Coupling Enhancement of Composite-Right/Left-Handed Loop Resonators for Filter

Applications

Humberto Lobato-Morales, Ricardo A. Chávez-Pérez, and José L. Medina-Monroy Electronics and Telecommunications Department, Centro de Investigación Científica y de Educación Superior de

Ensenada, CICESE, B. C., Mexico

Abstract—An enhanced method for the coupling of Composite-Right/Left-Handed (CRLH) loop resonators for filter design is presented in this paper. The proposed coupling mechanisms take advantage of the natural distribution of the E- and H-fields on a CRLH loop resonator, while maintaining the advantages in miniaturization and harmonic resonance suppression of such structures. For demonstration of the concept, two filters operating in the GSM-850 band are designed, fabricated and tested experimentally. Good agreement between the simulated and measured results is obtained.

Index Terms—Microwave Filters, Composite-Right/Left-Handed (CRLH), Loop Resonators, Planar Filters.

I. INTRODUCTION INCE the development of the Composite-Right/Left-Handed (CRLH) circuits in its planar form, several

microwave devices have been designed, including resonators, filters, antennas, among others, showing the main advantages of miniaturization and harmonic band suppression they provide [1]. Particularly for microstrip bandpass filter design, proposals using linear CRLH resonators operating in the zeroth-order mode are found in the literature [1]-[3]. In order to mention some of them, in [2] a three-pole filter is presented with good out-of-band performance; however, it consists on the coupling of different-dimension resonators (asymmetric coupling), adding a level of complexity in the design. A three-pole filter with resonator coupling on the top and bottom layers of the substrate is presented in [3] showing a wide bandpass response; however, it presents close adjacent bands produced by lower- and higher-order modes which are usually undesired for the real applications.

Different from the CRLH resonator in its linear form, the microstrip CRLH resonant loop is proposed and analyzed in [4], formed by closing a metamaterial transmission line in which the zeroth-order resonance and higher-order modes can be allocated with high flexibility due to the characteristic phase response of CRLH lines [1], [4]. The CRLH loop resonator have been proposed for filter design in [5] and [6], showing miniaturization of the structures and harmonic resonance elimination, which are highly desired for communication applications. However, due to the configuration of the closed CRLH loops, difficulties in the coupling arise and additional large linear structures must be

used, which in turn generate undesired resonances and can cause interference within the operating passband or even outside [5]-[7]. An approach in the coupling improvement with this kind of resonators can be seen in [8], where a four-pole filter is proposed exploiting the dual-mode capacity of the loops; however, no full analysis on the coupling mechanisms neither resonator losses are presented.

A method for the coupling enhancement of CRLH loop resonators for filter design is presented in this paper, which is based on the natural distribution of the E- and H-fields on the resonator. Two bandpass filters for mobile communications are designed using the proposed coupling scheme without the use of additional complex structures and keeping the advantages of low dimensions and harmonic suppression.

The paper is organized as follows: Section II describes the CRLH loop resonator and the proposed coupling mechanisms; design of the filters are presented in Section III; results and discussion are exposed in Section IV.

II. COUPLING OF CRLH LOOP RESONATORS

A. Design of the Resonant Loop As mentioned before, a CRLH loop resonator can be

formed by closing a metamaterial transmission line having a particular phase response. Particularly, the zeroth-order mode is preferred because it allows a resonator to operate at a specific frequency with significant low dimensions, compared with conventional λg closed loop resonators or even linear λg/2 resonators (being λg a guided wavelength) [1], [4]-[6]. This mode is obtained when the total phase along the loop CRLH = 0° by cancellation between the LH (Left-Hand) and RH (Right-Hand) phase propagations, LH and RH, respectively [1], [4], as stated in

22

effCRLH LH RH

L L

N f dcf L C

εφ φ φ π

π= + = − , (1)

where N is the number of LH unit-cells, LL and CL inductor and capacitor values of the LH part; d is total length of the RH line and εeff corresponds to the dielectric effective permittivity of the used substrate; f is frequency in evaluation and the

S

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velocity of light in a vacuum is stated as c. The reader is referred to [1] for details in the design of CRLH microstrip structures.

