Fully Planar Implementation of Generalized Composite RightlLeft Handed Transmission Lines for Quad-band Applications

Miguel Dunin-Sindreu, Gerard Siso, lordi Bonache and Ferran Martin

GEMMAICIMITEC, Departament d'Enginyeria Electronica. Universitat Autonoma de Barcelona. 08193 BELLA TERRA (Barcelona), Spain. E-mail: Ferran.Martin@uab.es

Abstract - In this work, generalized composite right/left handed (CRLH) transmission lines are implemented in a fully planar configuration in coplanar waveguide (CPW) technology. These artificial lines exhibit two left handed (or backward) transmission bands and two right handed (or forward) transmission bands alternating, and are therefore of interest for the synthesis of quad-band microwave components. The lines are implemented by loading a host CPW with open split ring resonators (OSRRs) and open complementary split ring resonators (OCSRRs). Accurate circuit models of the different line elements, taking the parasitics into account, and the whole structure are experimentally validated. These lines are applied in this work to the design of a quad-band power divider operative at the GSM (900MHz and 1800MHz) and GPS (1176.45 MHz and 1575.42 MHz) frequency bands. The main innovative aspect of this contribution is the implementation of the reported quad­band structure in planar technology, without the presence of lumped components. This is also the first time that OSRRs and OCSRRs are combined for the synthesis of a quad-band structure.

Index Terms - Metamaterial transmission lines, split ring resonators, quad-band components, coplanar waveguides (CPW).

I. INTRODUCTION

Composite right/left handed (CRLH) transmission lines are artificial lines consisting on a host line loaded with reactive elements and exhibiting backward wave propagation at low frequencies and forward wave propagating at high frequencies. Such lines have been implemented in various technologies (including microstrip [1,2] CPW [3,4], LTCC [5] and MMIC [6], among others) by either loading the host line with series capacitances and shunt inductances (CL-Ioaded approach), or by loading the host line with electrically small resonators, such as split ring resonators, SRRs [7], or complementary split ring resonators, CSRRs [8] (resonant­type approach). Among the numerous applications of these CRLH lines, the implementation of dual-band microwave components, on the basis of impedance and dispersion engineering, has been very relevant [9-lO).

Recently, the concept of generalized CRLH line was introduced with the aim of increasing the number of transmission bands [11-13]. This is necessary to achieve multiband (rather than only dual-band) functionality. To this end, the host lines must be loaded with a larger number of reactive elements (as compared to the conventional CRLH lines), in order to generate the necessary zeros and poles (in

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the series and shunt reactances of the unit cell of the lines) to achieve multiple bands [13). One possible (although not exclusive) T-circuit model that may be used as the basis for the implementation of a quad-band transmission line is depicted in Fig. 1. In order to achieve quad-band functionality, four reactive elements for the series and shunt branch of the T­circuit model are required. Thanks to the presence of these eight elements, we have the necessary design flexibility to force the characteristic impedance (actually image impedance) and phase shift (electrical length) of the unit cell structure to the desired values at four arbitrary frequencies. This univocally determines the element values of the circuit of Fig. I. The resulting dispersion diagram (which exhibits two left handed bands and two right handed bands alternating) and image impedance (which is frequency dependent) will provide the design parameters (phase shift and impedance) at the operating frequencies, and each frequency will lie at a different transmission band. Using the scheme of Fig. 1, a quad-band impedance inverter, applied to the design of a Wilkinson power divider has been recently proposed [14]. The structure was realized in microstrip technology by combining semi-lumped (planar) and lumped components.

In the present paper, we report the implementation of a fully planar quad-band impedance inverter in CPW technology on the basis of the circuit of Fig. 1. Such artificial line, implemented by means of electrically small open resonators, is then applied to the synthesis of a quad-band power divider.

----�

Fig. I. Circuit model (unit cell) of the quad-band CRLH

transmission lines reported in [II].

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II. TOPOLOGY AND ACCURATE CIRCUIT MODEL OF THE QUAD­BAND CRLH TRANSMISSION LINE

The main purpose of this work is to implement quad-band CRLH transmission lines in a fully planar configuration. We have recently demonstrated [15] that dual-band components can be implemented in CPW technology by loading a host CPW line with series connected open split ring resonators (OSRR) [16] and shunt connected open complementary split ring resonators (OCSRRs) [17]. Since OSRRs and OCSRRs behave as open series and open parallel resonant tanks, respectively, the application of these particles to the design of CRLH transmission lines with dual-band functionality is straightforward (in spite of the presence of line parasitics) as was discussed in [15,18]. Moreover, OSRRs and OCSRRs are electrically small particles and hence such resonators are of interest to implement small size devices. Since the generalized model for quad-band CRLH lines of Fig. 1 contains series and parallel resonators in both series and shunt connection with the line, the physical implementation of the quad-band transmission line structure by using OSRRs and OCSRRs seems to be simple, as it was for the dual-band structures reported in [15,18]. However, depending on the element values of the different resonators, certain variations in the topology of the cited particles may be required, or, in some cases, it may be necessary to make use of other semi-lumped (i.e. fully planar) structures.

