I. INTRODUCTION
Slots milled in the narrow and broad wall of a rectangular waveguide found wide applications in radars due to their numerous advantages, like, high power handling capability, simple feeding, low loss, ease of fabrication, etc. That is why studies on slotted waveguide have been the interests of several researchers since last six decades. A literature survey on it reveals that most of these works are on the calculation of self and mutual admittance, reflection coefficients of the antenna. Works on waveguide slot antenna for achieving omnidirectional radiation pattern [Reference Sangster and Wang1, Reference Mondal and Chakrabarty2] were also reported.
A breakthrough in the waveguide-based circuit and antenna research was obtained in 2002 when Marque's et al. [Reference Marque's, Martel, Mesa and Medina3] analyzed the propagation of electromagnetic waves in a hollow waveguide, loaded with split ring resonators (SRR) at periodic interval. It was shown that electromagnetic (EM) transmission in such structure is achievable within a specific frequency band, even if the transverse dimensions of the waveguide are much smaller than the desired free-space wavelength. In 2005, Hrabar et al. proposed the analysis of a rectangular waveguide filled with anisotropic uniaxial metamaterial with transversal negative effective permeability [Reference Hrabar, Bartolic and Sipus4]. The analysis suggested that these waveguides can support propagation of the backward wave below the cut-off frequency. It was also observed that the transversal dimension of this waveguide can be arbitrarily smaller than half of a wavelength in the filling material, provided that the transversal permeability is negative. This method is useful for fabrication of miniaturized rectangular waveguide. In the same year the equivalent circuit models and electromagnetic behaviors of SRR and complementary SRR in a transmission line were proposed by Baena et al. [Reference Baena5]. In 2009 [Reference Rajo-Iglesias, Teruel and Kehn6] Rajo-Iglesias et al. presented the analysis of multiband SRR loaded rectangular waveguide. It provided a simple method to obtain two/three passbands (stopbands) below (above) the cut-off frequency in a waveguide, using various configurations of resonators within the waveguide. It also revealed that by choosing appropriate SRR sizes as well as dielectric materials, the passbands can be easily tuned. In 2010, Park et al. reported a frequency tuneable waveguide antenna with miniaturized aperture using a varactor loaded SRR [Reference Park, Oh, Lee and Park7]. In 2014, a dual band, high-gain antenna, based on SRR and corrugated plane, was presented by Ding et al. [Reference Ding, Li, Chang and Quin8]. They claimed that half power beam width can be reduced by approximately 100° and suggested that such antennas can find application in wideband communication systems.
This work presents the application of SRRs in conventional waveguide slot array to achieve performance improvement and multiband characteristics. Since single SRR is a better choice for gain enhancement [Reference Cao, Zhang, Liu, Yu, Guo and Wei9], we have used single SRR structure. Three dielectric slab loaded single SRRs have been placed on the transverse plane of a conventional waveguide slot array antenna to achieve dual-band characteristics. It has been shown that insertion of SRR on the transverse plane of a slotted waveguide has the effect of increase in gain and front to back ratio as compared with conventional waveguide slot array. An equivalent circuit of the proposed antenna also has been presented.
II. DUAL BAND SLOT ARRAY ANTENNA AND ITS EQUIVALENT CIRCUIT
Three-dimensional (3D) view of the proposed dual band slot array antenna is shown in Fig. 1(a) whereas the SRR cell is shown in Fig. 1(b). The lengths of the two slots are 16 and 15.8 mm, respectively. Respective slot offsets are 3 and 5 mm (from center).
Fig. 1. Proposed dual band slot array antenna (a) 3D view, (b) SRR cell with dimensions a = 22.86 mm, b = 10.16 mm, g = 2.1 mm, k = 1.8 mm, t = 0.3, Substrate: Rogers RO 4350 with substrate height h = 0.762 mm, dielectric constant of ε r = 3.66, and loss tangent tan δ = 0.004.
A SRR cell on the transverse plane of a rectangular waveguide shown in Fig. 2(a), acts as a LCR circuit of Fig. 2(b). The individual R, L, C values can be found using the relations [Reference Fallahazadeh, Bahrami and Tayarani10]:
$$L_i = \displaystyle{1 \over {(2\pi f_i )^2 C_i}}, $$
$$C_i = \displaystyle{{\sqrt {0.5(R_i + 2Z_0 )^2 - 4Z_0^2}} \over {2.83\pi Z_0 R_i B_i}}, $$
$$R_i = \left. {2Z_0 \left( {{1 / {\left \vert {S_{21,i}} \right \vert - 1}}} \right)} \right \vert _{f = f_i}, $$
where i = 1, 2, f
i
is the resonant frequency, Z
0 is the characteristic impedance, B
i
is the 3 dB bandwidth of
$\left. {S_{21,i}} \right\vert_{f = \,f_i} $
. For f
i
= 8 GHz, B
i
= 0.8 GHz and Z
0 = 660 Ω, the theoretical values of lumped elements will be R
1 = 39.29 kΩ, L
1 = 2.47 nH and C
1 = 0.155 pF. The simulated frequency responses of the circuits, shown in Fig. 2, are plotted and compared in Fig. 3.
