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VC 2012 Wiley Periodicals, Inc.

BROADBAND LEFT-HANDED RECTANGULAR WAVEGUIDE USING A SHORTED STUB AND TWISTED E-PLANE POSTS

Dong-Jin Kim and Jeong-Hae Lee

Department of Electronic and Electrical Engineering, Hongik University, Seoul 121-791, Korea; Corresponding author: jeonglee@hongik.ac.kr

Received 31 July 2012

ABSTRACT: A broadband left-handed (LH) waveguide operating above the cutoff frequency is presented. The unit cell consists of oneshorted stub and two-twisted posts. The structure induces double loops in the surface currents, resulting in enhanced inductance which broadens the negative permeability region. To analyze the LH properties of the structure, a 2-port network cross-connected equivalent circuit is derived. The measured results of the LH waveguide constructed with five unit cells in an X-band are in good agreement with simulated data and show a good transmission property as well as a broad LH fractional bandwidth of 26.5%. VC 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:835–840, 2013; View this article online at wileyonlinelibrary.com. DOI: 10.1002/mop.27419

Key words: left-handed transmission line; metamaterials; waveguide

1. INTRODUCTION

Various meta-structures have been developed over the past decade to suit metamaterials’ anomalous properties such as inverse Snell’s law, backward wave propagation, infinite wavelength wave propagation, and others [1]. A great number of meta-

structures have used planar types as the realization of negative permeability and permittivity is relatively simple [2–4]. However, even though a waveguide has advantages of high power capability and low loss characteristic, attempts to make a metamaterial transmission line using a waveguide have been accomplished with difficulty because of the limitations of the waveguide structure itself. Most previous metamaterial waveguides have been designed below the cutoff frequency of a rectangular waveguide where an inherent shunt inductance occurs [5–10]. This presents problems for real-world application, particularly regarding the relatively poor transmission characteristics in the pass band due to a weak matching condition between the input and output waveguide, the large dielectric or conductor losses. Actually, the left-handed (LH) structures built using split ring resonators (SRRs) [5, 6] or dielectric-filled corrugations [7], which provide an effective permeability of negative value, have high insertion losses greater than 10 dB in the pass band even though they produce a LH propagation region below the cutoff frequency.

Conversely, the previously reported LH waveguides working above the cutoff frequency were combined with inductive irises instead of the cutoff waveguide, which present an effective permittivity of negative value, and SRRs [11, 12] or shorted stub [13]. However, they have a serious problem in the narrow LH fractional bandwidth, that is, less than 5%, because the negative permeability regions with SRRs or shorted stub in a rectangular waveguide are very narrow. Recently, authors proposed a LH waveguide with two double L-shaped stub and E-plane post providing a LH fractional bandwidth of 12.7% [14]. Nevertheless, the structure consisting of two shorted stub still has problems such as a bulky volume and a limitation of LH bandwidth.

This letter presents a broadband LH rectangular waveguide to overcome the drawbacks including a poor transmission loss and a narrow LH band of the general LH waveguides. The meta-struc- ture employs a cross-connected structure using a shorted stub and twisted E-plane posts to broaden and down-shift the region of negative permeability. Moreover, as the LH waveguide is designed above the cutoff frequency and does not need any dielectric material, a small insertion loss would be expected.

2. PROPERTIES OF THE CROSS-CONNECTED LH STRUCTURE

Figure 1 shows the unit cell of a cross-connected LH waveguide consisting of one-shorted stub and two-twisted E-plane posts. Specifically, the two-twisted E-plane posts cross-connect the top plane and bottom plane of the waveguide on both sides of the shorted stub. Generally, a shorted stub on the broad side of a rectangular waveguide represented by a parallel LC circuit acts as a resonator with negative value of effective permeability near the resonance frequency, similar to an SRR. An E-plane post in a waveguide, including a shunt inductance, performs a negative value of effective permittivity above the cutoff frequency of a rectangular waveguide. Thus, the combination of a shorted stub and an E-plane post can generate an LH property with simultaneous negative permittivity and negative permeability. To obtain a broad negative permeability region, a resonant circuit with a larger inductance value is required in the upper band of a stub resonance frequency. This is because the effective permeability primarily depends on the resonant elements and the inherent inductance of a rectangular waveguide. However, because the two surface currents flow in opposition between the shorted stub and two straight posts, resulting in a reduced H-field as shown in Figure 2(a), the inductance value of the resonant circuit is small. Therefore, the LH waveguide using straight E-plane posts has a

