Broadband and low-loss composite
right/left-handed transmission line based on
broadside-coupled lines
Xin Xu, Magnus Karlsson and Shaofang Gong
The self-archived postprint version of this journal article is available at Linköping University Institutional Repository (DiVA):
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-159130
N.B.: When citing this work, cite the original publication.
Xu, X., Karlsson, M., Gong, S., (2019), Broadband and low-loss composite right/left-handed transmission line based on broadside-coupled lines, International Journal of RF and Microwave Computer-Aided Engineering, 29(8), e21763. https://doi.org/10.1002/mmce.21763
Original publication available at:
https://doi.org/10.1002/mmce.21763
Copyright: Wiley
Broadband and Low-Loss Composite Right/Left-Handed Transmission
Line Based on Broadside-Coupled Lines
Xin Xu1, Magnus Karlsson2 and Shaofang Gong2
1 School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2 Department of Science and Technology ITN, Linköping University, S-601 74 Norrköping, Sweden
Correspondence
School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Email: xindereck0512@uestc.edu.cn; xindereck0512@163.com
Abstract
A novel composite right/left-handed (CRLH) transmission line (TL) structure is proposed and investigated. This structure consists of a pair of broadside-coupled lines and a shorted stub. First, its fundamental characteristics and the relation between its electrical parameters and bandwidth are studied utilizing the TL theory. Then, closed-form design equations with flexible parameter selection are given. Finally, several microstrip implementations of the proposed structure are developed to verify our theoretical results. It is shown that the proposed structure can achieve a very wide left-handed (LH) and right-left-handed (RH) bandwidth with low insertion loss and low return loss.
Keyword -Composite right/left handed (CRLH) transmission line (TL), metamaterial, broadside-coupled line, boadband, low-loss.
I. INTRODUCTION
Metamaterials are artificial structures which exhibit negative permittivity ε and permeability µ having completely different electromagnetic characteristics as compared to conventional material. Thus, metamaterials, which are commonly referred to left-handed (LH) materials, have been given extensive attention in recent years. Early in
1960s, the Russian physicist Veselago theoretically investigated the electrodynamics of a medium with negative values of permittivity and permeability [1]. He called this type of materials LH medium since the phase and group velocities are antiparallel, which results in counterintuitive phenomena concerning Snell’s Law, the Doppler effect, and the Vavilov Cerenkov effect, etc. The experimental verification of LH materials was first demonstrated in [2] and [3] utilizing metallic wires to attain negative permittivity ε and an array of split ring resonators (SRRs) [4] to achieve negative permeability µ. Since then many studies have been conducted to demonstrate the characteristics of LH materials based on SRRs [5]-[9]. However, because of their 3-D constructions, the metamaterials utilizing SRRs are difficult to be utilized in microwave systems. Moreover, they consist of weakly coupled units which results in high loss, while achieving negative ε and µ only in a narrow bandwidth. Later on, researchers come to realize that metamaterials can be achieved using a transmission line (TL) approach [10]-[15]. However, due to the parasitic parameters introduced by TLs, a purely homogeneous LH-TL is difficult to find. Normally, the material parameters of any LH-TL change from negative to positive as the frequency increases, which shows a combination of RH- and LH-TL. This spawns the concept of CRLH-TL [16]. Since then, the unique properties of the CRLH-TL have been applied in practical applications such as wideband/dual-band couplers [17]-[19], filters [20]-[22], broadband phase shifters [23]-[25] and antennas [26]-[28].
One convenient way to realize CRLH-TL is using lumped-element components such as surface- mount technology (SMT) components because they are readily available and can achieve large values of inductance and capacitance. However, due to the parasitic parameters introduced by SMT components, they can only be used at low frequencies. Furthermore, the discrete values of SMT components make them not available at arbitrary frequencies.
As the frequency increases, other structures and technologies should be applied. Distributed components can realize continuous values to meet specific requirements of high operating frequencies. In [29]-[31], the authors proposed a CRLH TL unit cell topology based on the lattice network. Another solution is the utilization of coupled-lines as unit cell elements [32]-[35]. They take advantage of the even- and odd-mode of the coupled-lines to provide the reactances of the CRLH-TL unit cell.
In this paper, we present a new type of CRLH-TL that is composed of broadside-coupled lines and a shorted stub with improved bandwidth and low insertion loss. The proposed structure does not use any lumped-element component to synthesize the required material parameters, enabling high operating frequency with low insertion loss. Moreover, the broadside-coupled lines show the advantage in expanding the bandwidth. The new CRLH-TL is very suitable for microwave and even millimeter-wave applications.
