диафрагмированные волноводные фильтры / a3c47df6-a88a-46be-9d98-cc4571a82436

4.J.P. Kim and W.S. Park, Analysis and network modeling of an aperturecoupled microstrip patch antenna, IEEE Trans Antennas Propagat 49 (2001), 849 – 854.

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6.T. Itoh, Numerical techniques in microwave and millimeter-wave structures, Wiley, New York, 1989.

7.D.M. Pozar, Microwave engineering, 3rd ed., Wiley, New York, 2005.

© 2006 Wiley Periodicals, Inc.

LEFT-HANDED RECTANGULAR WAVEGUIDE BANDSTOP FILTERS

Alexander Shelkovnikov and Djuradj Budimir

Wireless Communications Research Group

Department of Electronic Systems

University of Westminster

115 New Cavendish Street

London, W1W 6UW, United Kingdom

Received 31 October 2005

ABSTRACT: A novel type of rectangular waveguide bandstop filter is presented. Incorporating a dielectric slab patterned with single splitring resonators (SRRs), the electromagnetic properties of the structures are modified to allow propagation of backward waves in the rectangular waveguide. Filters are created through integration of SRRs, wireline, and additional metal strips as a loading for the propagation media. Using the printed circuit board (PCB) technique, SRRs, wireline, and metal strips are etched on a dielectric substrate and the slab is then inserted in the central plane of the metallic waveguide. A three-unit cell SRR-loaded waveguide is investigated against a three-unit cell LHM waveguide configuration. A three-unit LHM rectangular waveguide bandstop filter is designed and analyzed in order to performance wide stopband performance. The simulated results are presented for a WG-18 waveguide. LHM rectangular waveguide bandstop filters are compact, low cost, and suitable for mass production. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 846 – 848, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop. 21494

Key words: bandstop filters; left-handed media; periodic structure; rectangular waveguides; split-ring resonators

1. INTRODUCTION

Electrodynamics of substances with simultaneously negative values of electric permittivity and magnetic permeability studied by Veselago in the late 1960s [1], has recently found its application in artificial composite materials. Left-handed materials (LHMs), as

Figure 1 One-unit LHM rectangular waveguide

Figure 2 (a) Three-unit SRR-loaded rectangular waveguide; (b) threeunit LHM rectangular waveguide

they are also known, have been widely investigated [2– 4] and various structures have been experimentally realized at microwaves [5–7]. Such materials have been found to support backward waves and reverse some of the basic electromagnetic phenomena, such as Doppler effect and Cherenkov radiation. It has been experimentally shown that using a material incorporated with thin metal wires [2] and split-ring resonators (SRRs) [3], negative permittivity and negative permeability, respectively, can be achieved, and proves useful to be applied for changing the guiding properties of an electromagnetic wave at microwave and millime- ter-wave frequencies.

Rectangular waveguides have been widely applied in various telecommunication systems as a basic guiding structure for many years, and are still very useful where high-power capability and low insertion loss in the passband is required. Therefore, the task of building compact, low-cost, and easily fabricated waveguide structures is important for the development of modern wireless technology. From electromagnetic theory [8], it is well known that a rectangular waveguide is characterized by its transversal dimension, that is, being at least half the wavelength, in order to satisfy the boundary conditions for propagation of electromagnetic waves. Thus, the available bandwidth for a particular system has been determined by the corresponding waveguide frequency range.

The high-pass behavior of a hollow metallic waveguide can be characterized by its section and cut-off frequency. By employing left-handed materials for a conventional rectangular waveguide, the propagation characteristics and high-pass behavior of the structure can be altered and achieved for operation in the lower band.

In this paper, we employ single split-ring resonators (SRRs) and integrated printed-circuit board technology to investigate stopband characteristics of the waveguide. Further, we also incorporate metallic discontinuities in the E-plane of the integrated insert in order to realize novel LHM rectangular waveguide bandstop filters exhibiting a wide stopband over the desired frequencies.

Figure 3 Simulated transmission coefficient S21 of a three-unit SRRloaded waveguide (solid) and a three-unit LHM waveguide (dashed)

2. LHM RECTANGULAR WAVEGUIDES

Split-ring resonators, small resonant elements with a high quality factor at microwaves, are used to build left-handed materials [3]. Embedded in a hollow metallic waveguide, SRRs excited by a magnetic field parallel to ring axis induce backward wave propagation. Figure 1 shows the topology of a one-unit LHM rectangular waveguide.

