left-handed transmission lines

RADIO SCIENCE, VOL. 46, RS5008, doi:10.1029/2010RS004617, 2011

Novel composite right‐/left‐handed transmission lines using fractal geometry and compact microwave devices application He‐Xiu Xu,1 Guang‐Ming Wang,1 and Jian‐Gang Liang1 Received 21 December 2010; revised 28 May 2011; accepted 23 June 2011; published 20 September 2011.

[1] In this paper, novel electrically small resonant‐type composite right‐/left‐handed transmission lines (CRLH TLs) combining fractal geometry are proposed and systematically exploited. Two sets of planar CRLH cell structure are involved including the proposed one based on cascaded complementary single split ring resonator (CCSSRR) and improved one based on complementary split ring resonators (CSRRs). Fractal perturbation in these CRLH TLs is from the point of super compactness. The left‐handed (LH) electromagnetic wave propagation characteristic and miniaturization principle are investigated in depth by electrical simulation, EM simulation and finally demonstrated by effective constitutive EM parameters. To illustrate possible application, a dual‐band BPF covered satellite DMB band and WiMAX band, and a monoband branch‐line coupler covered GSM band are designed, fabricated, and measured. Consistent results between full‐wave simulation and measurement have confirmed the design concept. Measurement results indicate that the fractal perturbation is a good strategy for further miniaturization, enhanced selectivity and maintenance of good in‐band performance in both designs especially for the coupler which achieves a comparable 81% size reduction relative to its conventional counterpart. Citation: Xu, H.‐X., G.‐M. Wang, and J.‐G. Liang (2011), Novel composite right‐/left‐handed transmission lines using fractal geometry and compact microwave devices application, Radio Sci., 46, RS5008, doi:10.1029/2010RS004617.

1. Introduction [2] Resonant‐type composite right‐/left‐handed transmission line (CRLH TL) has not driven a lot of attention until the complementary split ring resonators (CSRRs) etched in the ground plane of microstrip line is first proposed and demonstrated with a negative permittivity in the vicinity of resonant frequency [Falcone et al., 2004a]. Subsequently, the possibility to fabricate planar CRLH TL by incorporating the CSRRs and series gap is proved by Falcone et al. [2004b]. In recent years, resonant‐type CRLH TLs have gone through a great development. For instance, CRLH TL implemented by incorporating the series capacitive gap, CSRRs, and additional ground inductors, which enabled a further degree of flexibility [Bonache et al., 2006], by etching a CSRRs on the conductor strip, which is exploited as a good strategy to those systems where the ground plane cannot be etched [Gil et al., 2008], using complementary spiral resonators (CSRs) for further miniaturization and open complementary split ring resonator (OCSRR) for high selectivity [Selga et al., 2009], introducing the fractal geometry in CSRRs for size reduction and enhanced selectivity [Crnojevic‐Bengin et al., 2008], adopting complementary single split ring resonator (CSSRR) 1

Department of Electromagnetic Field and Microwave Technique, Missile Institute, Air Force Engineering University, Sanyuan, China. Copyright 2011 by the American Geophysical Union. 0048‐6604/11/2010RS004617

[Xu et al., 2011a], and cascaded CSSRR(CCSSRR) [Xu et al., 2011b], etc. [3] Although the fractal perturbation in CSRRs results in a significant lower resonance and in turn an electrically smaller left‐handed (LH) particle [Crnojevic‐Bengin et al. [2008], the large insertion loss of the CRLH TL whose peak value is more than 10 dB has limited its popularization in practical application. The CCSSRR‐loaded CRLH TL [Xu et al., 2011b] owns advantages of easier adjustment for balanced condition relative to CSRRs‐loaded and CSSRR‐loaded ones and thus can be engineered for broadband design, however, the resultant structure also brings another issue of larger occupied area which deserves further improvement. [4] In view of them, the goal of this article is aimed to propose and synthesize novel CRLH TLs to deal with those drawbacks. The use of a single technology does not always fulfill the requirement of super compactness. Consequently, the combined technology of fractal geometry and CRLH TL is a good candidate and preferably considered. The paper is organized as follows. In section 2, two sets of CRLH TLs using Sierpinski‐shaped CCSSRR (S‐CCSSRR) and Minkowski‐loop shaped CSRRs (ML‐CSRRs) are initially proposed, followed by a deep research of the electromagnetic (EM) characteristic and miniaturization principle. Then simple applications of them in the effective design of a dual‐ band (DB) bandpass filter (BPF) and a monoband (MB) branch‐line coupler (BLC) are exploited in section 3. Detailed design procedures and guidelines are also involved

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XU ET AL.: NOVEL CRLH TL AND DEVICES APPLICATION

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which should be a reference value for future design. Finally, a major conclusion is highlighted in section 4.

