design and application of composite right/left-handed transmission line based on complementary...

Design and Application of CompositeRight/Left-Handed Transmission Line Based onComplementary Meander Archimedean SpiralResonator

Ke Lu, Guang-ming Wang, Ya-wei Wang, Hui-yong Zeng

Missile Institute, Air Force Engineering University, Sanyuan 713800, China

Received 28 April 2011; accepted 4 August 2011

ABSTRACT: A novel composite right/left-handed transmission line based on the comple-

mentary meander Archimedean spiral resonator (CMASR) is proposed and investigated in

detail. The composite property of the proposed structure is demonstrated and the right-

handed frequency band is initially pointed out for the structure derived from the comple-

mentary Archimedean spiral resonator (CASR). One modified method of extracting the

lumped elements based on the analytical analysis is proposed to investigate the equivalent

circuit model. The results indicate that this method can accelerate the extracting process

effectively and the circuit model using the extracted elements can predict the property of

the given structure excellently. Then, the influence of primary geometrical parameters is

investigated through the parametric analysis, which provides the directive guideline. When

compared with CASR, CMASR can lower the operating frequency further with keeping the

effective area roughly constant. To explore and validate the composite property, one broad-

band bandpass filter is designed through tuning the left- and right-handed frequency bands

into the quasi-balance condition. The measured results indicate that the fractional band-

width is about 88.3%. VC 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 00:000–000,

2012.

Keywords: complementary meander Archimedean spiral resonator; composite right/left-handed

transmission line; broadband bandpass filter

I. INTRODUCTION

The composite right/left-handed transmission line is a type

of one-dimensional metamaterial, which is the special for-

mation of the bulk left-handed media. This concept is pri-

marily utilized to design the microwave components with

the modified performance, such as phase shifter, branch

coupler, and leaky-wave antenna [1–3]. In the variety of

realized the composite right/left-handed transmission line,

the microstrip prototype composed of series gap on the con-

ducting strip and the complementary split rings resonators

have been investigated thoroughly, whereas the correspond-

ing equivalent circuit model and analytical theory have

been proposed to explain the operation principle [4–6].

Because of the composite property, there are two passbands

for this composite right/left-handed transmission line, one

at the lower frequency band with the backward wave prop-

erty, namely the left-handed behavior and the other at the

higher frequency band with forward wave (right-handed)

behavior, which is derived from the parasitic elements of

the host line. Then, the given left-handed, right-handed

passbands and the passband of the second resonance were

integrated together to get ultra wide passband through intro-

ducing additional grounded stubs [6, 7]. Moreover, the

given structures have been applied to miniaturize the power

dividers [8]. The complementary split rings improved with

fractal geometries have been proposed to get the miniaturi-

zation of the metamaterial cells [9]. In Refs. [10, 11], one

novel compact metamaterial cell, the complementary Archi-

medean spiral resonator (CASR) was proposed. This cell

was utilized to replace the complementary split rings reso-

nator to synthesis the left-handed transmission line, which

opens a new door to design the composite right/left-handed

transmission line. The total attention in Ref. [10] was

Correspondence to: K. Lu; e-mail: [email protected]

VC 2012 Wiley Periodicals, Inc.

DOI 10.1002/mmce.20571Published online in Wiley Online Library

(wileyonlinelibrary.com).

1

focused on the left-handed passband while the influence of

the geometrical parameters and the right-handed frequency

band were not included. Recently, one novel transmission

line with two composite right/left-handed passbands has

been proposed in Ref. [12].

In this article, one improved version of CASR, the

complementary meander Archimedean spiral resonator

(CMASR) is proposed and investigated. CMASR is real-

ized through meandering CASR with the sine. The mean-

der Archimedean spiral has been applied to design the

miniaturized antennas due to its special geometrical pat-

tern [13, 14]. Moreover, it is demonstrated that the proto-

type based on CMASR satisfies the long-wavelength limit

so that the given prototype has very compact dimension.

