IEICE Transactions on Electronics
Online ISSN : 1745-1353
Print ISSN : 0916-8524
Volume E99.C, Issue 7
Displaying 1-26 of 26 articles from this issue
Special Section on Recent Advances in Simulation Techniques and Their Applications for Electronics
  • Zhewang MA
    2016 Volume E99.C Issue 7 Pages 734
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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  • Yan CHEN, Yu ZHANG, Guanghui ZHANG, Xunwang ZHAO, ShaoHua WU, Qing ZHA ...
    Article type: INVITED PAPER
    2016 Volume E99.C Issue 7 Pages 735-743
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    In this paper, a Many Integrated Core Architecture (MIC) accelerated parallel method of moment (MoM) algorithm is proposed to solve electromagnetic problems in practical applications, where MIC means a kind of coprocessor or accelerator in computer systems which is used to accelerate the computation performed by Central Processing Unit (CPU). Three critical points are introduced in this paper in detail. The first one is the design of the parallel framework, which ensures that the algorithm can run on distributed memory platform with multiple nodes. The hybrid Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) programming model is designed to achieve the purposes. The second one is the out-of-core algorithm, which greatly breaks the restriction of MIC memory. The third one is the pipeline algorithm which overlaps the data movement with MIC computation. The pipeline algorithm successfully hides the communication and thus greatly enhances the performance of hybrid MIC/CPU MoM. Numerical result indicates that the proposed algorithm has good parallel efficiency and scalability, and twice faster performance when compared with the corresponding CPU algorithm.
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  • Masataka OHIRA, Kazuma YAMANAKA, Zhewang MA
    Article type: PAPER
    2016 Volume E99.C Issue 7 Pages 744-750
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    This paper proposes a new design formula of coupling coefficient between antenna and resonator for an efficient design of filtering antennas consisting of an antenna and resonators. The filtering antenna can be designed by introducing a well-established filter design theory. For such a design approach, an external Q factor at input port, coupling coefficients, and a radiation Q factor of the antenna need to be evaluated. However, conventional design methods have a time-consuming procedure, since there are no effective techniques to evaluate the coupling coefficient between resonator and antenna. To solve the problem, we derive the new design formula using only amplitude property of input reflection responses obtained from a coupled structure of resonator and antenna. As an example, a third-order filtering antenna is synthesized, designed, and tested at 2.45 GHz, which numerically and experimentally validates the effectiveness of the derived equation.
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  • Kosei TANII, Koji WADA
    Article type: PAPER
    2016 Volume E99.C Issue 7 Pages 751-760
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    A triplexer is presented by using bandpass filters (BPFs) which consist of two-stage of wideband resonator and additional open-circuited stubs. The resonator is firstly proposed by using a coupled-line and an inductive element loaded transmission line. This resonator produces the wide passband by a dual-mode resonance, high attenuation level at stopbands, and the steepness at the edge of the passband due to the attenuation poles. In order to understand the behavior of the resonator, the conditions for resonances and attenuation poles are especially solved and their current densities are analyzed by an electromagnetic simulation. Secondly, three types of wideband BPFs are constituted and finally a wideband triplexer is composed by using these BPFs. The basic characteristics of the proposed BPFs and the matching methodology enable to realize the triplexer whose desired passbands are around 3.1-5.1 GHz, 5.85-7.85 GHz, and 8.6-10.6 GHz with high isolation performance at the other passbands. The proposed triplexer is predominance in the flexible bandwidth or wide operating frequency range. All the BPFs and the triplexer are implemented on a planar printed circuit board assuming the use of the microstrip line structure.
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  • Kaida DONG, Jingyan MO, Yuhong HE, Zhewang MA, Xuexia YANG
    Article type: PAPER
    2016 Volume E99.C Issue 7 Pages 761-765
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    A compact millimeter-wave three-pole dual-band bandpass filter (BPF) by using substrate-integrated waveguide (SIW) dual-mode cavities is developed in this paper. The proposed filter consists of three SIW dual-mode cavities, in which the TE201 and TE102 modes are used to form two passbands. The center frequencies of the two passbands can be readily changed by varying the lengths and/or widths of the SIW cavities. Meanwhile three transmission zeros are produced with appropriate design of the input and output of the SIW cavities, which increase significantly the isolation between the two passbands and their roll-off rate of attenuations. The dual-band BPF filter is designed, fabricated and measured. The measured center frequencies of the two passbands are 26.75GHz and 31.55GHz, respectively. The 3dB-passbands are 26.35-27.15GHz (3%) and 31.29-31.81GHz (1.6%), respectively, with maximum insertion loss of 2.64dB and 4.2dB, respectively, and return loss larger than 12dB in both passbands. A good agreement between the simulated and measured filter characteristics is obtained.
