диафрагмированные волноводные фильтры / 09d112e5-0298-41b2-97df-92f9c6a4ccfa

Abstract – Split-ring resonators (SRR) are used both in microstrip and waveguide metamaterial structures to obtain negative values of permeability, whereas complementary splitring resonators (CSRR) result in negative permittivity when placed below the microstrip. While the orientation of SRR positioned next to the microstrip transmission line significantly influences its performances, it is generally accepted that such dependence does not exist in the case of CSRR-loaded microstrip or SRR-loaded waveguide. In this paper, we show that SRR and CSRR can not be arbitrarily orientated, neither in microstrip nor in waveguide structures. The influence of the orientation is especially visible in the case of multiple CSRR geometries. To validate simulation results, microstrip lines loaded with multiple CSRRs were designed, fabricated and measured.

Keywords – Metamaterials, Left-handed lines, Split-ring resonators.

I. INTRODUCTION

Metamaterials have recently attracted considerable attention because of their unusual magnetic and electric properties, generally not found in nature. Metamaterials are artificial structures designed using unit cells with sub-wavelength dimensions, called particles, which exhibit extreme values of effective permittivity and permeability. A special sub-class of metamaterials are so called left-handed (LH) metamaterials, that simultaneously exhibit negative values of effective constitutive parameters.

The first particle that exhibits negative permittivity by decreasing the plasmon frequency into microwave range was proposed in mid nineties, [1]. Shortly afterwards, a particle called split-ring resonator (SRR) was introduced, that provides negative permeability at microwave frequencies, [2]. By combining these two structures, the existence of LH metamaterials was experimentally proved in 2001, [3]. In the years to follow, the configurations using SRRs have attracted a lot of attention, [4], [5].

In the microstrip technology, SRRs can only be etched on the upper substrate side, next to the transmission line. Such structure is a single-negative material, which exhibits only negative effective permeability. Using the Babinet principle, a complementary structure was proposed in [6], namely the complementary split-ring resonator (CSRR). CSRRs are etched in the ground plane, beneath the microstrip, and thus

contribute to the negative effective dielectric permittivity of the structure. In order to obtain LH behavior, effective negative permeability has to be introduced to the structure. This is achieved by periodically etching capacitive gaps in the microstrip line.

Apart from the microstrip technology, SRRs can be used in waveguides as well. A number of results have recently been reported in the literature, [7].

In this paper, the influence of the orientation of SRR and CSRR in both microstrip and waveguide structures is analyzed in detail. It is widely accepted that the orientation of the particle influences the performances only in the case of SRR-loaded microstrip lines. However, we will show that the orientation has to be taken into account in the design of all other metamaterial structures as well. The influence to the performances is especially visible in the case of multiple CSRRs, recently introduced in [8] with the aim of further miniaturization of the unit cells. To validate simulation results, LH microstrip lines with multiple CSRR were designed, fabricated and measured.

II.CONFIGURATIONS AND RESULTS

A.SRR-Loaded Microstrip Line

Microstrip line loaded with one SRR is shown in Fig. 1. The line is realized on a 1.27mm Taconic CER-10 substrate, with εr=9.8 and dielectric loss tangent equal to 0.0025. The outer dimensions of the SRR are equal to 5x5mm, while the SRR line width, spacing between the rings and the size of the splits are chosen to be the minimal available in standard PCB technology, i.e. equal to 100μm.

The orientation of the SRR in respect to the line has been changed, so that the split of the outer ring was placed in one of four positions: up (as shown in Fig. 1), down (next to the microstrip line), left and right. In the same time, the split of the inner ring was appropriately relocated.

1Vasa Radonić and Vesna Crnojević-Bengin are with the Faculty of Technical Science, University of Novi Sad, Trg D. Obradovića 6, 21000 Novi Sad. Serbia, E-mail: vasarad@uns.ns.ac.yu; bengin@uns.ns.ac.yu.

2Branka Jokanović is with the IMTEL-Komunikacije, 11070 Belgrade, Serbia, E-mail: branka@insimtel.com.