2. Proposed Miniaturized CRLH TL 2.1. S‐CCSSRR‐Loaded CRLH Cell [5] Fractal geometry combined with EM theory has led to an innovative concept and a heated topic in microwave devices and antennas design. It is particular interesting for its space‐filling and self‐similarity property, and is specified by iteration factor (IF) and iteration order (IO). The IF represents the construction law or initial shape of the fractal geometry while IO indicates how many iteration processes have been carried out. In this section, we propose a set of novel CRLH cells based on fractal‐shaped CCSSRR and study the behavior in depth. Two types of fractal geometry are involved, the former one is Sierpinski fractal, and the latter one is classical Koch curve. For convenience, the resultant two types of CCSSRR are denoted as S‐CCSSRR and K‐CCSSRR, respectively. Fractal perturbation in CCSSRR does not introduce any additional lumped elements but results in a variation of elements value in the equivalent circuit model, consequently, the circuit model proposed and validated by Xu et al. [2011b] is also appropriate for current CRLH particle based on fractal‐shaped CCSSRR. [6] In the first case, the CCSSRR slot is fully constructed as a Sierpinski shape of different IO while the overall footprint of the particle is kept constant. Figure 1 shows the topology of the proposed particles and corresponding equivalent T‐circuit model. As can be seen, novel CRLH cell incorporates an S‐CCSSRR on the ground plane, and a capacitive gap above the K‐CCSSRR on the signal strip for proper excitation. The CCSSRR is formed by a fundamental CSSRR with a center pole separating the particle into two identical smaller CSSRR, and two splits symmetrically locate in the center top side of each smaller CSSRR. Zeroth‐ order S‐CCSSRR is mentioned in terms of clarity and comparison convenience. There are two shunt branches in the circuit model accounting for the effect of the fundamental and smaller CSSRR, where Cg models the gap capacitance, Ls models the line inductance, C1 represents the electric coupling between the conductor line and the fundamental CSSRR which is described by means of a parallel resonant tank Lp1, Cp1. In like manner, C2 models the electric coupling between the line and the smaller CSSRR which is characterized by a resonant tank Lp2, Cp2. Therefore, novel LH particle with additional lumped elements in the circuit model allows several degrees of freedom in CRLH TL design. [7] According to the classical circuit theory, two transmission zeros associated with resonances of two shunt branches are theoretically predicted as

Figure 1. Topology of the proposed CRLH cells based on S‐CCSSRR of (a) zeroth order, (b) first order, (c) second order, and (d) corresponding equivalent T‐circuit model. Note that the S‐CCSSRR, ground plane and signal line are depicted in white, the light gray and dark gray, respectively. Detailed geometrical parameters of S‐CCSSRR are g1 = g2 = g3 = 0.3 mm, w3 = 9.8 mm.

fz1 ¼

1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ; 2 Lp1 C1 þ Cp1

ð1Þ

fz2 ¼

1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi : 2 Lp2 C2 þ Cp2

ð2Þ

The additional transmission zero of fz2 on the edge of RH band has obviously enhanced the selectivity and harmonic