narrow region of negative permeability due to its decreased inductance. On the other hand, in case of an LH waveguide having cross-connected posts, the double loops of surface currents are flowing in the same direction along the two twisted posts and a stub, enhancing the H-field in the LH structure as shown in Figure 2(b). As a result, as the inductance becomes large, and the negative permeability band of the cross-connected structure is down-shifted and broadened.

In order to confirm the characteristics of the LH waveguides with straight E-plane posts and with the proposed structure, 2- port network equivalent circuits are derived as shown in Figure 3, respectively. As mentioned in the earlier paragraph, the equivalent circuit includes the resonant circuits of Ls and Cs corresponding to the shorted stub and T-equivalent circuit of Cp

and Lp corresponding to the E-plane posts. In particular, in the case of the LH waveguide with twisted E-plane posts, the shunt inductances (Lp) caused by the twisted posts are cross-connecting ports 1 and 2 with respect to the stub as shown in Figure 3(b), because the LH waveguide is a cross-connected type. Additionally, to complete the circuit modeling, the inherent elements of Lw and Cw, obtained from transmission line parameters of a rectangular waveguide, should be added. The Lw and Cw depending on the waveguide structure is calculated as follows [15]

where L0 and C0 are the per unit length inductance and capaci-

tance, respectively, of a rectangular waveguide. k is given by p

x le, b is the propagation constant of a TE10 mode, and l is the physical length of a unit cell. The Z0 for the power-voltage definition of the waveguide characteristic impedance is given by [16]

r8 9

2 l>b> (3)

Z0 ¼ : ; e a

where a and b are the width and height, respectively, of a rectangular waveguide.

Using P-T transformations, the equivalent circuits of Figure 3 can be represented by the T-equivalent circuits as depicted in Figure 4, which includes ZT and YT corresponding to the effective permeability and permittivity, respectively [17]. The LH bandwidths of the structures primarily depend on the series impedance (ZT) because the shunt admittance (YT) corresponding to the effective permittivity keeps a negative value in the frequency band of interest as shown in Figure 4(a). Thus, to design a broad LH waveguide, the structure should have a wider region of negative permeability.

The imaginary part of the ZT of the LH structure can be approximated as follows:

where xr is the angular resonance frequency of a parallel circuit of Ls and Cs. To obtain a negative permeability, the frequency should be larger than the resonance frequency and the inductance of Ls should be large enough to overcome the inherent waveguide inductance of Lw in Eq. (4). This suggests that the larger Ls has a broader region of negative permeability when the frequency is above the resonance frequency. As discussed in Figure 2, the cross-connected posts enhanced the inductance of Ls. Thus, the cross-type with twisted posts has an extremely broad region of negative permeability compared with that of the noncross type using the straight posts as shown in Figure 4(b). The extracted lumped element values of equivalent circuits for the LH waveguides, listed in Table 1, also support the hypotheses above. To compare the circuit parameters of the two structures, the shorted stub on the broadside of a rectangular waveguide is set at: st ¼ 8 mm, sl ¼ 3 mm, and its resonance frequency is 10.13 GHz. The parameters of Ls, Cs, Lp, and Cp can be extracted by fitting the S-parameters with a full-wave simulation and circuit simulation in the frequency band of interest. The results of the circuit modeling clearly show that the

Figure 4 Comparison of imaginary parts of the shunt admittance (YT) and series impedances (ZT) of the T-equivalent circuit for cross and noncross types. (a) Shunt admittances (YT). (b) Series impedances (ZT)

inductance Ls of the general LH waveguide with the straight posts is considerably reduced compared with the stub-only structure, while the Ls of the proposed structure is enhanced by the twisted E-plane posts. In other words, the reduced inductance of Ls from that of the general LH waveguide gives a narrow negative permeability band of 10.05 10.48 GHz. Also, in case of a LH waveguide with double L-shaped stub and E-plane posts [12], it has nearly the same inductance value with only stub structure as the E-plane posts do not affect the surface current of the two shorted stub. On the contrary, by adding the twisted posts, the inductance of Ls is enhanced by the double loops in Figure 2(b), resulting in a broad region of negative permeability,