II. PROPOSED STRUCTURE AND ANALYSIS A. Proposed Unit Cell and Basic CRLH-TL Theory
The unit cell of the proposed CRLH-TL is presented in Fig. 1(a). A pair of broadside-coupled lines introduce the series inductance LR and capacitance CL as well as the shunt capacitance CR. The shunt inductance LL is brought in by a shorted stub. LR and CR are the RH elements and LL and CL are the LH elements. The equivalent circuit of the unit cell is shown in Fig. 1(b) and the CRLH elements are derived as
CL =Cp / 2 (1a) CR =2Cpg +2Cg (1b) L s L = (1c) L 2 R p L = L (1d) where Cp and Lp correspond to the capacitance and inductance of the broadside-coupled lines and Ls is the inductance of shorted stub. Note that the equivalent circuit here contains two additional capacitances, Cpg corresponding to the grounded capacitance of the top layer of the broadside-coupled line, and Cg of the bottom layer of the broadside-coupled line to the ground. Thus, Cpg can be rewritten as
Cpg pg p g C C C = + (2) For simplicity, only the lossless case is considered. The expression of propagation
(a)
(b)
Fig. 1. Proposed CRLH-TL unit cell with broadside-coupled lines and a shorted stub. (a) Schematic. (b) Equivalent circuit model.
( ) 1 1 ( R )( R ) L L s L C z C L ω β ω ω ω ω = − − ∆ (3) where ∆z is the incremental length and
1 2 1 min( , ) ( ) 1 max( , ) t se sh t se sh s ω ω ω ω ω ω ω ω ω − < = = > = (4) ωse and ωsh are the series and shunt resonance frequencies
1 1 , se sh R L R L L C C L ω = ω = (5) The expressions above show that a stopband occurs in the frequency range from ωt1 to ωt2 because β is imaginary. If ωt1 and ωt2 are the same, i.e. LRCL = CRLL, this condition is called balanced case, and the stopband reduces to a single frequency
0
1 1
R L R L
L C C L
ω = = (6) Thus, the characteristic impedance of the balanced CRLH-TL is
0 L R L R L R L L Z Z Z C C = = = = (7) where ZL and ZR are the LH and RH characteristic impedances, respectively.
(a)
(b)
Fig. 2. Equivalent circuit of a balanced CRLH-TL unit cell. (a) LH part. (b) RH part. B. Transmission Characteristics Analysis
The previous description has shown that the transition frequency ω0 acts as the
dividing point of the LH and RH range of the CRLH-TL, and the practical performance of them is determined by the values of LR, CR, LL and CL .
The equivalent circuit of a balanced CRLH-TL unit cell can be divided into LH and RH parts as shown in Fig. 2. The LH part is a highpass filter with a transmission pole located at 1 2 2 0 1 p LD C Z Z ω = − (8) where ZLD is the load impedance. Equation (8) indicates that ω1 exists only when Z0 is
larger than ZLD otherwise ω1 is infinity or imaginary, and it moves toward a low
poles located at 2 2 2 2 2 2 2 2,3 2 4 ( 2 ) ( ) 2 g p g p g p pg pg g pg pg LD LD LD g p pg C L C L C L C C C C C Z Z Z C L C ω + − ± + − = (9)
Note that (9) is too complicated to find the relation between RH parameters directly. However, we may consider Cpg = Cg for simplicity, so ω2 and ω3 will then be
2 1 g p C L ω = (10a) 2 0 2 3 2 2 LD g p Z Z C L ω − = (10b) In contrast to ω1, ω3 exists only when Z0 is smaller than ZLD. Meanwhile, ω2 and ω3
increase as Cg or Lp decreases. The balanced CRLH-TL has an inherent pole at ω0 due to
β = 0, so when Z0 < ZLD there are three transmission poles at ω0, ω2 and ω3. The RH
bandwidth can be expanded if ω2,3 > ω0. When Z0 = ZLD, only two transmission poles exist at ω0 and ω2. When Z0 > ZLD, there are three transmission poles at ω0, ω1 and
ω2. The LH bandwidth can be expanded if ω1 < ω0.
C. Theoretical Results
According to the above derivation and analysis, the number and the location of the transmission poles of the proposed CRLH-TL unit can be controlled by the impedance ratio between ZLD and Z0 and the RH-LH elements CR, LR, CL and LL. In order to validate above analytical results, some simulations with different unit element values and Z0 are demonstrated. For the purpose of comparison, we choose ω0/2π = 1 GHz and ZLD = 50Ω. The characteristic impedance Z0 is chosen to be 40, 50 and 60 Ω, respectively.