Placed in the rectangular waveguide E-plane, along the line of symmetry and parallel to the wall, the media created by SRRs can be viewed as LHM consisting of a series of unit cells. When the unit-cell dimension is much smaller than a wavelength, a series of these unit cells may be considered as homogeneous media.

The single C-shaped form of SRRs also can provide the lefthanded properties of the structure. It is designed as a single square metallic ring interrupted by a small gap.

The design of a one-unit waveguide contains a single SRR on a dielectric substrate. This substrate is transversely integrated into the central plane of a hollow metallic waveguide.

To investigate the influence of a periodic arrangement of SRRs in a rectangular waveguide in order to create negative permittivity, the structure is realized in two configurations. A three-unit SRRloaded rectangular waveguide is compared to a three-unit LHM rectangular waveguide. The layout of the three-unit SRR-loaded rectangular waveguide is illustrated in Figure 2(a). The simulated transmission coefficient S21 is denoted by a solid line in Figure 3.

The second configuration, shown in Figure 2(b), is a transmission line designed in a finline topology where single SRRs are placed on the top plane of a dielectric and a thin wire line is realized at the back side of the substrate. The simulated transmission coefficient S21 for this waveguide is illustrated by a dashed line in Figure 3.

The dielectric substrate used to design an insert is RT/Duroid 5880, with permittivity r 2.2, tan 9 10 4 and thickness

TABLE 1 Dimensions of Single Split-Ring Resonator (SRR)

Figure 4 Three-unit LHM rectangular-waveguide bandstop filter

h 0.254 mm. The ring dimensions of the single SRR are presented in Table 1.

3. LHM RECTANGULAR WAVEGUIDE BANDSTOP FILTERS

The LHM rectangular waveguide bandstop filter is designed as a three-unit structure. By adding adjacent resonant elements to the period of SRRs, we can create bandstop-filter performance. Metallic discontinuities are realized as transversely embedded rectangular metal strips and are integrated on the same plane of a dielectric substrate so as to maintain simplicity of fabrication. A three-unit SRR-loaded insert is embedded into the central plane of the metallic waveguide. The layout of the proposed bandstop filter is shown in Figure 4. Its corresponding dimensions are presented in Table 2.

The structure is designed using a standard WG-18 rectangular waveguide (with section size 15.799 7.899 mm). Three copper single SRRs are etched on top of the same RT/Duroid 5880 substrate. Four transverse metal strips are also patterned on the top plane, while the wire line is etched on the back side of the dielectric. The thickness of copper patterns is 0.017 mm. The insert is integrated to the central plane of the waveguide to form a three-unit LHM rectangular waveguide bandstop filter. Its dimensions are shown in Table 2.

In order to illustrate the feasibility of the proposed filter, a three-unit SRR-loaded rectangular waveguide bandstop filter is designed and simulated at the X-band using a commercial 3D electromagnetic simulator. The lengths of the unit cells and dimensions of the SRRs are calculated corresponding to the operating frequency band, as given in Table 1. The total length of the filter (including waveguide) feeding is 22.1 mm. The scattering parameters of the bandstop filter are presented in Figure 5.

4. CONCLUSION

Three-unit single SRR-loaded and LHM rectangular waveguides have been investigated. A periodic arrangement of single SRR units, much less than one wavelength long, in a rectangular waveguide has been shown to provide a stopband in the desired

TABLE 2 Dimensions of an LHM Waveguide Bandstop Filter

Figure 5 Simulated scattering parameters of the three-unit LHM rectangular waveguide bandstop filter

frequency band. By incorporating a wire line on the back side of a dielectric substrate, an LHM waveguide has been realized. A novel LHM rectangular waveguide bandstop filter, which is compact and simple to fabricate, has been designed and simulated.

REFERENCES

1. V.G. Veselago, The electrodynamics of substances with simultaneously negative values of and , Soviet Phys Uspekhi 10 (1968), 509 –514.

2.J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans Microwave Theory Tech 47 (1999), 2075–2084.

