Compact DualBand ThreeWay Metamaterial PowerDivider with a Hybrid CRLH PhaseShift Line
 Author: Jang Kyeongnam, Kahng Sungtek, Jeon Jinsu, Wu Qun
 Organization: Jang Kyeongnam; Kahng Sungtek; Jeon Jinsu; Wu Qun
 Publish: Journal of electromagnetic engineering and science Volume 14, Issue1, p15~24, 00 March 2014

ABSTRACT
A compact dualband threeway metamaterial power divider is proposed that has three inphase outputs. Fully printed composite rightand lefthanded (CRLH) unequal and equal power dividers are first implemented for 900MHz and 2.4GHz bands with the powerdivision ratios of 2:1 and 1:1, respectively. An initial 1:1:1 power divider is then achieved by incorporating the input of the twoway equal block into an output of the unequal block, and trimming the interconnection parameters. The condition of an identical phase at the three outputs of the power divider is then met by devising a hybrid CRLH phaseshift line to compensate for the different phase errors at the two frequencies. This scheme is confirmed by predicting the performance of the power divider with circuit analysis and fullwave simulation and measuring the fabricated prototype. They results show agreement; the inphase outputs as well as the desirable powerdivision are accomplished and outdo the conventional techniques.

KEYWORD
Delay Line , DualBand , Metamaterial , PhaseShift Line , Power Divider , SizeReduction.