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Figure 2. S‐parameters of proposed CRLH TL based on S‐CCSSRR of different IO. suppression of the CRLH cell to a great extent with respect to conventional CSRRs‐loaded cell. The balanced condition occurs when the series resonance fs is equivalent to the resonance of the two shunt branches fp. In this case, the LH band switches to the RH region without a gap. [8] For characterization, analysis of novel CRLH cells depicted in Figure 1 is performed on the F4B‐2 substrate with a thickness of 0.8 mm and a dielectric constant of 2.65 by planar EM simulation software Ansoft Designer. Figure 2 shows the simulated full‐wave S‐parameters. Consulting Figure 2, four most important aspects should be emphasized. First, the balanced wide passband is obviously spitted into two narrower bands by engineering the square slot as Sierpinski shape of the first and second IO. These two bands have been demonstrated as a LH and a RH band, respectively by latter effective constitutive EM parameters. Second, these two bands both shift toward lower frequencies when IO increases from the first to the second, e.g., the center frequency of LH band varies from 3.4 to 2.6 GHz while the RH band from 4.2 to 3.4 GHz. Therefore, the maximum downscale of center frequency is obtained approximate to 30.7%. Third, a further inspection from the narrower band characterized by 3 dB insertion loss illustrates that the second‐order S‐CCSSRR‐loaded cell exhibits higher loaded quality factor (QL) than residual cases. This can be successfully interpreted through the lower input/output couplings that current cell exhibits. Fourth, as expected, two transmission zeros are located below the edge of LH band and above the edge of RH band, respectively, in three cases. [9] The frequency shifting toward lower band as IO increases from first to second is attributing to that fractal perturbation in CCSSRR with zig‐zag boundary has significantly extended the current path along the boundary. This interpretation gives strong support to the fact that a contrary phenomenon is observed when IO increases from the zeroth to the first due to that the slot perimeter of the first‐order S‐CCSSRR is shorter than that of zeroth‐order one. The increase of slot perimeter is associated with the increase of LP1, CP1 and LP2, CP2, which mainly determine the upper limit of LH band fp. It is interesting to mention that the primary transmission zero does not shifted toward lower band

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when IO increases from zeroth to second which can be explained through that the gradually reduced unoccupied area leads to a much smaller C1 as IO increases. Hence, the reduced interval between the fundamental LH band and transmission zero facilitates the high selectivity of second‐ order cell to a great extent. [10] Since it was successfully demonstrated that the CCSSRR‐loaded CRLH cell is working on the balanced condition with continuous transition from LH band to RH one [Xu et al., 2011b], it is essential to prove that the induced two bands of second‐order S‐CCSSRR‐loaded CRLH cell are the LH and RH band, respectively. In this regard, the effective constitutive EM parameters are extracted from full‐ wave simulated S‐parameters by an improved NRW (Nicolson‐Ross‐Weir) method developed by Xu et al. [2011c]. Figure 3 shows the effective constitutive EM parameters. It is obvious that these results give strong support to all results obtained from EM simulation. Very distinct negative refractive index and propagation constant are obtained in the band of 2.61 to 2.68 GHz, while the positive value in the band of 3.4 to 3.48 GHz, respectively. In these frequency ranges, the imaginary part of refractive index accounting for electric and magnetic loss is approximate to zero, which allows signals to transmit freely.

Figure 3. Constitutive EM parameters of second‐order S‐CCSSRR‐loaded CRLH cell based on full‐wave S‐parameters plotted in Figure 2. (a) Effective refractive index and propagation constant and (b) effective permeability and permittivity.

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fixed. The topology of the engineered CRLH cells is illustrated in Figure 4. The same substrate and simulation software mentioned above are adopted for characterization. Figure 5 plots the frequency response of these proposed cells. As expected, there is still a composite LH and RH passband in full K‐CCSSRR case while by contraries, a separate narrow LH band and RH band in partial K‐CCSSRR case. We conclude that novel CRLH TL is intrinsically balanced only when three vertical slots are absolutely identical. The mechanism of increased QL of the fully K‐CCSSRR‐ loaded cell relative to the partially loaded cell is identical with that of S‐CCSSRR‐loaded cells in first‐ and second‐order case. 2.2. ML‐CSRRs‐Loaded CRLH Cell [13] In this section, Minkowski loop is adopted in the concentric square CSRRs to form a set of more compact sub‐ wavelength particles. Figure 6 plots the topology of these cells and their corresponding equivalent T‐circuit model. As can be observed, engineered CRLH cells are constructed by ML‐CSRRs of different IO (realizing negative permittivity) etched on the ground plane and capacitive gap (realizing negative permeability) on the upper conductor line. Low‐ impedance patch (LIP) introduced on upper conductor strip is from the point of view of easy impedance match and addressing the drawback of large insertion loss of Crnojevic‐ Bengin et al. [2008]. In current design, Minkowski loop is specified by its horizontal IF s and vertical IF d. The s and d are associated with w1 and w2, respectively as follows:

