi103@sjtu.edu.cn; wallish@sjtu.edu.cn; tm222@sjtu.edu.cn; jfmao@

sjtu.edu.cn).

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

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TNANO.2014.2358641

build up resonators because MWCNTs have much more con-

ducting channels. Furthermore, since the MWCNTs have many

large-diameter shells, they have relatively long mean free paths

[14], [15] and even the semiconducting shells can be conduc-

tive [16]. Thus, the conducting performance of the MWCNT

is better than the SWCNT bundle with the same geometry,

which leads to less power dissipation in MWCNT resonators.

As a consequence, the unloaded Q-factor of an MWCNT res-

onator is expected to be higher than that of an SWCNT one.

A half-wavelength microstrip resonator based on an array of

MWCNTs, with high unloaded Q-factor, has been proposed and

simply characterized by the authors [13]. In [13], the MWCNT

is considered as a parallel connection of CNT shells, where the

couplings between the shells are ignored. The resonator perfor-

mance is roughly estimated under such an assumption.

Although the MWCNT consists of an array of concentric

rolled graphene layers, it is not a simple combination of par-

allel shells in circuit modeling due to the existence of mutual

inductances and electrostatic capacitance among them. In re-

cent years, several modeling approaches have been proposed

to analyze MWCNTs, such as the equivalent single conductor

(ESC) model and the multiconductor transmission-line (MTL)

model [17]–[19]. The ESC model is based on the assumption

that the voltages at arbitrary cross section of the MWCNT are

with the same value when it is excited in common mode conﬁg-

uration. With the ESC model, the MWCNT is governed by the

simpliﬁed equations of a single transmission line. Therefore, the

computational complexity is reduced signiﬁcantly and the fast

simulation of the MWCNT becomes possible. As demonstrated

in [19], the ESC model is accurate when applied for intercon-

nects. However, for the MWCNT resonator, it is important to

obtain the current distribution on the shells for the performance

characterization, where the MTL method is more suitable.

In this paper, a half-wavelength microstrip MWCNT res-

onator is designed and its performance is carefully analyzed.

In Section II, the equivalent circuit of the MWCNT resonator

is given; the resonant frequency, as well as the corresponding

Q-factors, is calculated and compared with the ESC and MTL

models. In Section III, different kinds of power dissipation in

the MWCNT resonator are evaluated in detail with the MTL

model and the Q-factors of the proposed resonator are derived. In

Section IV, the effect of the temperature drift is further investi-

gated. A short conclusion is drawn in Section V.

II. C

IRCUIT MODEL OF MWCNT RESONATOR

AT HIGH FREQUENCIES

The conﬁguration of a half-wavelength MWCNT microstrip

resonator is shown in Fig. 1. A single MWCNT is placed on the

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