Ⅰ. INTRODUCTION
Every wireless communication system incorporates microwave power dividers, couplers, filters, and relevant parts [15]. In particular, since one path has to be branched (i.e., as found in an array antenna or comparator), the power divider is required at the junction between the route on one side and several ways on the other side. The rapid growth of the telecommunication industry has prompted microwave technologies to push the envelope to meet users’ demands, and power dividers have been developed to cope with the multiple bands for system integration, wide bands for broadband service, etc. [6,7]. While achievements have been made in diversified and upgraded functions of the radiofrequency (RF) equipment, the constraints placed on the physical size have become the developers’ main concern. The response to these design priorities has been to focus a great amount of research on the production of sizereduced advanced power dividers, created by bending and folding, cascaded multi stages, grid array, slot coupling between layers, RLC loads, etc., without loss of generality [811].
These conventional techniques, although prevalent, have the limitation of loss from multiple stages, restrictions in embedding a confined space, and higher cost due to stackup fabrication. Alternative methods have been sought to iron out these problems, which have attracted substantial attention from the RF community [1216]. For example, Caloz and Itoh [12] introduced composite right and lefthanded (CRLH) transmission lines; their attempts to realize the thenfancy phenomena of the backward wave, lefthanded propagation, nonlinear dispersion, and zeroth order resonance (ZOR) resulted in a long periodic geometry that comprised 24 cells of distributed elements [12]. They successfully demonstrated its metamaterial characteristics, but this geometry was too large for incorporation into a device. Hence, many cells of lumped elements were cascaded in series to generate +90° or 90° and were attached to the arms of couplers and power dividers. Similarly, Marques et al. [13] formed a pair of slot rings under each of the arms of the Wilkinson power divider for the purpose of reducing the overall size. Inoue et al. [14] introduced an LTCC CRLHtype component similar to the lumped elementbased multiple cells. A printed and small power divider with a metamaterialinspired Tjunction was shown by Saenz et al. [15], but it lacked a theoretical aspect, and its applicability to current challenges is doubted.
This paper proposes an improved method for fabrication of a smaller and more advanced component that will overcome the drawbacks of earlier metamaterial and ordinary approaches. A novel threeway dualband CRLH power divider is designed to have a very small footprint and the equal power division and inphase outputs. Differing from [16], a CRLH and short threeway dualband power dividing structure is presented that provides a dualband phaseerror correction line. The solution process starts from the separate implementation of the 2:1 unequal and 1:1 equal power dividing blocks that are fully printed and metamaterials. This is followed by plugging the inputs of the equal block into an output of the unequal block for an initial 1:1:1 power divider, and slightly tuning the interconnection segment. This initial configuration and its possible modification inevitably give rise to phase errors between the outputs. Hence, we need a phase compensation line that works for the dualband objective, but this is difficult to obtain only with the ordinary delay line for the single band or its harmonic relations. The dualband phase compensation is accomplished by a hybrid CRLH phaseshift line as a mixture of the distributed and lumped elements, for the sake of efficiency and convenience. The design method is validated by evaluating the proposed metamaterial structure by circuit analysis and fullwave simulation in the solution process. This novel 1:1:1 power divider is manufactured through a lowcost fabrication with an inexpensive cheap substrate and its performance is measured to confirm its desirable power division ratio and equalized phases at the output ports, especially considering that its physical placement is friendly to RF system layouts. Its sizereduction effect and technical applicability are also addressed.
Ⅱ. THE PROPOSED CIRCUIT CONFIGURATION AND DESIGN OF ELEMENTARY BLOCKS
A novel, compact threeway power divider with CRLH characteristics is schematized in the following figure and compared to three examples that used other techniques.
Fig. 1(a) shows the composition of the proposed structure. The unequal power divider block is sequentially combined with the equal block, and both blocks are realized as printed CRLH devices with small footprints. Fig. 1(b) is an extension of the Wilkinson power divider to three ways, but has a single band. Elongated segments are added to the first stage in Fig. 1(c), and four stages are placed in chain in Fig. 1(d). Fig. 1(b)(d) heavily depend on the quarterwave long arm for each stage, with extra delay lines, but fail to achieve effective sizereduction. However, since a dualband CRLH phaseshift line will be substituted for the singleband and quarterwave long arms of the traditional Wilkinson power divider, Fig. 1(a) will be appropriate for the present objective.
The equivalent circuit of the aforementioned phaseshift lines for the dualband unequal and equal power divider blocks shown in Fig. 1(a) is set up as follows.
Fig 2(a) is used to create phase