TABLE 1 Extracted Circuit Parameters

Figure 5 Fractional LH bandwidth versus the parameters of the equivalent circuit

as shown in Figure 4(b). This enhanced inductance also downshifts the resonance frequency and, therefore, decreases the size of the shorted stub. In section 4, the size of the structure will be discussed in greater detail.

3. RESULTS

To examine the properties of the LH waveguide as a function of the size of the stub and posts, variations in bandwidth were observed by varying the values of the circuit elements. Figure 5 shows the fractional bandwidth resulting from changes in this single variable. The results show that the LH bandwidth is proportional to Ls, inversely proportional to Cs and Cp, and almost constant with Lp. In addition, the circuit parameters of Ls, Cs, Lp, and Cp, versus the size of the stub and the E-plane post, are separately extracted using a circuit simulation. Consequently, it is observed that the LH bandwidth increased as the stub width (sl) increased and the depth (st) decreased. In addition, as the thickness (w or s) is increased and the gap between two posts is decreased, the bandwidth became broader. However, if the fractional bandwidth was broader than 30%, the transmission level lost quality. Therefore, a unit cell with maximal bandwidth and

Figure 6 Fabricated broadband LH waveguide with five unit-cells. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com]

Figure 7 Dispersion curves of the broadband LH waveguide

reasonable insertion losses (less than 2 dB), the optimal dimensions are given in Figure 1. The LH structure is implemented in a WR-90 waveguide (a b ¼ 22.68 10.16 mm2) and its cutoff frequency is 6.56 GHz. The extracted circuit parameters of the designed structure are: Ls ¼ 2.322 nH, Cs ¼ 0.182 pF, Lp ¼ 2.010 nH, and Cp ¼ 0.4173 pF. To investigate the properties of the LH structure, the periodic structure is composed of five unit cells and fabricated as shown in Figure 6. The LH waveguide is simply and directly excited using standard X-band waveguide adapters without any particular excitation technique. Figure 7 shows the dispersion curves of the LH waveguide using an Eigen mode simulation (Ansoft’s HFSS) of the unit cell, and a circuit simulation (Ansoft’s Designer) of the equivalent circuit and its measurement. As shown, the dispersion curves were in accord and their bandwidths closely matched the region of negative permeability as shown in Figure 4(b).

The S-parameters of the LH bands in simulation (7.53–9.92 GHz) and measured in experiment (7.54–9.84 GHz), as shown in Figure 8, are in good agreements with those of the dispersion curves in Figure 7.

4. DISCUSSION

This letter presents a LH rectangular waveguide that overcomes the bandwidth limitation and transmission property of the previously reported LH waveguide structure. To demonstrate the differences between the other LH waveguides and our structure, the LH waveguides referred in this letter are compared in Table 2. The table shows that the structure with twisted posts

Figure 8 Simulated and measured S-parameters

has an impressively broad LH bandwidth (26.5%) compared with previously designs except for the structure presented in Ref. 7 which produces the LH band below the cutoff frequency of TM11 mode.

Comparing the unit-cell size of each realization, the size of the proposed structure was not reduced over the previous LH waveguides because our structure operates above the cutoff frequency and has a shorted stub. In detail, the LH waveguides using SRRs [5, 6], and the Ref. 11 do not need an extra space on the outside of the host waveguide because the structure contains the negative permeability elements of SRRs in the inner part of the structure itself. Second, the dielectric filled corrugation [7] can generate a negative permeability despite its small size, compared with a shorted stub without dielectric materials. Also, the LH waveguide operating below the cutoff frequency can naturally have a compact size. Thus, while the proposed structure using an air-filled short stub constructed on the outside of a host waveguide may be bulky, the structure contributes to the design of a compact LH waveguide working above the cutoff frequency and using a shorted stub without dielectric materials. In general, a shorted stub on the broadside of a rectangular waveguide has a region of negative permeability when its length is around kg/4 (kg: a guided wavelength). For example, to design the LH structure, which is embodied in a standard X-band waveguide (WR-90) operating around 8 GHz, the length of the stub is should be set at nearly 16 mm. However, the presented structure has a stub length of only 8 mm in spite of operating at a lower frequency. In fact, as shown in Table 2, the length of the