Through extracting the phased constant, the composite

property of the given structure composed of series gap

and CMASR is demonstrated. It is demonstrated that

CMASR may be the only effective method to lower the

operating frequency of CASR. Then, the parametric analy-

sis of the primary geometrical parameters of CMASR is

implemented, and the tuning rules to accelerate the design

process are achieved. To verify the above analysis, one

broadband bandpass filter is designed through adjusting

the left and right-handed frequency bands into the quasi-

balance condition. After optimization, one prototype is

fabricated and measured. The measured result indicates

that the lower and higher cutoff frequencies of the pass-

band are 1.48 and 3.75 GHz, respectively. Thus, the frac-

tional bandwidth of 88.3% has been achieved.

II. PROPERTY OF THE PROPOSED STRUCTURE ANDEQUIVALENT CIRCUIT MODEL

A. The Characteristic of the Proposed StructureFigure 1 shows the initial layout of the proposed structure,

which is composed of a bifilar meander Archimedean spi-

ral resonator etched in the ground plane underneath the

microstrip line and the series gap on the conducting strip.

The single meander Archimedean spiral can be defined by

Eq. (1) in the polar coordinate.

r ¼ r0 þ a/nþm � ðð/� /stÞ=ð/end � /stÞÞ � sinðk/Þ ð1Þ

where the given meander Archimedean spiral is achieved

by inserting sinusoidal function into Archimedean func-

tion. In (1), r0 is the original radius of the spiral line

which is usually set to zero, a is the scale factor, and u is

the winding angle, rising from the starting angle ust to the

ending angle uend. ust is always set to 0 rad. In addition,

m and k are the amplitude and the period of the sinusoidal

wave, respectively. Furthermore, n denotes the constant

determining how tightly the spiral is wrapped, which is

always set to 1 for simplicity. In principle, the Archime-

dean spiral is the special case that m is equal to zero in

Eq. (1). The width of the meander Archimedean spiral

arm is denoted as spwidth. Another arm can be achieved

through rotating the abovementioned single spiral arm by

180�. What is more, the width of the series gap on the

conducting strip is represented by sgap.The geometrical parameters of the initial prototype are

listed in Table I. The substrate with relative dielectric

constant of 2.2 and thickness of 1.5 mm is utilized in both

simulation and fabrication. The given prototype is simu-

lated with HFSS and the results are shown in Figure 2. It

is seen that the given prototype exhibits two passbands in

the given frequency range while the passband at the lower

frequency range is represented by band1 and the other

passband at higher frequency range is donated to band2.

At the lower frequency range, there is one transmission

Figure 1 Layout of the proposed structure. The black color

denotes the conducting strip, the brown color denotes the ground

plane and the white color represents the etched pattern on the

ground plane. ‘‘w1’’ denotes the width of the 50-X microstrip line

while ‘‘w2’’ represents the width of the complementary meander

Archimedean spiral resonator. [Color figure can be viewed in the

online issue, which is available at wileyonlinelibrary.com.]

TABLE I Summary of the Geometrical Parameters ofthe Initial Prototype

a ust uend m k spwidth sgap

0.8 0 4p 1.2 20 1.2 mm 1 mm

Figure 2 Fullwave simulated S parameters of the initial proto-

type. [Color figure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

2 Lu et al.

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 000, No. 000, Month 2012

zero (ft) at the frequency of 0.5 GHz and w2 of the initial

prototype is 22.5 mm.

First, it is necessary to determine whether the proposed

prototype satisfies the long-wavelength limit, which is

necessary for the investigation of metamaterial [15]. The

effective dielectric permittivity of the proposed is calcu-

lated using Eq. (2) given in Ref. [16].

ee ¼ er þ 1

2þ er � 1

2ð1þ 12

h

w1Þ�1

2w1

h�1 (2)

where h is the thickness of the substrate. The calculated

effective dielectric permittivity is equal to 1.87 and the

wavelength at the center frequency of the passband, 0.9

GHz is 243.7 mm. It is seen that w2 ¼ 22.5 mm is smaller

than one-tenth of 243.7 mm. To understand the propaga-

tion characteristics of the given unit, the phase constant bis extracted using Eq. (3). This equation is obtained from

the relation of the phase constant and the ABCD matrix

of the unit cell given in Ref. [17], integrating with the

associations of the ABCD and S matrices.

bd ¼ cos�1ð1� S11S22 þ S21S122S21

Þ (3)

where d is the length of the unit cell, which is constant in

this case.