Fig. 3 shows the simulation results of S11 with different inductances and capacitances,
the design parameters are listed in Table I. It is clear that a transmission pole is fixed at ω0 and wide bandwidth is achieved with large LH element values but small RH element
values. In Fig. 3(a), when Z0 < 50 Ω the bandwidth extension is due to increasing of the
offsets of ω2 and ω3 from ω0, which is obtained by decreasing RH element values.
a real number. When Z0 = 50 Ω, Fig. 3(b) shows the similar phenomenon of the
bandwidth with Fig. 3(a), only the inband performance is affected by the vanishing of ω3.
As shown in Fig. 3(c), when Z0 > 50 Ω, a wider LH bandwidth is achieved with the
appearance of ω1 and it can be substantially expanded by increasing LH element values.
(a) Z0 = 40 Ω
(b) Z0 = 50 Ω
(c) Z0 = 60 Ω
CRLH-TL unit shown in Fig. 1(b). (a) Z0 = 40 Ω. (b) Z0 = 50 Ω. (c) Z0 = 60 Ω.
(a) Z0 = 40 Ω
(b) Z0 = 50 Ω
(c) Z0 = 60 Ω
Fig. 4. Simulation results of the phase response of S21 for the CRLH-TL unit shown in
Fig. 1(b) using the parameters of Table I. (a) Z0 = 40 Ω. (b) Z0 = 50 Ω. (c) Z0 = 60 Ω.
Z0(Ω) Cp(pF ) Lp(nH) Cg (pF ) Cpg (pF ) Ls(nH) 2 12.67 6.39 1.52 1.6 40 4 6.33 2.44 1.52 3.2 8 3.17 1.05 0.93 6.4 2 12.67 3.76 1.31 2.5 50 4 6.33 1.46 1.07 5 8 3.17 0.66 0.61 10 2 12.67 2.42 1.09 3.6 60 4 6.33 0.98 0.78 7.2 8 3.17 0.45 0.43 14.4
Fig. 4 shows the phase responses of S21 corresponding to Fig. 3. The linear part of the
phase curves becomes wider as bandwidth increase, which offers a method to obtain ultra-wideband linear-phase characteristics. Thus, we have to increase CL and LL or decrease CR and LR to get a wide bandwidth. Considering the restricted condition of (6) and (7), the expansion of bandwidth turns to increase the values of CL and LL.
D. Design Equations
Fig. 5 depicts the layout of the proposed CRLH-TL unit cell. The width and length of the broadside- coupled lines and the shorted stub are wa, la, wb and lb. The capacitance associated with broadside-coupled lines and the inductance of the shorted stub can be expressed as 1 1 a a p w l C t ε = (11a) 2 2 a a g w l C t ε = (11b) p g pg p g C C C C C = + (11c) 2 0 0 tan( ) b b s Z l L c ω ε ω ε = (11d)
Fig. 5. Layout of the proposed CRLH-TL unit cell. A pair of broadside-coupled lines are introduced to realize CL. LL is provided by the shorted stub. The inductance associated with broadside-coupled lines and the capacitance between the middle layer and ground can be treated as LR and CR, respectively.
where t1 and t2 are the thicknesses of the two layers, Zb is the characteristic impedance of the shorted stub, c0 is the speed of light in vacuum, and ε0 is the permittivity of vacuum.
In order to simplify our design, the fringing effect is neglected.
Based on former conclusion, large CL, LL and small CR, LR are needed to obtain wide bandwidth. Therefore, layer 1 (t1) should be as thin as possible, while layer 2 (t2) should
be thick. Thus, we can get Cp>>Cg and (11c) can be simplified to Cpg ≈ Cg, meanwhile (1b) is rewritten to CR ≈ 4Cg. There is also edge coupling between the two TLs on the same layer, but it is too weak to consider.
By substituting (1) and (11) into (6) or (7), we can obtain the ratio between LH and RH inductances and capacitances
1 2 1 2 2 1 2 1 1 2 2 1 ( ) 4 (2 ) L L R R L C t t t m L C t t t ε ε ε ε ε ε + = = = + (12) Thus all the CRLH elements can be derived from dimension parameters, and can be used to analyze some complicated components. Conversely, for a given ω0 and Z0, the
dimensions of the unit cell can be deduced. By substituting (12) into (6), the LH elements can be rewritten as
0 0 L m C Z ω = (13a) 0 0 L Z m L ω = (13b)
The value of wa can be deduced once Z0 is determined [36], then make (1a) and (13a)
equal we can get the length of the coupled lines
1 1 0 0 2 a a t m l Z w ε ω = (14) It is obvious from (14) that la decreases as wa increases, so the size reduction can be realized with a large wa. Once wa and la are known, the relation between the length and width of the shorted stub are found from
0 0 1 0 2 0 1 2 arctan b b a a c mt l Z w l ε ω ε ω ε = (15) where Zb is the characteristic impedance of the shorted stub, and it can be calculated from the width wb [36]. Therefore, solving (15) with a given wb we can get lb, and then all the dimensions are obtained.