3.D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schultz, Composite medium with simultaneously negative permeability and per-

mittivity, Phys Rev Lett 84 (2000), 4184 – 4187.

4.R.A. Shelby, D.R. Smith, and S. Schultz, Experimental verification of a negative index of refraction, Science 292 (2001), 77–79.

5.P. Gay-Balmaz and O.J.F. Martin, Interacting magnetic resonators for left-handed metamaterials, 2001 Euro Conf Digest, London, UK, 2001.

6.C. Caloz and T. Itoh, Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmis-

sion line, 2004 IEEE Trans Antennas Propagat 52 (2004), 1159 –1166.

7.T. Decoopman, O. Vanbesien, and D. Lippens, Demonstration of a backward wave in a single split ring resonator and wire loaded finline, IEEE Microwave Wireless Compon Lett 14 (2004), 507–509.

8.R.E. Collin, Foundations for microwave engineers, 2nd ed., IEEE Press, New York, 1991.

© 2006 Wiley Periodicals, Inc.

CAPACITANCE CHARACTERIZATION OF MULTIPATH INTERCONNECTS FOR NANOTECHNOLOGY CIRCUITS

A. K. Goel and N. R. Eady

Department of Electrical & Computer Engineering

Michigan Technological University

Houghton, MI 49931

Received 28 October 2005

ABSTRACT: A multipath interconnect carries a signal on an electrical circuit by using the concept of parallel processing, that is, by providing two or more paths between the driver and the load. These paths are stacked vertically and isolated from one another by insulating layers

between them. In this paper, we have used the Green’s function method to determine the parasitic capacitances associated with a system of nanoscale multipath interconnects fabricated on a silicon-based substrate.

© 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 848 – 852, 2006; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/mop.21495

Key words: nanotechnology; interconnects; capacitances; Green’s function; VLSI

1. INTRODUCTION

On state-of-the-art microelectronic circuits, the transistors and other devices are often connected by metallic interconnects, although optical and superconducting interconnects have also been considered. On this front, recent improvements have resulted in replacing aluminum interconnects with copper lines, which has resulted in lower propagation delays and hence higher chip speeds. “Nanotechnology” refers to the technology for designing, fabricating, and applying nanometer-scale systems to the development of next-generation systems including nanocomputers. Formation of digital nanocomputers that promise dramatically increased computational speed and density requires the successful formation of molecular-scale devices that can switch between the on and off states. Even after the challenges of fabricating the molecular devices are successfully overcome, we still face the problem of connecting these devices in a circuit to carry the information from the output of one device to the input of the next device. This problem is usually referred to as the “interconnect problem.” The interconnect problem arises due to the extremely high density of devices in the circuit as well as the extremely high rapidity at which the information needs to be transmitted from one point in the circuit to the next. This requires an unprecedented high density of interconnects operating at unprecedented high speeds. Furthermore, an extremely large number of interconnects are needed, not just for connecting the devices in a circuit but also for connecting the circuits together. This can lead to the excessive heating problem in addition to the unacceptably high crosstalk introduced by the very close proximity of the rather large number of interconnects. New interconnect strategies are required to tackle these problems. Ideas that have been tossed around are “wireless” interconnects and “stochastic” transmission, but these are at best theoretical at present.

2. MULTIPATH INTERCONNECTS

As a possible solution of the interconnect problem, we have proposed “multipath interconnects,” a modified version of the traditional metallic interconnects [1]. The modification consists of using the concept of parallel processing by providing two or more paths between the driver and the load to carry the signal on an electrical circuit. These paths are stacked vertically and isolated from one another by insulating layers between them, thereby taking the same area on the chip as a standard single-path interconnect. Such a structure can carry much larger currents on the chip and this interconnect structure can be built by an extension of the existing microelectronics fabrication infrastructure. Recently, we performed computer simulations of the propagation delays expected in a multipath interconnect [1]. Our results indicated that the overall interconnect delay would decrease as the number of paths is increased. Since these interconnects are expected to carry high current densities which can cause excessive local heating, we have also performed an analysis of the electromigration-induced failure of the multipath interconnects [1]. These results suggest that the median time to failure for a multipath interconnect increases as the number of paths is increased. Clearly, the multipath interconnects