w

(a) (b)

w

( )

Fig. 2. Topology of the designed quad-band CPW impedance

inverters. The dimensions are: W = 4.5 mm, G = 0.524 mm, b = 3

mm. The width and separation of all the meanders is of 0.2 mm for

Fig.2(a) and 0.16 mm for Fig.2(b). For the design of Fig. 2(a): a = 2.8

mm, 1= 22.5 mm. For the series connected OSRRs, rext = 2.6 mm, C = 0.2 mm, d = 0.15 mm; for the shunt connected OSRR, rext = 2.5 mm,

C = 0.2 mm, and d = 0.2 mm; for the OCSRR, rext = 1.4 mm, C = 0.2

mm, and d = 0.6 mm. For the design of Fig. 2(b): a = 3.7 mm, 1 = 22.2 mm. For the series connected OSRRs, rexl = 2.8 mm, C = 0.3

mm, d = 0.2 mm; for the shunt connected OSRR, rexl = 2.5 mm, C = 0.16 mm, and d = 1.04 mm; for the OCSRR, rexl = 1.3 mm, C = 0.2

mm, and d = 0.5 mm. rexl, C and d are the extemal radius, width and

separation of the rings.

As a case study, we have considered in this work the implementation of a quad-band impedance inverter operative at the GSM (h = 0.9 GHz, it = 1.8 GHz) and the GPS (J; = 1. 17642 GHz, h = 1.57542 GHz) frequency bands. The characteristic impedance has been forced to be 35.35Q at

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these frequencies, in order to subsequently implement a quad­band Y-junction power divider as a proof of concept demonstrator. The electrical length of the structure is forced to be -900 (left handed bands) at the odd frequencies, and +900 (right handed bands) at the even frequencies. The values of the circuit model corresponding to Fig.l that satisfy these conditions are: Llls = 22.458 nH, Chs = 0.766 pF, LhP = 0.883 nH, CliP = 14.06 pF, Lvs = 8.785 nH, Cvs = 1.4 14 pF, Lvp = 1.915 nH, Cvp = 8.986 pF. With these line parameters and frequencies, the element values have forced us to implement the parallel resonators of the series branch by parallel connecting a capacitive patch and a meander inductor. However, the other resonators are either OSRRs or OCSRRs. The topology of the final quad-band impedance inverter is depicted in Fig. 2(a).

In a first order approximation, the structure of Fig. 2(a) can be described by the generalized CRLH model shown in Fig. 1. However, for an accurate description, line parasitics must be taken into account, as was done in [15,18] for the description of dual-band CRLH lines implemented by combining OSRRs and OCSRRs. Thus, the accurate circuit model of the quad-band CRLH line of Fig. 2(a) is that depicted in Fig. 3.

2Lhp (b) (a) LIMI2 2C�

_ ----

--�. Lj� i--I

C, Clip 12 I

C2

'=' -=

L L

Cvp

Fig. 3. Accurate circuit model for the structure of Fig. 2 divided

in the series branch (a) and shunt branch (b).

The procedure to determine the layout is as follows. In a first step, we determine the element values of the generalized quad-band CRLH model of Fig. 1. To this end, we force the complex propagation constant, given by

Z (OJ) cosh;i = 1 +_s

- (1) Zp(OJ)

(where Zs(m) and Z/m) are the series and shunt impedances of the T-circuit model of the generalized CRLH line) to be purely imaginary at the design frequencies and to provide a

phase shift of -900 at hand h' and +900 at h and it. Simultaneously, the characteristic impedance, given by

ZB =�Zs«(j)[Zs«(j)+2Zp«(j)] (2)

is set to 35.35Q at the four design frequencies. From this, we obtain 8 equations, and the element values are univocally determined. Once the element values are known, we obtain the layout of each section so that the element parameters (inferred from curve fitting) of the resonators coincide with those of the generalized model of Fig. 1. By doing this, we also obtain the values of the parasitic elements. The next step is to tune the resonator values in the electrical model of Fig. 3 until the required values of impedance and phase at the operating frequencies are obtained (this is simple and fast because this is done at the circuit level). Finally, we modify the topology of the different resonators at the layout level in

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order to fit the electromagnetic simulation of each section of the structure to the circuit simulation. This is simple because the variation of the element values in the tuning procedure of the previous step gives us the guide to modify the geometry of the different resonators (this does not affect substantially the effects of the parasitics). With this, we directly obtain the layout of the whole structure which provides the required values of characteristic impedance and phase at the operating frequencies. No additional tuning or optimization is required. The resulting layout of the quad-band impedance inverter is that depicted in Fig. 2(a). The electrical size of the device is 0. 105I!.xO.074A, I!. being the guided wavelength at the lower frequency band (900 MHz). The considered substrate is the Rogers R030JO with thickness h = 0.254 mm, dielectric constant 10, = 11.2 and loss tangent tan8 = 0.0023.