III. EXPERIMENTAL VERIFICATION A. Design Process
Based on the previous analysis, the design procedure can be summarized as follows:
Determine the substrates and get ε1, t1, ε2 and t2.
Choose Z0 (wa) to get wa (Z0) and calculate la at desired ω0. Choose a proper wb and solve lb from (15).
B. Selection of Dimension Parameters
For theoretical verification, some samples are designed. The transition frequency ω0 is
chosen to be 1, 2 and 3 GHz, respectively. The substrate Rogers RO4350B with εr = 3.66 and thicknesses of t1 = 0.168 mm and t2 = 1.524 mm has been used. We take 1
GHz as an example because the design process is similar to other frequencies.
Fig. 6 shows the calculated parameters of the proposed CRLH-TL unit cell at 1 GHz with different wa. In Fig. 6(a), LL decreases as wa increases, but it decreases slower than the rate of CL, which results in a wider bandwidth with large wa.
For given wa and la, the length of the shorted stub lb can be deduced from (15) by setting the value of wb. Fig. 6(b) shows the comparison of lb with different wa and wb. Note that, although we can choose arbitrary values of wa and wb, lb becomes larger as wa
decreases or wb increases. When the electrical length of the shorted stub is longer than quarter wavelength, a transmission zero is generated and the inband performance is affected. Thus, wb should be small enough so that a short lb can be achieved with a given wa.
(a)
(b)
Fig. 6. Calculated parameters of the proposed CRLH-TL unit cell at ω0/2π = 1 GHz. (a)
Fig. 7. Picture of the manufactured CRLH-TLs. The CRLH-TLs designed at ω0/2π = 1
GHz utilizing 1, 2, 3- and 4-unit cells. The numbers of the unit cell at ω0/2π = 2 and 3
GHz are 2 and 3.
C. Broadband CRLH-TL Samples
In our design, wa of 3.67 mm is identical to the 50 Ω microstrip transmission line width on the top layer. Then la can be obtained at different ω0. In order to avoid large lb, we choose the smallest width of the shorted stub that can be achieved, wb = 0.25 mm. Thus, lb can be calculated from (15).
Simulations were performed with Ansoft’s High Frequency Structure Simulator (HFSS). The values of dimensions are listed in Table II. A picture of the manufactured CRLH-TLs is presented in Fig. 7. The broadside-coupled lines are at both sides of the top substrate, the shorted stub is at the bottom side of the top substrate. Two substrates are fixed together with plastic screws and the shorted stub is grounded via a plated hole to the bottom side of the lower substrate
TABLE II. Design parameters of the proposed CRLH-TL unit cell at different frequency
0 0/ 2 f =ω π . f0(GHz) wa(mm) la(mm) wb (mm) lb (mm) 1 3.67 9.8 0.25 12.3 2 3.67 4.67 0.25 7.05 3 3.67 3.2 0.25 4.46
IV. RESULTS
Fig. 8 shows the simulated and measured results of the CRLH-TL in terms of S-parameters. As seen from Fig. 8(a), there are three transmission poles inside the passband and one of them is at ω0/2π = 1 GHz, the other two correspond to ω2 and ω3. The
measured return loss is better than 10 dB over a very wide frequency range from 0.53 to 6.93 GHz, whereas the insertion loss is smaller than 1 dB over the entire passband. The 10 dB bandwidths of N = 2, 3 and 4 are 0.57 to 6.53 GHz, 0.53 to 6.93 GHz and 0.63 to 6.67 GHz, respectively. The insertion loss deteriorates from 0.19 to 0.63 dB at 1 GHz and 0.71 to 1.73 dB at 6 GHz as the number of the unit cells and the frequency increase. This is primarily due to the air gap between the two layers and dielectric loss.
(a) N=1 (b) N=2
(c) N=1 (d) N=2
Fig. 8. Simulated and measured results of the proposed CRLH-TL at ω0/2π = 1 GHz
with number of the unit cell of N = 1, 2 ,3 and 4.
The measured phase responses of S21 are illustrated in Fig. 9. It shows that a very wide
length. The corresponding zero phase frequencies are 1.08, 1.13, 1.07 and 1.07 GHz, respectively, which are very close to the designated frequency. The discrepancy of ω0
may be caused by fabrication errors and parasitic effects introduced by the SMA connectors.