stub in the proposed structure (0.55 k0) is reduced by 32% over that of the LH structure (0.81 k0) in Ref. 13 which uses an inductive iris and a shorted stub without dielectric material. This result indicates that the enhanced inductance of Ls down-shifts the resonance frequency of the stub and can therefore shrink the size of the shorted stub.

Moreover, the proposed structure has improved transmission characteristic (|S21|<2.3 dB), over to the previous reported LH waveguides, because the structure is free from the dielectric loss in addition to operating above the cutoff frequency. Although the transmission characteristic of the LH waveguide is far worse for real-world application in a band-pass filter but it can be applied to create a compact waveguide filter if the responses such as insertion loss, group delay are optimized. Additionally, the structure can be applied to real-world applications such as leaky-wave antennas supporting backward radiation, backwardwave oscillators generating RF sources, and the like.

5. CONCLUSION

A broadband LH rectangular waveguide operating above the cutoff frequency is presented. It consists of using a shorted stub without a dielectric material and twisted E-plane posts. The LH structure with cross-connected posts creates double loops in the surface currents between the twisted posts and stub and enhances the inductance of the stub. This peculiarity of the cross-con- nected structure broadens the negative permeability the region of the shorted stub due to the increased inductance. Therefore, an LH waveguide can have a broader LH band compared with the previous LH structure using SRRs, dielectric filled corrugations or a shorted stub. Also, the structure contributes to the design of compact LH waveguides working above the cutoff frequency and using a shorted stub without dielectric materials because of the enhanced inductance of Ls down-shifting the resonance frequency of the stub. Moreover, the transmission characteristic of the structure is improved compared with previously reported LH waveguides, especially structures below the cutoff frequency of the waveguide, because the structure is free from the dielectric loss as well as operating above the cutoff frequency. In order to design the LH waveguide, a cross-connected equivalent circuit was derived and the sizes of the structure were optimized. The measured results indicated that the proposed LH waveguide has good transmission property as well as a greatly improved LH fractional bandwidth of 26.5%.

ACKNOWLEDGMENT

This work was supported by the Mid-career Researcher Program through the MEST under NRF Grant 2010-0013273

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VC 2012 Wiley Periodicals, Inc.

NOVEL HYBRID FOUR-MODE MICROSTRIP BANDPASS FILTER USING TWO PARALLELED STUB-LOADED RESONATORS

Xuehui Guan,1,2 Xiaoyan Wang,1 Bin Wang,1 Ye Yuan,1 and Haiwen Liu1

1School of Information Engineering, East China Jiaotong University, Nanchang 330013, People’s Republic of China; Corresponding author: xuehuiguan@yahoo.com.cn

2State Key Laboratory of Millimeter Waves, Nanjing 210096, People’s Republic of China

Received 31 July 2012

ABSTRACT: A novel hybrid four-mode microstrip bandpass filter (BPF) is proposed in this paper. The filter is realized by association of two stub-loaded dual-mode resonators. Two similar stub-loaded dualmode resonators are set in parallel. By appropriately arranging the two dual-mode resonators and the coupling between resonators with the microstrip feed lines, a new hybrid four-mode BPF is achieved. The evenand odd-mode theory is introduced to minutely analyze dual-mode resonators. Moreover the circuit model and coupling matrix of the filter are built to further explain the proposed circuit. The proposed BPF is simulated, fabricated, and measured. Two transmission zeros have been achieved in the transition band of the filter, which improve the performance of the filter. The EM simulated and measured results are presented and excellent agreement is obtained validates the design concept. VC 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:840–845, 2013; View this article online at wileyonlinelibrary.com. DOI: 10.1002/mop.27418

Key words: hybrid four-mode filter; coupling matrix; stub-loaded dualmode resonator