Fig. 2. SRR loaded waveguide (a) schematic diagram and (b) equivalent circuit.
Fig. 3. Comparison of the circuit model response and full-wave simulated response of an SRR loaded WR–90 waveguide.
It is well known that a longitudinal slot in the broad wall of a waveguide behaves as a shunt admittance, which can be expressed as
$$Y = - Y_0 \displaystyle{{2\Gamma} \over {1 + \Gamma}}, $$
where Y 0 is the characteristic admittance of the rectangular waveguide and Γ is the reflection coefficient. Therefore the equivalent circuit of the proposed antenna can be modeled as shown in Fig. 4. The optimized values of the lumped components are R 1 = 39.22 kΩ, L 1 = 2.47 nH, C 1 = 0.153 pF, R 2 = 39.22 kΩ, L 2 = 2.49 nH, C 2 = 0.153 pF, R 3 = 39.22 kΩ, L 3 = 2.39 nH, and C 3 = 0.155 pF. The calculated values of slot admittances are 0.2828 − 0.2477i Siemen and 0.2578 − 0.2077i Siemen. The values of the lumped components for the respective slots are 2.01 kΩ, 0.0309 nH and 3.01 kΩ, 0.0294 nH. The electrical lengths of the transmission line inverters are 247° and 256°, respectively.
Fig. 4. Equivalent circuit of the proposed dual band slotted waveguide antenna.
The fabricated antenna is shown in Fig. 5. Standard WR-90 slotted waveguide has been used to design the slot array antenna whereas Rogers RO 4350 with substrate height h = 0.762 mm, dielectric constant of ε r = 3.66, and loss tangent tan δ = 0.004 has been used as a dielectric substrate for the fabrication of SRR. Frequency response of the equivalent circuit in Fig. 4 has been plotted and compared with the measured and high frequency structural simulator (HFSS) simulated frequency response of the proposed antenna in Fig. 6, which are in good agreement.
Fig. 5. Fabricated antenna (a) top view, and (b) placement of SRR cells.
Fig. 6. Comparison of the simulated frequency response of the equivalent circuit with the measured and simulated frequency response of the proposed dual band slot array antenna. Measured frequency response of a CSAA is also shown for comparison.
III. RESULTS AND DISCUSSION
The proposed antenna has been simulated using Ansys HFSS (Version 14.0) and then fabricated and measured using Keysight N5221A PNA Network Analyzer. The simulated and measured reflection coefficients (in dB) of the proposed antenna have been plotted and compared in Fig. 6. The figure reveals that the proposed antenna resonates at two frequencies, 8.88 and 10.3 GHz with respective input return loss 21.11 and 25.06 dB. Due to unavailability of anechoic chamber, the measurements have been carried out in a normal laboratory environment. This introduced some error in the measurement, mainly due to reflections from nearby objects. In addition, finite fabrication tolerances, losses in the connectors, finite air gap between the removable bottom broad wall and the rest of the waveguide structure also have contributed to the measurement error.
To understand the radiation and network characteristics, the surface current distributions on the waveguide and SRR cells are plotted in Figs 7 and 8, respectively. The figures reveal that the slots and SRRs are excited at 8.88 and 10.3 GHz whereas at 8 and 12 GHz, none of them are excited. This is in accordance with Fig. 6 where we have obtained deeps in S 11 (in dB) at 8.8 and 10.3 GHz, and return losses are 0 dB at 8 and 12 GHz. Figures 7 and 8 reveals that slot 1 (length: 16 mm) and SRR 3 are primarily responsible for radiation at 8.8 GHz whereas the slot 2 (length: 15.8 mm) and SRR 2 are primarily responsible for radiation at 10.3 GHz. SRR 1 is getting excited at both the frequencies because of the incident TE10 mode.
Fig. 7. Surface current distributions on the proposed slot array at (a) 8 GHz, (b) 8.88 GHz, (c) 10.3 GHz, and (d) 12 GHz.
Fig. 8. Surface current distributions on the SRRs at (a) 8 GHz, (d) 8.88 GHz, (c) 10.3 GHz, and (d) 12 GHz.
Simulated and measured co-pol and cross-pol radiation patterns of the proposed antenna in both orthogonal planes at both resonance frequencies are shown and compared in Fig. 9. Reasonable agreement has been obtained between them. It has been observed that the cross-polarization level is 40–50 dB lower at the broadside direction. This is another advantage of proposed antenna. The 3D radiation patterns of the conventional and proposed slot array are shown in Fig. 10.
Fig. 9. Simulated and measured Co-Pol and Cross-Pol plot radiation patterns of the proposed antenna at (a) 8.88 GHz at XZ-plane, (b) 8.88 GHz at YZ-plane, (c) 10.3 GHz at XZ-plane, (d) 10.3 GHz at YZ-plane.