Figure 4. Topology of K‐CCSSRR‐loaded CRLH cell based on (a) partial and (b) full Koch curves of third order, the height of the center pole is 12 mm, and residual geometrical parameters are g1 = g2 = g3 = 0.3 mm, and w3 = 8.9 mm. [11] Consulting Figure 3b, we conclude that S‐CCSSRR is responsible to the exhibited negative effective permittivity occurred from 2.61 to 2.67 GHz. Below 3.4 GHz, the effective permeability is negative. Therefore the simultaneous negative LH band solely depends on band of negative permittivity. Moreover, the upper transmission zero is associated with the exhibited single negative permeability around 3.8 GHz. It is useful to mention that the smaller CSSRR (responsible to the magnetic resonance) is externally driven through the component of the magnetic field contained in the plane of the particle, while the fundamental CSSRR (responsible to electric response) is still excited electrically. [12] It is commonly believed that fractal perturbation in antennas or devices typically brings DB or multiband behavior due to the self‐similarity. However, in current design, key factor of the resultant DB characteristic is due to that the Sierpinski‐shaped slot introduces additional asymmetry, namely the height of center pole is different from that of two sided vertical branches, and in turn destroys the balanced condition. For further verification, two vertical branches and the center pole are partially and fully substituted by a Koch curve of third order while horizontal branches are

w1 þ 2g4 þ g3 ¼ ðw3 þ 2g4 þ g3 Þ;

ð3Þ

w2 ¼ w3 :

ð4Þ

Since it has been proved that the contribution of d to the miniaturization is much more outstanding than that of s [Xu et al., 2011a]. As a consequence, the geometrical parameters of ML‐CSRRs should be adjusted to benefit larger d for both first‐ and second‐order ML‐CSRRs. To this end, orientation of several fractal bends and physical parameters of second‐ order CSRRs are changed and are different from that of first‐order case. In the circuit model shown in Figure 6d,

Figure 5. S‐parameters of proposed CRLH cells based on partial and full K‐CCSSRR.

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Figure 6. Topology of the proposed CRLH cells implemented by ML‐CSRRs of (a) zeroth order, (b) first order, (c) second order, and (d) corresponding equivalent T‐circuit model. Note that the ML‐ CSRRs, ground plane and signal line are depicted in white, the light gray and dark gray, respectively. For zeroth‐order ML‐CSRRs, g2 = g3 = g4 = 0.4 mm; for first‐order case, g2 = g3 = g4 = 0.4 mm, s and d are set to be 0.39 and 0.31; for second‐order case, g2 = g3 = g4 = 0.3 mm, s and d are set to be 1/3 and 0.25. The residual geometrical parameters are kept identical and listed as a = 7 mm, h = 6.5 mm, ws = 1.56 mm, w3 = 12 mm, g1 = 0.25 mm. ML‐CSRRs is described by means of a parallel resonant tank formed by capacitance Cp and inductance Lp, capacitive gap is modeled by a capacitance Cg, Ls represents the line inductance, C is composed of the line capacitance and the electric coupling between signal line and ML‐CSRRs. The series resonance fse, shunt resonance fsh (namely the transmission zero), and resonance of the ML‐CSRRs f0 are determined as follows, respectively. The balanced condition is fulfilled when fse is quantitatively approximate to the f0. 1 pffiffiffiffiffiffiffiffiffiffi ; 2 Ls Cg

ð5Þ

1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ; 2 Lp Cp þ C

ð6Þ

fse ¼ fsh ¼

f0 ¼

1 pffiffiffiffiffiffiffiffiffiffi : 2 Lp Cp

ð7Þ

The substrate RT/duroid 5880 with dielectric constant of 2.2 and thickness of 0.508 mm is employed for characterization of the engineered cells depicted in Figure 6 and synthesis of the aftermentioned MB BLC. The proposed CRLH particles of different IO are investigated by means of EM simulation in conjunction with electrical simulation (circuit model) from Ansoft Serenade. During the electrical simulation, circuit parameters are extracted based on magnitude/phase fitting technique. Figure 7 compares the S‐parameters. A good agreement of frequency responses between EM simulation and electrical simulations is obtained which has

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fsh and f0 referring to equations (6) and (7). However, fsh is almost unaffected around 0.4 GHz in practice, which is due to that Cp is with value much smaller than C and thus contributes less to fsh. [15] Increased Cp mainly attributes to the extension of the overall circumference of ML‐CSRRs in virtue of space‐ filling property. It is interesting to mention that although the circumference of ML‐CSRRs is in proportion to IO, the Lp has not increased proportionally which is in a completely different mechanism from that CSSRR with gradually enhancive Lp [Xu et al., 2011a]. Almost unaffected Lp in current design is due to that opposite current distribution happens in the region of inset section which inhibits the enhancement of Lp. Figure 8 depicts the current density distribution of ML‐CSRRs in LH band. It is obvious that the current is restricted to the fractal boundary of the ring slot and is very weak in other places. This phenomenon cannot be observed out of LH band owing to the imperfect electric excitation. The current along the zigzag boundary has sig-