(a)

(b)

Fig. 1. Proposed CRLH loop resonator (a) geometry, (b) frequency response.

A CRLH loop resonator is designed to operate with a center frequency f0 = 0.85 GHz, which corresponds to the GSM-850 mobile communications band. The LH part consists of a two unit-cell transmission line designed with SMC (Surface-Mount-Component) series capacitors and shunt-stub inductors, and the RH part is simply a conventional 50 Ω transmission line [5], [6]. For coupling purposes, as will be shown later, the LH part is located only along one side of the loop. A Rogers® UL2000 substrate with relative dielectric permittivity εr = 2.6, tanδ = 0.0022, and height h = 1.524 mm is used for the design of the resonator. The geometry of the proposed resonator and its simulated frequency response S21 [9] are shown in Fig. 1. The E-field distribution at the zeroth-order and 1st-order resonances are included in the inset of Fig. 1(b).

For the zeroth-order resonance, although an infinite wavelength λg is theoretically predicted [1], [4], the distribution of the LH and RH parts along the loop resonator allows the E-field to concentrate on the RH transmission line section, and the H-field in the LH shunt stub inductors. Taking advantage of this effect, electric E- and magnetic H-couplings can be clearly defined and can be used to design a complete bandpass filter with the combination of both schemes following the widely-used resonator coupling method based on the external quality factor Qe (input and output resonators) and k coefficients (inter-resonator couplings) [7]. As seen in Fig. 1(b), the 1st-order (spurious)

resonance is far from the operating frequency more than 2.5 times and can be even farther with a correspondent design [4]; the E-field distribution at this frequency point (2.16 GHz) shows one complete wavelength along the loop [4].

(a)

(b)

Fig. 2. E-field distribution of the resonator (a) for Qe, (b) for k.

B. Electric Coupling As the E-field is concentrated in the RH part of the CRLH

loop, an electric E-coupling by means of two branched narrow lines can be used to feed the resonator with the input/output ports, as seen in Fig. 2(a). The external quality factor Qe (see Fig. 4 below) can then be adjusted by varying the length of the coupling lines dl. Distance between the coupling lines and the resonator is of 0.4 mm. Similarly, the inter-resonator coupling is obtained by proximity of two resonators with one of the RH sides of each, as seen in Fig. 2(b); by modifying the gap g between the loops, the k factor can be adjusted.

The EM interaction of two adjacent equal resonators (symmetric coupling) produce two resonances close to each other (see Fig. 4 below) [7]. In the coupling analysis, these frequencies arise from two conditions: first, an E-wall is virtually inserted along the symmetry plane producing the resonant frequency fe; second, a virtual H-wall along the same plane generates the resonance fm [7]. The inter-resonator E-coupling coefficient can be obtained by

2 2

2 2m e

Em e

f fk

f f−

=+

. (2)

In this case, insertion of the E-wall increases the capability to store charge of the resonator while the H-wall reduces it, producing fm > fe [7].

C. Magnetic Coupling A region with high concentration of the H-field occurs in

the LH part of the resonator, specifically, along the shunt stub inductors; thus, a magnetic H-coupling of the resonator can be obtained by using direct contact or proximity of such

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elements. The coupling schemes for Qe and k are displayed in Fig. 3 with the H-field distribution on the loop resonator.

(a)

(b)

Fig. 3. H-field distribution of the resonator (a) for Qe, and (b) for k.

For the type of coupling in Fig. 3(a), the Qe factor (Fig. 4) can be adjusted by varying position of the taps tp of the input/output port which are in direct contact (strong coupling) with the shunt stub inductors. Having two equal CRLH loop resonators, it is possible to adjust the k coefficient by changing the separation between the stub inductors s, as seen in Fig. 3(b).