Fig. 10 represents the measured results of the CRLH-TLs designed at 2 and 3 GHz, and it can be observed that very wide bandwidth and good performance are still achieved at these frequencies. The 10 dB bandwidths for ω0/2π = 2 GHz of N =1 and 2 are 0.77 to
13.01 GHz and 0.73 to 11.97 GHz, and the insertion loss is less than 1.5 dB. The 10 dB bandwidths for ω0/2π = 3 GHz of N =1 and 2 are 1.24 to 14.17 GHz and 1.47 to 13.41
GHz, and the insertion loss is less than 1.8 dB. The corresponding zero phase frequencies are 2.03 and 3.11 GHz as shown in Fig. 10(c).
Fig. 9. Phase of S21 for the proposed CRLH-TL at ω0/2π = 1 GHz with number of the
unit cell of N= 1, 2 ,3 and 4.
(b)
(c)
Fig. 10. Measured results of the CRLH-TLs designed at ω0/2π = 2 and 3 GHz. (a)
S-parameters of ω0/2π = 2 GHz with N = 2 and 3. (b) S-parameters of ω0/2π = 3 GHz with
N = 2 and 3. (c) Phase of S21 for the four samples. V. DISCUSSION
A comparison of the proposed CRLH-TL with other reported CRLH-TL structures is listed in Table III. The proposed structure can achieve much wider bandwidth than the reported structures. Meanwhile, our structure has lower insertion loss in comparison with [33] and [34]. Although the number of unit cells in our case is less than [33], the insertion loss at the same transition frequency 1.54 GHz of N = 1, 2, 3 and 4 are 0.19, 0.31, 0.44 and 0.51 dB, which shows a predictable lower insertion loss when the number of the unit cells is identical.
TABLE III. Comparison of the proposed CRLH-TL with other reported CRLH-TL structures.
Ref. f (GHz) 0 N |S21|max(dB) 10dB BW ~ L H f f (GHz) H L f f [33] 1.54 5 2.4 1.25~2 1.6 [34] 2.45/5.1 9 8 1.5~5.9 3.93 [35] 2 7 N/A 1~3.6 3.6 This Work 1 4 1.73 0.63~6.67 10.59 VI. CONCLUSION
A novel CRLH-TL consists of broadside-coupled lines and a shorted stub has been presented. First, the transmission characteristics have been studied utilizing a TL theory, and the condition to generate transmission poles has been deduced. The theoretical results show that a bandwidth extension can be achieved by increasing the LH element values or decreasing RH element values. Then the design equations of the proposed CRLH-TL have been deduced based on its equivalent circuit. Finally, several CRLH-TL samples are fabricated using the proposed structure and the measured results are presented. It has been demonstrated that very wide bandwidth with low insertion loss and low return loss can be achieved with our proposed structures, which confirms our analytical and simulation results.
ACKNOWLEDGMENT
The author Xin Xu thanks for the financial support from China Scholarship Council (CSC, File NO. 201706075057). The authors would like to thank G. Knutsson, Linköping University, for his help and support with manufacture of prototypes.
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Xin Xu received the B.S. and Ph.D. degrees in electromagnetism and
microwave technology from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2007 and 2015, respectively. In 2015, he joined the School of Electronic Science and Engineering, UESTC, as a Research Assistant. He is currently a Visiting Scholar with the Communication Electronics Research Group, Linköping University, Sweden. His research interests include microwave and mm-wave circuits and systems.
Magnus Karlsson was born in Västervik, Sweden in 1977. He
received his M.Sc., Licentiate of Engineering and Ph.D. degrees from Linköping University in Sweden, in 2002, 2005 and 2008, respectively. In 2003 he started in the Communication Electronics research group at Linköping University and is currently working as a senior researcher and lecturer. His main work involves wideband antenna techniques, wideband transceiver front-ends, and wireless communication.
Shaofang Gong received his B.Sc. degree in microelectronics from
Fudan University, China in 1982, and Licentiate of Engineering and Ph.D. degrees from Linköping University, Sweden in 1988 and 1990, respectively. Between 1991 and 1999, he was a senior researcher with the research institute RISE Acreo. From 2000 to 2001, he was the chief technology officer at a spin-off company from the research institute. In the meantime, he had an adjunct professorship at Linköping University. Since 2002, he has been the chair professor of Communication Electronics at Linköping University. His main research interest has been communication electronics including radio frequency and microwave system designs, high speed data transmissions and wireless sensor networks towards Internet of Things.