As shown in Figure 3, it is seen that, within the fre-

quency band from 0.85 to 1.25 GHz, approximately corre-

sponding to the band1 depicted in the Figure 2, the phase

constant is negative, which means that the propagation is

backward and the left-handed effect occurs in the given

frequency band. Simultaneously, the phase constant in the

higher frequency band from 1.7 to 2.5 GHz is positive.

The positive phase constant indicates that the propagation

is forward and right-handed. Thus, the proposed structure

exhibits the composite right/left-handed effect.

B. Equivalent Circuit ModelThen, the equivalent circuit model of the proposed proto-

type is presented in Figure 4 with the aim of describing

the primary operating principle explicitly. According to

the analysis implemented in Section II.A, the given proto-

type satisfies the long-wavelength limit, so that it can be

described by the lumped element circuit model. The simi-

lar circuit model is also utilized in Ref. [10] to describe

the backward wave microstrip line based on CASR.

In this model, L denotes the microstrip line inductance

while Cg denotes the gap capacitance and Cc is the cou-

pling capacitance between the line and the CMASR.

CMASR is described by one shunt LC resonator com-

posed of Cc and Lc. As referred in Refs. [4–6], four differ-

ent characteristic frequencies listed as follows can be

derived from this equivalent circuit model:

wt ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLrðCC þ CrÞ

p (4)

wL ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLrðCr þ 4

1Cgþ 4

Cc

Þq (5)

wH ¼ 1ffiffiffiffiffiffiffiffiffiLrCr

p (6)

wc ¼ 1ffiffiffiffiffiffiffiffiLCg

p (7)

wt represented the frequency of the transmission zero,

which can be obtained directly from the curve of S21. Thefrequency range limited by wL and wH is the left-handed

band and wH is also the intrinsic resonant frequency of

CMASR. Moreover, wc denotes the starting frequency

point of right-handed band, and this frequency is defined

by the cut-off frequency of the high-pass structure solely

formed by L and Cg. The given circuit model can describe

the left-handed frequency band more effectively, because

three characteristic frequencies are related with the left-

handed band. However, only wc is utilized to describe the

right-handed band. In fact, the given circuit model is ca-

pable of providing sufficient guidelines to tune the left-

handed and right-handed bands. Next, the values of the

lumped-elements should be extracted to describe the per-

formance of the initial prototype accurately. The curve-fit-

ting method utilized in the previous articles always suffers

from the tedious tuning process and the extreme extracted

Figure 4 Equivalent circuit model of the proposed prototype.

Figure 3 Extracted phase constant of the proposed prototype.

‘‘lhb’’ denotes the left-handed frequency band while ‘‘rhb’’ repre-

sents the right-handed frequency band. [Color figure can be

viewed in the online issue, which is available at

wileyonlinelibrary.com.]

Composite Right/Left-Handed Transmission Line 3

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

values of the lumped elements, because this method is

pure mathematical approach with the practical limitations

ignored. In this article, one modified method is proposed

to accelerate the extraction process and help to get the

appropriate values satisfying the practical limitation.

In view of the proposed circuit model, the series and

shunt impedances of this circuit model can be expressed

in the Eqs. (8) and (9), respectively.

ZS ¼ 1

jw2Cg

þ jwL

2(8)

ZP ¼ 1

jwCC

þjwLrjwCr

jwLr þ 1jwCr

(9)

The series and shunt impedance can satisfy the condition

as shown in the Eq. (10) at the special frequency, wp/2.