Similarly as for the E-coupling, the magnetic inter-resonator coupling coefficient can be calculated by

2 2

2 2e m

Me m

f fk

f f−

=+

, (3)

for which fe corresponds to the resonant frequency of the circuit when an E-wall is inserted in the symmetry plane reducing the stored flux in the resonator, and fm when an H-wall is inserted in the same plane increasing the stored flux; thus, fe > fm [7].

D. Quality Factors The useful quantity to estimate the losses in a microwave

resonator is the unloaded quality factor Qu [7]. Usually, the Qu value of a microstrip structure includes conductor, dielectric, and radiation losses [10]; however, for the proposed structure, quality factors of the SMC capacitances Qcap must be included:

1 1 1 1 1

u c d r capQ Q Q Q Q= + + + , (4)

where Qc, Qd, and Qr, refer to conductor, dielectric and radiation quality factors, respectively.

In simulations [11], the CRLH loop resonator is weakly coupled by means of a large gap with the input and output ports in order to satisfy the unloaded condition and allowing

Qu to be directly estimated. Conductor, dielectric, and radiation loss mechanisms are configured separately in simulations; the S-parameters of the SMC capacitors (provided by the manufacturer [12]) are included. The correspondent Q values are obtained from the transmission losses S21 curve of the frequency response using the generalized expression

0

3dB

fQ

f=

Δ, (5)

where f0 is the resonant frequency and Δf3dB corresponds to the 3dB bandwidth (see Fig. 4) [7]. The different Q factors of the resonator are tabulated in Table I.

TABLE I QUALITY FACTORS OF THE CRLH LOOP RESONATOR

Qu Qc Qd Qr Qcap 114.07 230.88 890.70 17,243 307.27

As noticed from Table I, the lowest loss mechanism is attributed to radiation (highest Q), as desired in microwave filters. The obtained Qcap value is in agreement with that provided by the SMC capacitor manufacturer in the datasheet [12]. The highest losses are produced by the conductor material (copper layer of thickness 17 μm). Although the inclusion of the SMC components add a level of energy loss, the unloaded quality factor Qu is still within good values for a microstrip structure, which strongly depends also on the choice of the dielectric substrate characteristics (dielectric permittivity and height), and the frequency of operation [7], [10].

III. FILTER DESIGN To demonstrate the capability of the CRLH loop resonator

for filter design, two 2nd-order Chebyshev bandpass filters are proposed operating at a center frequency f0 = 0.85 GHz, with a fractional bandwidth FBW = 0.03 (3 %) and ripple of 0.1 dB. The filters are designed and fabricated using the same Rogers® UL2000 substrate with which the resonator is designed and analyzed in the previous section.

A. Coupling Parameters The required filter coupling parameters [7] (input/output Qe

and inter-resonator k coefficient) can be calculated using

0 1e in

g gQ

FBW− = , 2 3e out

g gQ

FBW− = , and (6a)

121 2

FBWkg g

= , (6b)

where the elements g0 to g3 are the lowpass filter parameters and are directly taken from [7], throwing the quantities Qe-in = Qe-out = 28.22, and k12 = 0.0413.

In simulations [11], a parametric analysis is carried out for Qe and k following both E- and H-coupling schemes; lossless materials and the S-parameters of the SMC capacitors are configured. From the S21 responses, Qe is estimated using (5)

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having the single resonator strongly coupled to the input/output port and weakly coupled to the second port in evaluation. For the k coefficient (2) or (3) can be used depending upon the case or simply the generalized expression shown in the inset of Fig. 4, having both resonators weakly coupled to the input and output ports [7]. The obtained results are shown in Fig. 5.

Fig. 4. Extraction of Qe and k from the simulated transmission loss S21.

(a)

(b)

Fig. 5. Simulated coupling parameters (a) Qe, and (b) k.

Based on the coefficients in Fig. 5, Filter-1 is designed with E-coupled Qe and H-coupled k; initial values of the coupling line length and separation between the stub inductors of the resonators are dl = 20 mm and s = 1.6 mm, respectively.