Figure 7. S‐parameters of proposed ML‐CSRRs‐loaded CRLH cells. (a) EM simulation and (b) electrical simulation. Note that N represents the iteration number. confirmed the rationality of the circuit model. A further inspection reveals that the fundamental LH band has evidently shifted toward lower band as IO increases, thus an electrically smaller sub‐wavelength particle is developed. The downscale of frequency (with a maximum scale of 41.6%) seems to be enhanced when IO increases, e.g., the center frequency of the LH band has been lowered from 1.09 GHz (zeroth order) to 0.92 GHz (first order) and finally to 0.77 GHz (second order). [14] Table 1 compares the extracted lumped‐element parameters of these CRLH cells. It indicates that almost identical values of lumped elements except for different Cp can be concluded. The value of Cp of the second‐order ML‐ CSRRs‐loaded cell is more than five times bigger than that of zeroth‐order one. The increased Cp leads to a reduction of

Table 1. Extracted Lumped Parameters of CRLH Cells ML‐CSRRs Type

Ls (nH)

Cg (pF)

C (pF)

Lp (nH)

Cp (pF)

Zeroth‐order First‐order Second‐order

11.38 12.4 10.2

0.62 058 0.61

20.1 20 19.9

6.86 6.31 6.89

0.74 2.49 3.89

Figure 8. The current distribution of ML‐CSRRs in the LH band.

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RH band of CRLH cell can be engineered according to the specified second band and cut‐off frequency by tuning the width and height of LIP. Third, adopt the CELC and skillfully locate its merged two transmission zeros (see Figure 9b) above the RH band to enhance the out‐of‐band suppression and stopband bandwidth. This can be achieved by an optimization of slot width g, arm’s length L, and pole’s height h. Fourthly, determine the width of microstrip line for perfect impedance match by referring to the termination impedance, followed by a refined optimization of the total geometrical parameters. [18] Figure 10 plots the fabricated prototype of the finally developed DB BPF. The width and height of the LIP are optimized as 5.5 and 3.5 mm, respectively. The prototype whose occupied area is only 30 × 18 mm2 is very compact in size. Figure 11 compares the simulated and measured (through Anritsu ME7808A vector network analyzer) frequency response of the fabricated prototype. Reasonable agreement can be observed in the frequency band of interest. Very obvious dual band behavior covering the Satellite Digital Mobile Broadcasting (Satellite DMB, 2605–2655 MHz) band and WiMAX band (centered at 3.5 GHz) can be observed. Although the measured insertion

Figure 9. (a) Topology and (b) simulated full‐wave S‐ parameters of the proposed single negative transmission line (TL) based on CELC (depicted in white) etched on the conductor strip (depicted in dark gray); the ground plane is depicted in light gray. The geometrical parameters of CELC are L = 9.7 mm, h = 5.5 mm, g = 0.3 mm, and a = b = 6 mm. nificantly extended the current path and results in a larger Cp between metallic places separated by two rings.

3. Novel Microwave Devices Application 3.1. DB BPF Based on S‐CCSSRR‐Loaded CRLH TL [16] To illustrate possible application of the S‐CCSSRR‐ loaded CRLH cell, a narrow DB BPF based on second‐order S‐CCSSRR outlined in Figure 1 is designed, fabricated and measured. The complementary electric inductive‐capacitive resonator (CELC) shown in Figure 9a is considered on the conductor strip in terms of improved out‐of‐band suppression. In general, total four steps are involved in the implementation of the DB BPF and are derived as follows. [17] First, cautiously select the dimensions of S‐CCSSRR to locate the LH band in the specified primary band above the lower transmission zero. Given the dimensions of S‐CCSSRR, the upper transmission zero is also roughly obtained. To overcome the drawback of large insertion loss of S‐CCSSRR‐loaded cell in LH band, the next step consists in skillfully inserting a LIP above the S‐CCSSRR. Also the

Figure 10. Fabricated prototype of the designed DB BPF: (a) top view and (b) bottom view.

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Z ¼

Figure 11. Simulated and measured S‐parameters of the fabricated DB BPF.