Fig. 10. 3D radiation patterns of (a) conventional slot array, and (b) proposed slot array.
Simulated and measured peak gain of the proposed dual band slot array antenna have been plotted and compared in Fig. 11. The gain–frequency plot of a conventional slotted waveguide antenna is also shown in the same figure. The figure reveals that the gains of the proposed antenna at the respective resonance frequencies are 10.91 and 8.58 dB, which are greater than those of a conventional slotted waveguide antenna. The gains of a conventional slot array antenna (CSAA) at these frequencies are 7.62 and 6.1 dB, respectively. At and around the resonance frequencies, one or more of the slots and SRRs gets excited by the incident field (Fig. 8) and produce scattered fields in such a way that they add together towards the main lobe and enhance gain.
Fig. 11. Comparison of simulated and measured gain of the proposed dual band antenna. The gain–frequency plot of a conventional slotted waveguide antenna is also shown for comparison.
The plots of normalized radiated power (with respect to incident power) of the proposed and of a conventional slotted waveguide antenna, with frequency, are shown in Fig. 12. The figure reveals that the presence of the SRRs results more normalized radiated power (NRP). The NRP of a conventional slot array at 8.88 and 10.3 GHz are 0.271 and 0.071, respectively. The respective NRP of the proposed slot array are 0.505 and 0.364. In practice the SRRs behave as a matching element to the feed waveguide at these frequencies and hence reduce reflected power (Fig. 6). Alternatively it can be said that at and around the resonance frequencies, one or more of the slots and SRRs get excited and produce scattered fields in such a way that they cancel each other in the direction of the feed. The reduced reflected power, in turn, increases the normalized radiated power. The peak at 9.3 GHz, in Fig. 12, is due to the resonance of the slots.
Fig. 12. Plot of normalized radiated power as a function of frequency.
It may be noted from Figs 11 and 12 that there is a direct correspondence between the gain enhancement and increase in NRP. At 8.88 GHz the NRP is higher than that at 10.3 GHz, which also has been reflected in the antenna gain. The gain enhancement of the proposed antenna at 8.88 GHz is 2.33 dB, which is higher than that at 10.3 GHz. The higher gain/NRP at 8.88 GHz, as compared with 10.23 GHz is a consequence of the stronger excitation of the SRRs at 8.88 GHz, as compared with 10.23 GHz. This is supported by Figs 8(b) and 8(c), which shows that excitations of the SRRs at 8.88 GHz are much stronger that that at 10.3 GHz.
One of the important parameters that describe the radiation characteristics of an antenna is the front to back radiation ratio. Simulated front to back radiation ratio of the proposed dual band slot array antenna and of a CSAA are plotted in Fig. 13 for comparison. The figure reveals that the proposed antenna has 5–7 dB more front to back radiation ratio than a conventional waveguide slot array antenna in the entire return loss bandwidth. This may be explained as the cancellations of the backscattered waves from the slot and SRR cells.
Fig. 13. Simulated front to back radiation ratio of the proposed dual band antenna and conventional slotted waveguide antenna.
Radiation efficiencies of the proposed and of a CSAA are plotted and compared in Fig. 14. The figure reveals that radiation efficiency of the proposed antenna is more than 80% within the radiation bandwidth.
Fig. 14. Simulated radiation efficiencies of the proposed and a CSAA.
IV. CONCLUSION
In this work the authors have investigated the effects of SRR on the radiation and network characteristics of a slotted waveguide antenna. Three SRR cells have been placed on the transverse plane of a conventional slotted waveguide and are investigated for the first time. The analysis shows that the insertion of SRR cells has the effect of multi-band response, improved gain response, improved cross-polarization and improved front to back radiation ratio.
Avinash Chandra born in Sitamarhi (Bihar), India, in 1988. He received his B.Tech in Electronics and Communication Engineering from Integral University Lucknow, India, in 2012. He is currently pursuing his Ph.D. as Senior Research Fellow in Department of Electronics Engineering from Indian School of Mines Dhanbad, India. He served as Junior Research Fellow in the Department of Electronics Engineering, Indian School of Mines Dhanbad, India, during 2014 to January 2016. He has authored two research paper in the peer referred International Journal. His research interests include Waveguide Aperture array, Slot Antenna and Metamaterial Antenna.
Sushrut Das received B.Sc. degree in Physics from Calcutta University, M.Sc. degree in Physics from Banaras Hindu University, M. Tech degree in Microwave from Burdwan University and Ph.D. degree in Engineering from Indian Institute of Technology, Kharagpur, India in the year 1999, 2001, 2003 and 2007 respectively. After that he joined Indian School of Mines, Dhanbad, India, where he is currently an Assistant Professor in the Department of Electronics Engineering. He has authored one book, Microwave Engineering (Oxford University press, 2014) and published several research papers in referred International Journals and conferences. He has received URSI (International Union of Radio Science) Young Scientist Award in Istanbul, Turkey in 2011. His research interest includes Microwave Antennas, Microwave passive structures, Wireless energy transfer and energy harvesting.