Φ _{1} for a lower frequencyf _{1} and phaseΦ _{2} for a higher frequencyf _{2}, where the ratio off _{2} tof _{1} is arbitrary due to the occurrence of the nonlinear dispersion curve. These phases and frequencies yield simultaneous equations containing the circuit elements, and mathematical manipulation rendersL ’s andC ’s as given in the equations [16].where
ω _{1} = 2πf _{1} andω _{2} = 2π f _{2}, andZ_{c} becomesZ_{k} _{1} for one path andZ_{k} _{2} for another path in an unequal power divider. In the present case, applyingΦ _{1} = +90° atf _{1} = 960 MHz andΦ _{2} = 90° atf _{2} = 2.4 GHz to Eq. (1) for Fig. 2(a) results in the CRLH phaseshift line of the following data.Fig. 3(a) shows the phase as desired after applying
Φ _{1} = +90° atf _{1} = 960 MHz andΦ _{2} = 90° atf _{2} = 2.4 GHz. This implies that this CRLH phaseshift line can be substituted for the quarterwave long arms for the dualband performance. Fig. 3(b) of the dispersion diagram presents the LH region includingf _{1}, the ZOR, and the RH region includingf _{2} as a metamaterial property. This phaseshift line is input into the upper and lower paths of the dualband unequal power divider as shown in Fig. 2(b). The characteristic impedance for each path is obtained with the following formulae, once we decide upon the power division ratio.Keeping in mind the connection to the equal block afterwards (to make the threeway power divider), the present unequal block should have the power division ratio of 2:1 with
Z_{k} _{1} = 51.5 Ω andZ_{k} _{2} = 103 Ω. These impedance values are input into Eq. (1) with the previously mentioned phases, and the circuit elements of the phaseshift lines for both the paths are determined:C_{R}, C_{L}, L_{R}, andL_{L} are 4.7 pF, 2.0 pF, 5.9 nH, 2.5 nH in the 51.5Ω path, andC_{R}, C_{L}, L_{R} , andL_{L} are 2.4 pF, 1.0 pF, 11.8 nH, 5.0 nH in the 103Ω path. These lead to Fig. 3, in fact. The frequency response of the overall unequal block in Fig. 2(b), taking into account the CRLH phaseshift lines of Fig. 3, is observed by adopting the upcoming even and oddmode analysis techniques.Fig. 4(a) comes from Fig. 2, as ports 2 and 3 are excited with the inphase signals and the bisection line is treated as an opencircuited state. Fig. 2 becomes Fig. 4(b), in the assumption that the outofphase signals are fed into ports 2 and 3, and the axis of antisymmetry is considered shortcircuited. This applies to both the impedance lines. The frequency response of Fig. 2(b) will be given in the form of Sparameters, and the Zparameters should be arranged for Fig. 2(a) and Fig. 4 in the first place. The series and shunt resonators in Fig. 2(a) are
With these, the diagonal and offdiagonal elements of the Zparameter matrix for the CRLH phaseshift line can be written as
The input impedance of the CRLH phaseshift line (the box in Fig. 4) is then obtained as
Z^{eK1}_{p1} simply equals Eq. (5) in the evenmode, as in Fig. 4. Simultaneously, in the oddmode case, the input impedance into the CRLH phaseshift line through
R ^{k1} from the output port becomeswhere
R ^{k1} meansR /(k ^{2}+1).For the equal block,
Z _{k1} (=Z _{k2} =Z_{C} ) becomes 70.7 Ω.As long as the impedance matrix is completed, the corresponding
S parameters can be expressed as follows.All the necessary
S parameters are described mathematically on the basis of the primaryZ parameters from Fig. 4 and the secondary ones of Eqs. (3)(6). This process works for the unequal block, and also for the equal one. Therefore, theS parameters are plotted as the frequency responses of the unequal and equal dualband power dividers.The predicted performance of the 2:1 unequal power divider is shown in Fig. 5(a), where 
S _{21} is 4.7 dB and 1.7 dB at 960 MHz and 2.4 GHz, as desired. S _{21} is equal to S _{31}, and the result of our code for the derived equations overlaps that of the commercial circuit analysis tool. Likewise, Fig. 5(b) shows a perfect agreement between the coding and the commercial program, and S _{21} = 3 dB and S _{31} = 3 dB as the 1:1 power division at the two target frequencies. The mathematical derivation has been validated and these elementary blocks are incorporated for the 1:1:1 power division.Ⅲ. THREEWAY DUALBAND POWER DIVIDER BY COMBINING THE TWO BLOCKS AND PHASE CORRECTION BY A HYBRID CRLH LINE
In this section, the unequal and equal blocks are interconnected to form the three equal outputs, and realized and tested in a fullwave simulation. One output is different from the remaining outputs in terms of phase for each of the two frequencies; therefore, the phase correction will be attained in an efficient way.
The unequal and equal powerdividing circuits of Figs. 4 and 5 are physically implemented by following the steps of [16] to consider fullprinting, and the input of the equal block is fed by the output of the 103Ω path of the unequal dualband power divider.
Fig. 6(a) and (b) illustrate how to connect the unequal dualband power divider to the equal block. In accordance with this scenario, the initial shape of the fully printed CRLH threeway dualband power divider is presented as in Fig. 6(c). The geometrical parameters of the two blocks remain almost unchanged from those of the structure of the 1:1:1 powerdivider except for the addition of the connecting part: W, L1_L, W_F, L_F, L2_L2, G_F2, L1_L3, W_F3, L_F3, L, L2_L, G_F, L1_L2, W_F2, L_F2, L2_L3, and G_F3 in Fig. 6(c) are 30.6, 3.5, 0.4, 5, 5.3, 0.1, 3.1, 0.4, 5, 43.7, 7.5, 0.2, 3.5, 0.6, 5.6, 4.1, and 0.3 mm, respectively, with FR4 of