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Zs ð j!Þ Zs ð j!Þ þ 2Zp ð j!Þ :

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ð9Þ

where Zs(jw) is the impedance of series branch and Zp(jw) is the impedance of shunt branch. The upper and lower limitation of the LH band is determined by frequencies f0 and fL which is obtained by deriving Zb to be null. At fL and f0, both and Zb take extreme values which theoretically enable us to implement l/4 impedance transformers with a controllable phase shift and impedance across a wide range. In current design, Zb is set to be 35.3W and 50W while is set to be +90° for both transformers at GSM band centered at 0.88 GHz, respectively. The main design procedure involves three steps. First, synthesize several groups of circuit parameters of circuit model depicted in Figure 6d by Ansoft Serenade to engineer an impedance transformer with specified electrical performance, followed by an insertion of the

loss with minimum value of 1.7 dB in the primary band is slightly large due to the applied CELC and Sierpinki‐shaped slot, the enhanced selectivity and out‐of‐band suppression more than 35 dB up to the first harmonic should be highlighted. The relative low suppression (maximum 7.2 dB in simulation case and 12 dB in measurement case) between two passbands can be solved by an introduction of in‐between transmission zero through a quarter‐wavelength open‐ circuited stub which would in turn increase the circuit area. 3.2. MB BLC Based on ML‐CSRRs‐Loaded CRLH TL [19] BLC is a four‐port network consisting of four l/4 impedance transformers with phase delay of 90°. Two of them are with characteristic impedance 50W while the other two 35.3W. Unfortunately, it suffers a large occupied area assuming that the operation band of interest is low. Up‐to‐ date, several strategies were exploited to facilitate the integration of the circuit, e.g., BLCs based on CRLH TL [Bonache et al., 2008; Zhang et al., 2005; Chi and Itoh, 2009], adopting higher‐order fractal curve [Chen and Wang, 2008; Ghali and Moselhy, 2004], using discontinuous microstrip line [Sun et al., 2005] and dual TL [Tang et al., 2008]. Although BLCs reported by Chen and Wang [2008] and Ghali and Moselhy [2004] have obtained a large miniaturization, the resultant multi fractal bends also brought other issues of deteriorative performance of devices and worse design precision. In this work, we substitute the first‐order ML‐CSRRs‐loaded cell with 90° phase advance for conventional l/4 TL to synthesize a compact BLC. The first‐ order ML‐CSRRs is selected as a trade‐off between the miniaturization and performance of BLC. 3.2.1. Synthesis of 35.3 and 50W Impedance Transformers [20] Since ML‐CSRRs is an electrically small particle, the Bloch‐Floquet theory can be applied in the synthesis of CRLH TL. The phase shift per cell and characteristic impedance Zb are given as cos ¼ cosðd Þ ¼ 1 þ

Zs ð j!Þ ; Zp ð j!Þ

ð8Þ

Figure 12. S‐parameters of 35.3 and 50 W impedance transformers. (a) Return and insertion loss and (b) transmission phase response. The geometrical parameters of 35.3W impedance transformer are ws = 2.5 mm, L = 49 mm, a = 6 mm, h = 6.5 mm, w1 = 4 mm, w2 = 4.2 mm, w3 = 12 mm, g1 = 0.25 mm, g2 = g3 = g4 = 0.4 mm. The most geometrical parameters of 50W impedance transformer are identical with that of 35.3W one except for ws = 1.6 mm, L = 38 mm, a = 7 mm.

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Figure 13. Fabricated prototype of conventional and proposed BLCs: (a) top view and (b) bottom view. obtained lumped elements into equations (8) and (9) to select the correct solution. Second, the geometrical parameters of the structure can be roughly synthesized, e.g., the width and height of the series gap are determined corresponding to Cg through analytical equations of Wang [2009], the length L and width ws of signal line are adjusted according to Ls and ZC, dimensions of ML‐CSRRs which mainly determine the frequency f0 are optimized according to Lp, Cp, and finally the width and height of LIP are tuned according to C. Third, construct the upper signal line (irrespective of LIP) as phase‐ equalizing Koch curves of first order for super compactness. [21] Figure 12 displays the simulated full‐wave S‐parameters in conjunction with physical parameters of the 35.3W and 50W impedance transformers, respectively. It indicates that both transformers operate at 0.88 GHz and obtain an exact 90° phase advance from the nonlinear curve of transmission phase response. Moreover, the impedance match with minimum return loss approximating to 35 dB is comparable. Exact results of both transformers have verified the effectiveness of the design. 3.2.2. Illustrative Results [22] By assembling the designed fractal‐shaped 35.3 and 50 W impedance transformers, a super compact BLC is developed. To experimentally validate the effectiveness of