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  • Yoshiki KAYANO, Hiroshi INOUE
    Article type: PAPER
    2016 Volume E99.C Issue 7 Pages 766-773
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    To provide basic considerations for the realization of method for suppressing the EMI from differential-paired lines on flexible printed circuits (FPC), the characteristics of the SI performance and shielding effectiveness (SE) of shielded-flexible printed circuits for differential-signaling are investigated in this paper experimentally and by a numerical modeling. Firstly, transmission characteristics of TDR measurement and frequency response of |Sdd21| are discussed, from view point of signal integrity. Secondly, as the characteristics of the SE performance for EMI, frequency responses of magnetic field are investigated. Although placement of conductive shield near the paired-lines decreases characteristics impedance, |Sdd21| for the “with Cu 5.5 µm-thickness copper shield” is not deteriorated compared with “without shield” and sufficient SE performance for magnetic field can be established. But, thin-shield deteriorates SI as well as SE performances. The frequency response of |Sdd21| at higher frequencies for the “Ag 0.1 µm” case has the steep loss roll off. A reflection loss resulted from impedance-mismatching is not dominant factor of the losses. The dominant factor may be magnetic field leakage due to very thin-conductive shield.
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  • Kazuki ICHIKAWA, Zejun ZHANG, Yasuhide TSUJI, Masashi EGUCHI
    Article type: PAPER
    2016 Volume E99.C Issue 7 Pages 774-779
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    We propose a novel single polarization photonic band gap fiber (SP-PBGF) with an anisotropic air hole lattice in the core. An SP-PBGF with an elliptical air hole lattice in the core recently proposed can easily realize SP guidance utilizing the large difference of cutoff frequency for the x- and y-polarized modes. In this paper, in order to achieve SP guidance based on the same principle of this PBGF, we utilize an anisotropic lattice of circular air holes instead of elliptical air holes to ease the fabrication difficulty. After investigating the influence of the structural parameters on SP guidance, it is numerically demonstrated that the designed SP-PBGF has 381 nm SP operating band.
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  • Yasuo OHTERA
    Article type: PAPER
    2016 Volume E99.C Issue 7 Pages 780-787
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    FDTD (Finite-Difference Time-Domain) method has been widely used for the analysis of photonic devices consisting of sub-wavelength structures. In recent years, increasing efforts have been made to implement the FDTD on GPGPUs (General-Purpose Graphic Processing Units), to shorten simulation time. On the other hand, it is widely recognized that most of the middle- and low-end GPGPUs have difference of computational performance, between single-precision and double-precision type arithmetics. Therefore the type selection of single/double precision for electromagnetic field variables in FDTD becomes a key issue from the viewpoint of the total simulation performance. In this study we investigated the difference of results between the use of single-precision and double-precision. As a most fundamental sub-wavelength photonic structure, we focused on an alternating multilayer (one dimensional periodic structure). Obtained results indicate that significant difference appears for the amplitudes of higher order spatial harmonic waves.
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  • Zaifeng YANG, Eng Leong TAN
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 788-792
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    An efficient three-dimensional (3-D) fundamental locally one-dimensional finite-difference time-domain (FLOD-FDTD) method incorporated with memristor is presented. The FLOD-FDTD method achieves higher efficiency and simplicity with matrix-operator-free right-hand sides (RHS). The updating equations of memristor-incorporated FLOD-FDTD method are derived in detail. Numerical results are provided to show the trade-off between efficiency and accuracy.
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  • Jun SONODA, Keimei KAINO, Motoyuki SATO
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 793-796
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    The finite-difference time-domain (FDTD) method has been widely used in recent years to analyze the propagation and scattering of electromagnetic waves. Because the FDTD method has second-order accuracy in space, its numerical dispersion error arises from truncated higher-order terms of the Taylor expansion. This error increases with the propagation distance in cases of large-scale analysis. The numerical dispersion error is expressed by a dispersion relation equation. It is difficult to solve this nonlinear equation which have many parameters. Consequently, a simple formula is necessary to substitute for the dispersion relation error. In this study, we have obtained a simple formula for the numerical dispersion error of 2-D and 3-D FDTD method in free space propagation.