III. RESULTS

The simulated S-parameters of the designed impedance inverter, using port impedances of 35.350, are depicted in Fig. 4. Both the electromagnetic (without losses) and circuit simulation (inferred from the Agilent ADS commercial software) are included in the figure. The simulated phase response and characteristic impedance of the designed quad­band impedance inverter are depicted in Figs. 5 and 6, respectively. The agreement between the electromagnetic and circuit simulation is good, and the required functionality of the impedance inverter is achieved at the whole operating frequencies in a good approximation. Thus, the proposed model of Fig. 3 is validated from these results.

11'-iii -20 � (/)" -30

Frequency (GHz) Fig. 4. Insertion and return losses corresponding to the structure

of Fig. 2(a). The values of the elements corresponding to the Fig.3 are: Lh, = 21 nH, Ch, = 0.775 pF, Lhp = 0.88 nH, ChP = 13.96 pF, L", =

8.8 nH, C", = 1.41 pF, L"p = 1.95 nH, C"p = 8.3 pF, C] = 0.41 pF, C, =

0.22 pF, L = 0.4 nH.

In order to implement an V-junction power divider, we have added two 500 access lines to the output port of the impedance inverter and a 500 access line to the input port. The resulting quad-band power divider is shown in Fig. 7. This device has been fabricated by means of a photo/mask etching technique, and its performance has been measured by means of an Agilent E8364B vector network analyzer. The simulated and measured power division and matching are depicted in Fig. 8.

Finally, in Fig.2 (b) it is shown the topology of another quad-band impedance inverter operative at the same GSM and

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GPS frequencies of Fig.2 (a) but with band guards of 30 MHz to the left and to the right of the h' hand h' h frequencies, respectively. Thus, we can cover the operational bandwidth of the GSM and GPS signals. The electrical size of the device is 0. 104I!.xO.082A, I!. being the guided wavelength at the lower frequency band (900 MHz). In Fig. 9 is shown the measured and simulated power division and matching of a power divider (not shown) implemented with this impedance inverter.

IV. CONCLUSIONS

In conclusion, we have proposed a novel type of quad-band CRLH transmission lines based on OSRRs and OCSRRs. These lines have been successfully applied to the design of a quad band Y -junction power divider. The small size and the compatibility with planar technology (lumped elements are avoided) are the more relevant aspects of these structures.

180 c-:------.,---:-----�

Ci 90 CII � CII gj 0

.t: ll-

(/)" -90

-180 ":---'.-,-'.,--_-:-'c:--�-c'-:: __ _:_':_--.J 0.6 0.9 1.2 1.5

Frequency (GHz) Fig. 5. Phase of the transmission coefficient for the structure of Fig. 2(a). Notice that it exhibits opposite sign to the electrical length.

The target values at the desired frequencies are indicated.

§: CII 90 o c::: ., 75 -c CII Q. 60 .5 o 45 � .;:: � E ., .t:

() 1.0 1.2 1.4 1.6 Frequency (GHz)

Fig. 6. Dependence of the characteristic

frequency for the structure of Fig. 2(a).

-�

, -_.

- -

1.8

impedance with

Fig. 7. Photograph of the fabricated quad-band Y -junction power divider implemented by means of the inverter of Fig. 2(a).

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0 m � -10 err m -20 �

;;; -30 C/') m � -40

OJ C/') -50 - - - -531 Meas.

0.9 1.2

-511.521 Meas. ...... S". S" EM Sim.

1.5 1.8 Frequency (GHz)

Fig. 8. Simulated and measured power division and matching for

the device of Fig. 7.

O ,,�----������--�r--. m � -10 C/')-m -20 � C/')M -30

m -40 � OJ C/') -50

0.9 1.2 1.5 1.8 Frequency (GHz)

Fig. 9. Simulated and measured power division and matching for

the power divider based on the impedance inverter of Fig. 2(b). The

band guards are indicated in the figure.

ACKNOWLEDGEMENT

This work has been supported by MEC-Spain (contract TEC2007 -680 13-C02-02 MET AINNOV A), Generalitat de Catalunya (project 2009SGR-421) and MCI-Spain (project CONSOLIDER EMET CSD2008-00066).

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