Fig. 1. SRR-loaded microstrip line.

The simulation results for all four configurations are compared in Fig. 2. As expected, the significant difference in the stop frequency exists only in the case when the outer split is positioned next to the microstrip (“down”). This can easily

be explained by simple analysis of the equivalent circuit of the structure, shown in Fig. 3, where the parallel resonant circuit with inductance Lr and capacitance Cr models the SRR and the host microstrip line is represented by the inductance L. The SRR is electrically coupled to the host microstrip line through the line capacitance Cc. By placing the outer split of the SRR next to the host microstrip, both capacitances Cr and Cc are changed, thus resulting in reduced value of the stop frequency of the structure.

Fig. 2. Simulation results for SRR-loaded microstrip lines with splits positioned at four possible locations.

Fig. 3. Equivalent circuit of SRR-loaded microstrip line.

B. Left-Handed Microstrip Line

In order to obtain left-handed behavior, two particles need to be combined in a single unit cell: one contributing to the negative effective permittivity of the structure, and the other resulting in negative effective permeability. A typical LH transmission line is shown in Fig. 4, which comprises of CSRRs etched in the ground plane and appropriately positioned capacitive gaps in the microstrip. Such line can be characterized as a narrow band pass filter.

Fig. 4. LH line with three unit cells: top (dark grey) and bottom (light grey) conductive layers are shown.

The equivalent circuit of the LH line is similar to the one shown in Fig. 3, except for additional series capacitance that

models the gaps in the host microstrip. However, in this case the change of orientation of the CSRR does not influence the values of capacitances Cr and Cc. This fact has led many researchers to believe that CSRRs can be oriented arbitrarily, with no influence to the performances of the structure.

In this paper, two different orientations of CSRR in respect to the microstrip are analyzed: Orientation 1, where splits are positioned in the direction perpendicular to the host microstrip line, and Orientation 2 where splits are positioned along the microstrip, depicted in Fig 5.

Fig. 5. Different orientations of CSRRs:

(a) Orientation 1, (b) Orientation 2.

Simulated responses of the proposed LH lines with two different orientations of CSRRs, are shown in Fig. 6. In the same figure, radiation loss is depicted as well, defined as:

Orientation 1

0.8

Orientation 2

0.6

ro

0.4

0.2

0

f [GHz]

(b)

Fig. 6. Simulation results for LH microstrip lines, for different orientations of splits: (a) s11 and s21 coefficients, (b) radiation loss.

It can be seen that the orientation of the splits influences the transmission coefficients in the terms of the pass band bandwidth, while the central frequency of the pass band remains almost unchanged. However, the more significant influence is observed in the reflection coefficients, and hence in the radiation curves. LH lines that use CSRRs with splits positioned in direction perpendicular to the transmission line (Orientation 1) exhibit no (or smaller) shift in frequency between the maximum of the transmission coefficient and the minimum of the reflection coefficient. Therefore, radiation loss in the case of LH lines with Orientation 1 is decreased. LH lines that use CSRRs with Orientation 2 (splits along the microstrip) suffer from increased radiation loss, due to the fact that they are non symmetrical structures.

C. SRR-Loaded Waveguide

Another promising application of SRR particles is in waveguide structures, where SRRs can be used in different ways. Here we analyze SRR positioned in the E-plane of the waveguide, shown in Fig. 7, which results in negative effective permeability. If the SRR is designed to resonate below the cut-off of the waveguide, an LH pass band will occur. On the other hand, if the SRR resonates at some frequency above the cut-off, a stop band in the frequency response will be created. In this paper, the latter situation is simulated. The standard WR-75 waveguide is used and the outer dimensions of the SRR are 3x3mm, while the SRR itself is designed using metallic wire with 0.25x0.25mm crosssection. Two orientations of the SRR were analyzed: one with split positioned at the vertical side of the SRR (Orientation 1, shown in Fig. 7), and the other where split is placed at the horizontal side of the SRR. As in the case of LH transmission lines, it is widely accepted that the position of the split in the SRR will not influence the performances.