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  • Shinichiro OHNUKI, Yuya KITAOKA, Takashi TAKEUCHI
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 797-800
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    A novel computational method based on a combination of the method of moments in the complex frequency domain and the fast inverse Laplace transform is proposed for solving time-domain electromagnetic problems. Using our proposed method, it is easy to estimate and control the computational error, and the observation time can be selected independently. We investigate canonical scattering problems and verify these advantages.
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  • Ryota SATO, Keimei KAINO, Jun SONODA
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 801-804
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    Pre-Cantor bar, the one-dimensional fractal media, consists of two kinds of materials. Using the transmission-line theory we will explain the double-exponential behavior of the minimum of the transmittance as a function of the stage number n, and obtain formulae of two kinds of scaling behaviors of the transmittance. From numerical calculations for n=1 to 5 we will find that the maximum of field amplitudes of resonance which increases double-exponentially with n is well estimated by the theoretical upper bound. We will show that after sorting field amplitudes for resonance frequencies of the 5th stage their distribution is a staircase function of the index.
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  • Shinya KITAGAWA, Ryosuke SUGA, Osamu HASHIMOTO, Kiyomichi ARAKI
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 805-808
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    Radar cross section (RCS) of a patch array antenna is reduced using a switchable absorption/transmission surface. The switchable surface performs as between a radar absorber and transmission surface using diodes at 9GHz. The switchable surface was applied to the radome of a patch array and its radiation pattern and RCS reduction were evaluated. The gain and the radiation pattern with the radome was equivalent to that without the radome. The RCS reduction with the radome was 25dB compared to that without the radome.
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  • Naoki TANAKA, Takashi HIKAGE, Toshio NOJIMA
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 809-812
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    This paper describes a numerical assessment methodology of pacemaker EMI triggered by HF-band wireless power transfer system. By using three dimensional full-wave numerical simulation based on finite element method, interference voltage induced at the connector of the pacemaker inside the phantom that is used for in-vitro EMI assessment is obtained. Simulated example includes different exposure scenarios in order to estimate the maximum interference voltage.
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  • Suguru IMAI, Kenji TAGUCHI, Tatsuya KASHIWA
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 813-816
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    In the development of inter-vehicle communication systems for a prevention of car crashes, it is important to know path loss characteristics at blind intersections in urban area. Thus field experiments and numerical simulations have been performed. By the way, transparent waves from building walls are not considered in many cases. The reason why is that it is the worst case in terms of the path loss at blind intersection surrounded by buildings in urban area. However, it would be important to know the effect of transparent wave on the path loss in actual environments. On the other hand, path loss models have been proposed to estimate easily the path loss in urban environment. In these models, the effect of transparent wave is not clear. In this paper, the effect of transparent wave from building walls on path loss characteristics at blind intersection in urban area is investigated by using the FDTD method. Additionally, the relationship between transparent wave and path loss models is also investigated.
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  • Jun SHIBAYAMA, Yusuke WADA, Junji YAMAUCHI, Hisamatsu NAKANO
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 817-819
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    Two plasmonic band-bass filters are analyzed: one is a grating-type filter and the other is a slit-type filter. The former shows a band-pass characteristic with a high transmission for a two-dimensional structure, while the latter exhibits a high transmission even for a three-dimensional structure with a thin metal layer.
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  • Ryosuke OZAKI, Tsuneki YAMASAKI
    Article type: BRIEF PAPER
    2016 Volume E99.C Issue 7 Pages 820-824
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    In this paper, we have investigated a new structure which combines dielectric cylinders with air-hole cylinders array, and analyzed the guiding problem for periodically dielectric waveguides by arbitrary shape of dielectric constants in the middle layer. In the numerical analysis, we examined an influence of the dielectric circular cylinder along a middle layer by using the energy distribution and complex propagation constants at the first stop band region compared with hollow dielectric cylinder. In addition, we also investigated the influence of dielectric structure with equivalence cross section compared with dielectric cylinders, and clarified an influence of dielectric structures in the middle layer by energy distribution analysis for TE0 mode.
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Regular Section
  • Ryan IMANSYAH, Tatsushi TANAKA, Luke HIMBELE, Haisong JIANG, Kiichi HA ...