Zpðjwp=2Þ ¼ �Zsðjwp=2Þ (10)

According to the T-network property, at this frequency,

the phase of the transmission coefficient is equal to 90�,namely, U(S21) ¼ p/2. wp/2 can be directly determined

from the phase shift performance. For the initial proto-

type, this frequency is about 1.25 GHz. Then, the Eqs. (4)

and (6) are rewritten as shown in Eqs. (11) and (12).

Lr ¼ðwH

wtÞ � 1

ðwHÞ21

CC

(11)

Cr ¼ CC

ðwH

wtÞ2 � 1

(12)

Then, the corresponding items in the Eqs. (9) and (10) are

substituted with the Eqs. (11) and (12), respectively. One

simplified expression can be achieved as shown in Eq.

(13).

1

jwp=2CC

þ 1

jwp=2CC

Q ¼ �ZSðwp=2Þ ðw2H�w2

t Þw2p=2

ðw2Hþw2

t Þw2t

¼ Q

(13)

Thus, Cc can be expressed as follows:

CC ¼ jð1þ QÞwp=2:ZSðwp=2Þ (14)

In addition, there is the analytical equation for Cg, but it

is only able to provide an approximate value which is

good starting point for optimization. The value of Lderived from the transmission line calculator is also in

approximation. Simultaneously, wH can be roughly limited

within one narrow frequency band according to the simu-

lated S21. Therefore, the minor adjustment of Cg, L, andwH is necessary. When Cg, L, and wH are determined, the

four characteristic frequencies and the other lumped ele-

ments can be calculated using the above equations. In

general, the adjustment process is quite effective and

Figure 5 Comparison of the full-wave simulated and the circuit

simulated results for the initial prototype proposed in Section A.

[Color figure can be viewed in the online issue, which is avail-

able at wileyonlinelibrary.com.]


simulated results for the prototype in case 2. The parameters

which are different from the ones of the initial prototype are pre-

sented in the inset. [Color figure can be viewed in the online

issue, which is available at wileyonlinelibrary.com.]


simulated results for the prototype in case 3. In this case, the se-

ries gap is replaced with the interdigital capacitance with 10 fin-

gers. [Color figure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

4 Lu et al.


convenient. To demonstrate that the given modal is gen-

eral and valid with firm evidence, the extraction process

aimed at three different prototypes is implemented. The

full-wave simulated results and the circuit simulated

results are compared in Figures 5–7, respectively. In these

figures, ‘‘cms’’ denotes the circuit model simulation and

‘‘fws’’ denotes the fullwave simulation. The extracted

results and the four characteristic frequencies are listed in

Tables II and III, respectively.

It is seen that, within the given frequency range, the

fullwave simulated results agree well with the circuit

simulated ones in all the cases. Especially, the four char-

acteristic frequencies describe the fullwave simulated

results excellently. Thus, the validity of the circuit model

and the proposed modified method is verified. It should be

noted that the given circuit model fails in the frequency

band over wc. This is the intrinsic limitations of the given

circuit model, because long-wavelength limit is not satis-

fied within the frequency band over wc. Some directive

guidelines can be obtained by using the circuit model. For

example, as shown in Tables II and III, the interdigital ca-

pacitance can lead to the increase of Cg and the left-

handed frequency band is closer to the right-handed fre-

quency band. Hence, it is potentially possible to achieve

broadband passband using CRHLTL based on CMASR.

III. INFLUENCE OF THE GEOMETRICAL PARAMETERS

When compared with CSRR, CASR can lower the operat-

ing frequency of the backward microstrip line greatly,

thanks to its intrinsic convoluted geometry [10]. If lower

operating frequency is required, the method utilizing frac-

tal geometries proposed in Ref. [9] is not very suitable for

CASR. First, the fractal geometries are not easy to model

and adjust in the electromagnetic software, because the

fractal geometries cannot be expressed by the analytical

equations. Moreover, for CMAR, its inner area is occu-

pied and the space between adjacent rings is quite limited.