ε_{r} = 4.4 as the substrate. The guided wavelength of 960 MHz calledλ_{g} requires the lengths of the CRLH phaseshift lines for the 51.5, 103, and 70.7 Ω paths to be 0.038λ_{g} , 0.031λ_{g} , and 0.034λ_{g} in that order, which must be much less than 0.25λ_{g} of one Wilkinson’s stage. The electrical size of the total foot print of Fig. 6(c) is estimated as 0.173λ_{g} ×0.247λ_{g} , and its implication is a significant sizereduction effect compared with the Wilkinson’s power divider for the single band and its multistage applications for the dualband operation. The performance is presented with the following figures.In Fig. 7(a) and (b), equal power division to the 3 output ports is achieved with nearly 6 dB of 
S _{21}, S _{31}, and S _{41} at 960 MHz and 2.4 GHz, simultaneously in the electromagnetic (EM) simulation and measurement. Fig. 7(c) and (d) have S _{23}, S _{24}, and S _{34}, and S _{ii} below 12 dB atf _{1} andf _{2}, more or less. Nonetheless, while the phases ofS _{31} andS _{41} are the same, they differ from the phase ofS _{21} as marked in Fig. 7(e). This causes the loss of a benefit of the inphase outputs of the standard power divider. The location of port 2 in Fig. 6 also looks neither natural nor adaptable to RF cabling and harnessing. Therefore, the phase discrepancy with different values at 960 MHz and 2.4 GHz should be fixed by considering a change in the position of port 2. The fact that port 2 is located on the opposite side of ports 3 and 4, and off the extension line from port 1 in Fig. 6(b) means that it can be made friendly to the system cabling and integration by moving it to the same side as port 4, as an optimal choice. Assuming this positioning plan for port 2, we need to assign a box and fill it with a device to compensate for the different phase errors at 960 MHz and 2.4 GHz. Before solving this problem, the phase errors at the two frequencies with regard to a new location of port 2 should be checked. The changed layout differs from Fig. 7(e) and is given below. If a line shorter than 39 mm is chosen for the connection box, the phase errors will be known, given the layout of the modified threeway power divider, as follows.The old port 2 in Fig. 7(e) is relocated, as shown in Fig. 8(a). A test line is inserted in the box to connect the output of the 103Ω path of the unequal block to the new port 2, and the phase errors (
ᐃ Φ _{1} andᐃ Φ _{2}) betweenS _{21} andS _{31} atf _{1} andf _{2} are found 14.5° and 168°, as observed in Fig. 8(b). A compact dualband phaseshift line forᐃ Φ _{1} andᐃ Φ _{2} is made by a hybrid CRLH structure comprising a distributed element as the RH segment and lumped elements as the LH segment, as shown in the inset of Fig. 8(c)Fig. 8(f). The RH segment is realized by a transmission line with L_R and W_L, while the two shortcircuited chips L and the series chip C are responsible for the LH segment. Following the procedures to determine L and C as the unequal and equal block realization using Eq. (1), L_R, W_L, L, and C for Fig. 8(c)Fig. 8(f) are calculated as 15 mm, 1.2 mm, 11 nH, and 1 pF, respectively, along with the following formulae regarding the RH segment.where
w ,t , andh mean the width and thickness of the metal signal trace, and the height of the microstripline substrate, in that order. This dualband hybrid CRLH phaseshift line attainsᐃ Φ _{1} atf _{1} andᐃ Φ _{2} atf _{2} as desired, and it is presented by the measured data in Fig. 8(c). Consequently, the phase errors of Fig. 8(d) and (e) are corrected, and the identical phases at the three output ports are accomplished as in Fig. 8(f). Its area is kept the same as 0.173λ_{g} × 0.247λ_{g} , which validates the miniaturization effect of the proposed scheme. The magnitudes of theS parameters of this final geometry are also plotted in Fig. 8(h)Fig. 8(j). The equal power division is achieved at the three output ports, although an insertion loss of around 0.5 dB from the ideal power of 4.7 dB occurs due to the accumulated dielectric loss of FR4 and the conduction loss of copper. The interport isolation is observed below 15 dB atf _{1} andf _{2}. In addition, a good impedance match is apparent at the ports, with a return loss below 15 dB at the two target frequencies. Lastly, the restriction of the ordinary delay line to meet only eitherᐃ Φ _{1} orᐃ Φ _{2} is described.The ordinary delay line is not able to achieve
ᐃ Φ _{1} andᐃ Φ _{2} at the target frequencies. The conventional delay line has the phase of a linear function; therefore, it works for a single band and its harmonics. In Fig. 9(a), the 169mm long delay line can make 14.5° atf _{1}, but fails to createᐃ Φ _{2} atf _{2}. In addition, a line of this length will also exceed the footprint of the proposed threeway power divider. The use of the 37.5mm long delay line also only satisfies 168° atf _{2}, but is forbidden atf _{1} forᐃ Φ _{1}. Therefore, our CRLH power divider outdoes the conventional components in that it results in a small size, but retains equal power division and inphase outputs based on the nonlinear dispersion properties.Ⅳ. CONCLUSION
This paper proposes a small sized threeway power divider with a 1:1:1 power division and inphase outputs to work for two frequencies. It consists of 2:1 unequal and equal dualband power dividers that are fully printed CRLH building blocks and incorporated to make a compact device to divide one RF input power into three ways. In particular, the phase errors between port 2 and ports 3 or 4 at 960 MHz and 2.4 GHz are observed in the initial threeway power divider, and they have been compensated for to equalize the output phases by designing a hybrid CRLH dualband phaseshift line. The suggested method is shown to be valid through circuit analysis based on the derived equations, a fullwave simulation, and the measurement of the fabricated prototype. The overall size is much less than that of Wilkinson and modified power dividers. This method is applicable to the designs of advanced power dividers.