    Article type: PAPER
    Subject area: Optoelectronics
    2016 Volume E99.C Issue 7 Pages 825-829
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    We have proposed and demonstrated the principle of optical mode switch. However, the crosstalk between modes has not yet reported due to the difficulty of mode recognition and distinction. To accomplish this mode crosstalk evaluation, we integrated multimode interference (MMI) mode filter with the optical mode switch in this work. As a result, for the both TE and TM modes, the crosstalk of approximately -10 dB has been evaluated experimentally.
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  • Shinichi TANAKA, Takao KATAYOSE, Hiroki NISHIZAWA, Ken'ichi HOSOYA, Ry ...
    Article type: PAPER
    Subject area: Microwaves, Millimeter-Waves
    2016 Volume E99.C Issue 7 Pages 830-836
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    We present a design method for miniaturizing double stub resonators that are potentially very useful for wide range of applications but have limited usage for MMICs due to their large footprint. The analytical design model, which we introduce in this paper, allows for determining the capacitances needed to achieve the targeted shrinking ratio while maintaining the original loaded-Q before miniaturization. To verify the model, 18-GHz stub resonators that are around 40% of the original sizes were designed and fabricated in GaAs MMIC technology. The effectiveness of the proposed technique is also demonstrated by a 9-GHz low phase-noise oscillator using the miniaturized resonator.
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  • Kazuya YAMAMOTO, Takayuki MATSUZUKA, Miyo MIYASHITA, Kenichi HORIGUCHI ...
    Article type: PAPER
    Subject area: Microwaves, Millimeter-Waves
    2016 Volume E99.C Issue 7 Pages 837-848
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    This paper describes, for the first time, the circuit design considerations and measurements of core building blocks that support a 1.9-GHz-band (Band I) BiFET MMIC three-power-mode power amplifier (PA) for WCDMA handset applications. The blocks are a reference voltage (Vref) generator, a control logic circuit, and ESD protection circuits. Our proposed Vref-generator, based on a current-mirror topology, can successfully suppress Vref variation against threshold voltage (Vth) dispersion in the FET as well as current gain dispersion in the HBT. On-wafer measurements over several wafer lots show that the standard deviation of Vref is as small as 18 mV over a Vth dispersion range from -0.6 V to -1.0 V. As a result, the measured quiescent current dispersion in the HPM is also suppressed to less than 5.4 mA, despite the fact that the average quiescent current is relatively high, at 81.3 mA. Several simulations reveal that small decoupling capacitances of approximately 1 pF added to the gate control lines of RF switch FETs ensure stable operation of the control logic even if an undesired RF coupling is present between an RF signal path and the gate lines. An empirical and useful design approach for ESD protection using HBT base-collector diodes allows easy and precise estimation of the HBM ESD robustness. With the above building blocks, a 3 mm × 3 mm PA was designed and fabricated by an in-house BiFET process. Measurements conducted under the conditions of a 3.4-V supply voltage and a 1.95-GHz WCDMA modulated signal are as follows. The PA delivers a 28.3-dBm output power (Pout), a 28.2-dB power gain (Gp), and 40% PAE while restricting the ACLR1 to less than -42 dBc in the HPM. In the MPM, 17.4 dBm of Pout, 15.9 dB of Gp, and 25.3% of PAE are obtained, while in the LPM, the PA delivers 7 dBm of Pout, 11.7 dB of Gp, and 13.9% of PAE. The HBM ESD robustness is 2 kV.
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  • GuangFu LI, Hsien-Shun WU, Ching-Kuang C. TZUANG
    Article type: PAPER
    Subject area: Microwaves, Millimeter-Waves
    2016 Volume E99.C Issue 7 Pages 849-855
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    An asymmetric left-handed coupled-line is presented to implement the tight forward coupler. Two left-handed transmission lines are coupled through its shunt inductors. The numerical procedures based on the generalized four-port scattering parameters combined with the periodical boundary conditions are applied to extract the modal characteristics of the asymmetric coupled-line, and theoretically predict that the proposed coupled-line can make a normalized phase constant of c mode 1.57 times larger than π mode for the forward coupler miniaturization. The design curves based on different overlapping length of the shunt inductors are reported for the coupler design. The procedures, so-called the port-reduction-method (PRM), are applied to experimentally characterize the coupler prototype using the two-port instruments. The measured results confirm that prototype uses 0.21 λg at 430 GHz to achieve -4.55 dB forward coupling with 13% 1-dB operating bandwidth.