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Figure 14. S‐parameters of designed BLC (a) simulation and (b) measurement. combined technology in BLC design, an example coupler is fabricated and measured. Conventional BLC is also designed and fabricated for comparison convenience. Figure 13 shows the fabricated prototypes of conventional and novel designed

Figure 15. Transmission phase imbalance |ffS 21 ‐ffS 31 | between ports 2 and 3.

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Table 2. Comparison of Compact BLCs BLCs

Scale of Miniaturization

Bonache et al. [2008] Chi and Itoh [2009] Chen and Wang [2008] Ghali and Moselhy [2004] Sun et al. [2005] Tang et al. [2008] Proposed

39.2% 10% 81.8% and 64.6% 75.3% 60% 63.9% 81%

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authors’ best knowledge, the designed BLC achieves one of the largest miniaturization among the available data.

4. Conclusion

BLCs. The footprint (34 × 25 mm2) of the proposed coupler has been significantly reduced by an approximate 80% of the area 63.5 × 66.5 mm2 that its conventional counterpart occupies. [23] Figure 14 exhibits the simulated and measured S‐parameters of the proposed BLC. Figure 15 compares the simulated and measured phase imbalance between ports 2 and 3. Reasonable agreement between simulation and measurement can be observed in the whole frequency band of interest except for slight frequency shift toward lower band 0.87 GHz in measurement case. This slight discrepancy is partly attributing to the tolerances that are inherent in the fabrication process and partly to the small fractal dimensions of ML‐CSRRs that result in low precision of the simulation results. [24] Measurement results indicate that the return and isolation loss (|S11| and |S41|) of novel BPF at the center frequency are 22.3 and 31.4 dB, respectively which are very comparable relative to 29.92 and 28.1 dB of conventional BLC. The slight larger return loss in both simulation and measurement cases is due to that several chamfered bends have been introduced in the upper lines of the BLC during the fractal implementation. It is just these bends induce the unexpected current discontinuity. The relative bandwidths characterized by |S11| and |S41| larger than 10 dB, and phase imbalance (ffS21‐ffS31) within 90° ± 3° are 9.6% and 6.5%, respectively which are narrower than that of conventional coupler (25.1% and 20.6%). The narrow bandwidth of proposed BLC is due to the relative steep phase response of the transformers (see Figure 12). Measurement results also reveal that proposed coupler has larger insertion loss of |S21| and |S31| (3.6 and 4.1 dB) with respect to conventional coupler (3.5 and 3.6 dB) due to the utilized ML‐CSRRs. Nevertheless, the insertion loss of the proposed BLC is within the scope of normal level and is very comparable with regard to already covered ones, e.g., 4.19 and 4.31 dB for the lower band while 4.43 and 4.72 dB for the upper band [Bonache et al., 2008], almost 4 and 5 dB for the second‐order BLC [Chen and Wang, 2008]. The exact phase imbalance of 90.3° should be emphasized compared to 93° [Bonache et al., 2008] and 86.8° [Zhang et al., 2005]. Moreover, the proposed BLC is with easier design procedure relative to that using many capacitive and inductive lines [Sun et al., 2005]. [25] Regarding the practical frequency shift of BLC, a scale 81% size reduction is newly evaluated. Comparison of miniaturization performance of the BLCs between this paper and previous works is highlighted in Table 2. To the

[26] It has been successfully proved that the combined technology of CRLH TL and fractal geometry results in a more compact subwavelength particle after the research of two types of CRLH cells using S‐CCSSRR and ML‐ CSRRs. The S‐CCSSRR‐loaded cell is intrinsically balanced when length of vertical branches and center pole is identical and features an additional shunt branch (transmission zero) in the circuit model which in turn enhanced the out‐of‐band suppression and design flexibility to a great extent. The super compactness is the major merit of the ML‐ CSRRs‐loaded cell. The applicability of these CRLH cells is demonstrated by two compact prototype devices. Advantages of the combined technique have qualified it as a good strategy and an innovative concept in compact microwave devices design. [27] Acknowledgments. This work is supported by the National Natural Science Foundation of China under grant 60971118.

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