Port 2

Port 1

Fig. 7. SRR in the E-plane of the waveguide, with split positioned at its vertical side (“Orientation 1”).

Simulated responses of both waveguides are shown in Fig. 8. It can be seen that a significant difference exists in the stop frequency as well as in the shape of the responses. This can be explained as follows: in the case denoted as “Orientation 2,” electric field inside the waveguide creates an electric dipole within the SRR. The existence of this dipole changes the equivalent capacitance of the SRR and therefore the whole structure performs differently.

Frequency [GHz]

Fig. 8. Simulation results for waveguides loaded with SRR with split on its vertical (Orientation 1) and

horizontal (Orientation 2) side.

III. LH MICROSTRIP LINES WITH

MULTIPLE CSRRS

The influence of the orientation of the CSRR to the performances is especially visible in the case of multiple CSRRs, recently introduced in [8] with the aim of further miniaturization of the unit cells. In Fig. 9 multiple CSRR with four concentric rings is shown.

Fig. 9. Multiple CSRR with four rings.

Simulation and measurement results for LH line with multiple CSRRs with four concentric rings are compared in Fig. 10. In this case, splits are positioned along the host microstrip.

Frequency [GHz]

Fig. 10. Simulation and measurement results for LH line that uses multiple CSRRs with splits positioned along the microstrip.

It can be seen that the frequency corresponding to the maximum of the transmission coefficient differs from the value corresponding to the minimum of the reflection coefficient. This is even more visible in the measured data. Additional simulations have shown that this discrepancy can not be explained by inaccuracy of the fabrication process, where the top and the bottom conductive layers were not ideally aligned. Moreover, LH lines of this type show great robustness to such misalignments.

However, in the case of splits positioned along the microstrip, the whole structure becomes unsymmetrical, and therefore exhibits a frequency shift between the maximum of the transmission coefficient and the minimum of the reflection coefficient, which results in the increased unwanted radiation. Therefore, in the design of resonant-type LH microstrip lines, CSRRs with splits positioned in the direction perpendicular to the host transmission line should always be used.

ACKNOWLEDGEMENT

This work is supported by Eureka project METATEC (METAmaterial–based TEchnology for broadband wireless Communications and RF identification), project no. E! 3853.

REFERENCES

[1]J. B. Pendry, A. J. Hoden, W. J. Stewart and I. Youngs, “Extremly low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett., vol. 76, num. 25, pp. 4773-4776, 17 June 1996

[2]J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart “Magnetism from conductors and enchanced nonlinear phenomena,” IEEE Trans. on microwave theory and technology, vol. 47, no. 11, pp. 2075-2084, Nov. 1999.

[3]R. A. Shelby, D. R. Smith and S. Schultz: “Experimental verification of a negative index of refraction,“ Science, Vol. 292, pp. 77-79, 2001,

[4]R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left handed media simulation and transmission of EM waves in subwavelength SRR-loaded metallic waveguides”, Phys. Rev. Lett., vol 89, pp. 183901-03, 2002.

[5]F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators”, IEEE Microwave Wireless Comp. Lett., vol. 13, pp. 511-513, Dec. 2003.

[6]F. Falcone, et al., “Babinet principle applied to metasurface and metamaterial design,” Phys. Rev. Lett., vol. 93, pp. 197 401(1)– 197 401(4), Nov. 2004.

[7]J. Carbonell, L. J. Roglaa, V. E. Boria, D. Lippens, “Design and experimental verification of backward-wave propagation in periodic waveguide structures,” IEEE Trans. Microwave Theor. Tech., vol. 54, no.4, pp. 1527-1533

[8]V. Crnojević-Bengin, V. Radonić, and B. Jokanović, “Lefthanded microstrip lines with multiple complementary split-ring and spiral resonators,” Microwave Opt. Technol. Lett., vol. 49, no.6, pp.1391-1395, June 2007.