Filter-2 is based on an H-coupled Qe and E-coupled k; initially, tap position and gap between the resonators are tp = 2.4 mm and g = 0.4 mm, respectively. Geometries of the filters are shown in Fig. 6; as noticed, their shapes and parameters present symmetry as there is only one k to adjust, and Qe-in = Qe-out. Total dimensions of both are 94 mm x 60 mm.

Fig. 6. Geometries of Filter-1 and Filter-2.

An optimization process is carried out in simulations, and the final values of dl and g for Filter-1 are 21 mm and 1.6 mm, respectively; while for Filter-2, tp = 2.2 mm and s = 0.4 mm.

IV. RESULTS AND DISCUSSION The filters are fabricated and tested experimentally using a

Keysight PNAX-series Vector Network Analyzer. The simulated (including material losses) and measured responses of the proposed filters are displayed in Fig. 7; photographs of the structures are also included in the correspondent inset.

For Filter-1, the measured center frequency is 0.81 GHz while the simulated is at 0.83 GHz; a shift of 20 MHz is observed; transmission losses in the passband result of 2.49 dB and 2.17 dB for the experiments and simulations, respectively. The measured bandwidth (at 3 dB) is of 4.98 %.

For Filter-2, the measured and simulated center frequencies are of 0.838 GHz and 0.844 GHz, respectively, having a difference of only 6 MHz. The measured transmission loss results of 1.53 dB, while the simulated is of 1.99 dB; the measured 3-dB bandwidth is of 5.59 %.

As seen in the results displayed in Fig. 7, a higher discrepancy between the measured and simulated structures is obtained for Filter-1, and is attributed mainly to the proximity of the coupling lines which slightly increases the virtual size of the loops lowering the resonant frequency; manufacture tolerances and differences in the S-parameters of the SMC

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capacitors used in simulations also contribute to such variations in both filter designs. Higher transmission and bandwidth are observed for Filter-2 due to the direct coupling of the resonators with the correspondent input/output ports (in contrast with Filter-1 which makes use of a gap coupling).

(a)

(b)

Fig. 7. Frequency responses and photograph of (a) Filter-1, (b) Filter-2.

The measured wideband responses of the filters are plotted in Fig. 8 showing the spurious frequencies (no harmonics) occurring at 2.2 GHz. For comparison purposes, dimensions of a single conventional loop resonator operating at 0.85 GHz over the same substrate result of 66 mm x 66 mm, while the proposed resonator occupies an area of only 33 mm x 38 mm, which represents a miniaturization of 71 %, as seen also in the inset of Fig. 8.

A weak spurious band is observed for Filter-1 appearing at 2.2 GHz, while for Filter-2 the same spurious results of higher magnitude. Allocation of these bands (spurious) can be properly changed in frequency (while maintaining the operating band) following the correspondent CRLH resonator design [1], [4]. In this work, the spurious band of Filter-2 cannot be treated as a second passband as the filter parameters (Qe and k coefficients) are achieved only for the fundamental

frequency band of 0.85 GHz, and they cannot be optimized separately for the different resonances. Apart from the desired and spurious bands, no other resonances (parasitic) are appearing.

Fig. 8. Wideband response of the filters and comparison of resonator dimensions.

Due to their small dimensions and low-loss passband, the presented filters based on the CRLH loop resonators result ideal for mobile communication applications as that allocated in the GSM-850 band. Moreover, the presented coupling schemes can be applied for the design of higher-order filters to increase selectivity and bandwidth of the correspondent channels.

V. CONCLUSION

The CRLH loop resonator with enhanced coupling schemes based on H- and E-field distributions have been presented. Two filters based on the proposed couplings and resonator have been designed for demonstration of the concept. The resonator has been analyzed in terms of its different Q factor and loss mechanisms. Measured and simulated responses have been obtained showing good performance and high agreement between them. Due to the mentioned characteristics, the proposed resonator and filters are good candidates for use in wireless mobile communications.

ACKNOWLEDGMENT The authors are pleased to thank technician René A. Torres-

Lira for his contribution in the fabrication of the prototypes.

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