Thus, the fractal geometries are difficult and complicated

to apply for CASR. In contrast, the proposed CMASR can

be modeled using the analytical equation, which will

surely facilitate the further investigation. Simultaneously,

the meander geometry can also elongate the electrical

length of the given resonator and lower the resonant fre-

quency as the fractal geometries. Thus, it is concluded

that CMASR is possibly the only effective method to

lower the resonant frequency of CASR. To demonstrate

the above effect, two different CRHLTLs are compared

and these two prototypes are loaded with CASR and

CMASR, respectively. Except m and k, other geometrical

parameters of these two prototypes are identical. The

simulated results are depicted in Figure 8.

As shown in Figure 8, the operating frequency of com-

posite right/left-handed transmission line (CRLHTL)

loaded with CMASR is lower than the one of CRLHTL

loaded with CASR �900 MHz. It means that the meander

geometry can lower the operating frequency to great

extent. Thus, the component based on CMASR is more

applicable in the low frequency band. To investigate

CRHL based on CMASR further, the parametric analysis

TABLE II Summary of the Extracted Lumped Elements

Cc (pF) Cg (pF) Cr (pF) L (nH) Lr (nH)

Case1 17.81 1.49 3.85 2.82 4.67

Case2 21.52 1.86 3.62 4.19 6.29

Case3 12.70 2.06 8.24 4.24 1.20

TABLE III Summary of the Four CharacteristicFrequencies

ft (GHz) fL (GHz) fH (GHz) fC (GHz)

Case1 0.500 0.806 1.185 2.451

Case2 0.400 0.662 1.053 1.800

Case3 1.000 1.257 1.594 1.700

Figure 8 Comparison of the fullwave-simulated S21 of

CRHLTLs loaded with CMSAR and CASR, respectively. For

CMASR, the geometrical parameters are as follows: a ¼ 0.8,

uend ¼ 2pm ¼ 0.8, k ¼ 16, spwidth ¼ 1.2 mm, sgap ¼ 1mm.

[Color figure can be viewed in the online issue, which is avail-

able at wileyonlinelibrary.com.]

Figure 9 Variation of the fullwave-simulated S parameters ver-

sus m. The other geometrical parameters are as follows: a ¼ 1,

uend ¼ 3p, k ¼ 20, spwidth ¼ 1.2 mm, sgap ¼ 1 mm. [Color figure

can be viewed in the online issue, which is available at




of the geometrical parameters is implemented. It is found

that two geometrical parameters, the period of the sinusoi-

dal wave-k and the width of the meander Archimedean

spiral arm-spwidth influence the frequency response to

small extent. For simplicity, the given results are not

depicted in detail, whereas the amplitude of the sinusoidal

wave-m and the ending angle-uend have great effect on

the frequency response. The parametric analysis of these

two parameters is depicted in Figures 9 and 10,

respectively.

As depicted in Figure 9, the increase of m makes the

passband move downward while other properties approxi-

mately remain unchanged, because the increased m elon-

gates the physical length of CMASR and the resonant fre-

quency moves downwards. Moreover, it should be noted

that this parameter is limited by the special geometry of

CMASR and it cannot be very high in practice. Thus, it

should be used to tune the frequency response in rela-

tively narrow range. Moreover, as shown in Figure 10, the

increase of uend will lower the passband to great extent.

Simultaneously, the bandwidth of the left-handed pass-

band is widened with the decrease of uend. Through the

above parametric analysis, the effective design guideline

to design the prototype satisfying the special requirement

is achieved which will accelerate the design procedure.

IV. DESIGN OF THE BROADBAND BANDPASS FILTER

In order to explore the composite right/left-handed prop-

erty of the proposed prototype, one broadband bandpass

filter is designed. In general, the given broad passband is

obtained through making the left-handed and right-handed

passband get close enough, namely tuning these two bands

into the quasi-balance condition. The conclusion derived

from the equivalent circuit model analysis in section 2.2

indicates that the right-handed frequency band can be

tuned by Cg and the increased Cg can be realized by

replacing the series gap with the interdigital capacitance.