[Fig. 1.] The topological or structural differences between the proposed and other power dividers. (a) Topology of the proposed power divider, (b) expanded Wilkinson, (c) United States Patent 7164903, and (d) a product of InStock Wireless Components, Inc.

[Fig. 2.] The equivalent circuits of the composite right and lefthanded (CRLH) phaseshift line (a) and the unequal power divider (b).

[Fig. 3.] The characteristics of the composite right and lefthanded (CRLH) phaseshift line: (a) phase and (b) dispersion diagram.

[Fig. 4.] The circuit models on (a) the evenmode and (b) oddmode.

[Fig. 5.] The circuit simulated frequency responses of the unequal and equal power dividers for the dualband application (a) Sparameters of the unequal block (b) Sparameters of the equal block.

[Fig. 6.] Cascading the two blocks and the layout of the threeway composite right and lefthanded (CRLH) power divider. (a) Scheme of connection, (b) equivalent circuit, and (c) topview.

[Fig. 7.] The fullwave simulated and measured results of the proposed dualband compact threeway power divider. (a) Sparameters from the electromagnetic (EM) simulation, (b) powerdivision performances, (c) interport isolation performances, (d) reflection coefficients, and (e) phases at the outputs.

[Fig. 8.] The threeway dualband power divider with a new location of port 2 and the insertion of the phase compensating hybrid composite right and lefthanded (CRLH) line for the inphase outputs. (a) Moving port 2, (b) phase errors (？Φ1 and ？Φ2) at f1 and f2, (c) ？Φ1 and ？Φ2 achieved by the phase correcting hybrid CRLH dualband line, (d) equivalent circuit of inphase power divider, (e) the phase correcting line added to the layout as the finalized threeway dualband power divider, (f) photograph of the manufactured prototype, (g) inphase outputs obtained, (h) power division, (i) isolation, and (j) return loss.

[Fig. 9.] Ordinary delay line forbidden at (a) ？Φ2 and (b) ？Φ1.