On the other hand, the left-handed frequency band can be

controlled by the amplitude of the sinusoidal wave-m or

the ending angle-uend according to the parametric analysis

in Section III. As pointed out in Ref. [18], the accurate

derivation of the structure physical parameters from the

circuit element is complicated or even impossible. Thus,

the above conclusions just provide some directive guide-

line to get the required property while further optimization

is necessary. Under the given directive guidelines, the tun-

ing process is quite effective and the applicable filter per-

formance is achieved successfully. In order to validate the

above analysis, the given bandpass filter is fabricated and

measured. Photograph of the fabricated prototype is shown

in Figure 11. The prototype was measured using Anritsu

ME7808A vector network analyzer while the simulated

and measured results are shown in Figure 12.

As depicted in the Figure 12, the simulated and meas-

ured results agree well, especially in the lower frequency

band. The measured S11 in the passband deteriorates to

some extent due to the fabrication inaccuracy. Moreover,

the lower and higher cutoff frequencies of the passband

Figure 10 Variation of the fullwave-simulated S21 versus uend.The other geometrical parameters are as follows: a ¼ 1, m ¼ 0.5, k¼ 20, spwidth ¼ 1.2 mm, sgap ¼ 1 mm. [Color figure can be viewed

in the online issue, which is available at wileyonlinelibrary.com.]

Figure 11 Photographs of the fabricated broadband bandpass fil-

ter. (a) Front side and (b) back side. [Color figure can be viewed in

the online issue, which is available at wileyonlinelibrary.com.]

Figure 12 Simulated and measured S parameters of the fabri-

cated prototype. ‘‘SIM’’ denotes the simulated results while

‘‘MEA’’ represents the measured results. [Color figure can be

viewed in the online issue, which is available at


6 Lu et al.


are 1.48 and 3.75GHz, respectively. Thus, the fractional

bandwidth of 88.3% is achieved.

V. CONCLUSIONS

In this article, a novel composite right/left-handed transmis-

sion line based on the CMASR is proposed and investigated.

The composite property is demonstrated through extracting

the phase constant. One modified method of extracting the

lumped elements in the equivalent circuit model is proposed.

When compared with the CASR, CMASR can further lower

the operating frequency. Then, the parametric analysis of the

primary geometrical parameters is implemented to get the

design guideline. Through tuning the left-handed and right-

handed frequency bands into the quasi-balance condition, the

broadband bandpass characteristic has been achieved. One

broadband passband filter is fabricated and measured, and

good passband property is achieved. This structure will be

applied to design microwave components operating within

the low frequency band.

ACKNOWLEDGMENT

This work is supported by the National Natural Science

Foundation of China under Grant Nos. 60971118. The

authors thank the China North Electronic Engineering

Research Institute for the fabrication.

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BIOGRAPHIES

Ke Lu received the B.S. degree in

electrical engineering and M.S. degree

in the communication and information

systems in 2006 and 2009, respec-

tively, from the Air Force Engineering

University, where he is currently

working toward the Ph.D. degree. His

research interests include the design

and application of metamaterials.

Guang-Ming Wang received his BS

and MS degrees from the Missile

institute of Air Force Engineering

University, Xi’an, China, in 1982

and 1990, respectively, and his PhD

degree from the electronic science

and technology university, Chengdu,

China, in 1994. Then, He joined the

Air Force Engineering University as a professor in 2000

and is now the head of the Microwave Laboratory center

in it. His current interests include microwave circuits

based on metamaterials, antennas and propagation.



Ya-Wei Wang received the B.S.

degree in electrical engineering and

M.S. degree in the microwave project

in 2008 and 2011, respectively, from

the Air Force Engineering University,

where he is currently working toward

the Ph.D. degree. His focuses on the

design of the ultra-wide band antenna.

Hui-yong Zeng received the B.S.

degree in electrical engineering and

M.S. degree in the microwave project in

2007 and 2010, respectively, from the

Air Force Engineering University, where

he is currently working toward the Ph.D.

degree. His research interests include the

design of the novel metamaterial.

8 Lu et al.


design and application of composite right/left-handed transmission line based on complementary...

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