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  • Koji TAKINAMI, Hiroyuki MOTOZUKA, Tomoya URUSHIHARA, Masashi KOBAYASHI ...
    Article type: PAPER
    Subject area: Microwaves, Millimeter-Waves
    2016 Volume E99.C Issue 7 Pages 856-865
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    This paper presents a 60 GHz analog/digital beamforming receiver that effectively suppresses interference signals, targeting the IEEE 802.11ad/WiGig standard. Combining two-stream analog frontends with interference rejection digital signal processing, the analog beamforming steers the antenna beam to the desired direction while the digital beamforming provides gain suppression in the interference direction. A prototype has been built with 40 nm CMOS analog frontends as well as offline baseband digital signal processing. Measurements show a 3.1 dB EVM advantage over conventional two-stream diversity during a packet collision situation.
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  • Abdulfattah M. OBEID, Syed Manzoor QASIM, Mohammed S. BENSALEH, Abdull ...
    Article type: PAPER
    Subject area: Electronic Circuits
    2016 Volume E99.C Issue 7 Pages 866-877
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    Reconfigurable architectures have emerged as an optimal choice for the hardware realization of digital signal processing (DSP) algorithms. Reconfigurable architecture is either fine-grained or coarse-grained depending on the granularity of reconfiguration used. The flexibility offered by fine-grained devices such as field programmable gate array (FPGA) comes at a significant cost of huge routing area, power consumption and speed overheads. To overcome these issues, several coarse-grained reconfigurable architectures have been proposed. In this paper, a scalable and hybrid dynamically reconfigurable architecture, HyDRA, is proposed for efficient hardware realization of computation intensive DSP algorithms. The proposed architecture is greatly influenced by reported VLSI architectures of a variety of DSP algorithms. It is designed using parameterized VHDL model which allows experimenting with a variety of design features by simply modifying some constants. The proposed architecture with 8×8 processing element array is synthesized using UMC 0.25µm and LF 150nm CMOS technologies respectively. For quantitative evaluation, the architecture is also realized using Xilinx Virtex-7 FPGA. The area and timing results are presented to provide an estimate of each block of the architecture. DSP algorithms such as 32-tap finite impulse response (FIR) filters, 16-point radix-2 single path delay feedback (R2SDF) fast fourier transform (FFT) and R2SDF discrete cosine transform (DCT) are mapped and routed on the proposed architecture.
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  • Ing-Chao LIN, Yen-Han LEE, Sheng-Wei WANG
    Article type: PAPER
    Subject area: Integrated Electronics
    2016 Volume E99.C Issue 7 Pages 878-891
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    Ternary content addressable memory (TCAM), which can store 0, 1, or X in its cells, is widely used to store routing tables in network routers. Negative bias temperature instability (NBTI) and positive bias temperature instability (PBTI), which increase Vth and degrade transistor switching speed, have become major reliability challenges. This study analyzes the signal probability of routing tables. The results show that many cells retain static stress and suffer significant degradation caused by NBTI and PBTI effects. The bit flipping technique is improved and proactive power gating recovery is proposed to mitigate NBTI and PBTI effects. In order to maintain the functionality of TCAM after bit flipping, a novel TCAM cell design is proposed. Simulation results show that compared to the original architecture, the bit flipping technique improves read static noise margin (SNM) for data and mask cells by 16.84% and 29.94%, respectively, and reduces search time degradation by 12.95%. The power gating technique improves read SNM for data and mask cells by 12.31% and 20.92%, respectively, and reduces search time degradation by 17.57%. When both techniques are used, read SNM for data and mask cells is improved by 17.74% and 30.53%, respectively, and search time degradation is reduced by 21.01%.
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  • Yi ZHANG, Guoqiang ZHAO, Houjun SUN, Mang HE, Qiang CHEN
    Article type: BRIEF PAPER
    Subject area: Electromagnetic Theory
    2016 Volume E99.C Issue 7 Pages 892-894
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    Digital phase shifters are widely used to achieve space scanning in phased array antenna, and beam pointing accuracy depends on the bit number and resolution of the digital phase shifter. This paper proposes a novel phase feeding method to reduce the phase quantization error effects. A linear formula for the beam pointing deviation of a linear uniform array in condition of phase quantization error is derived, and the linear programming algorithm is introduced to achieve the minimum beam pointing deviation. Simulations are based on the pattern of the phased array, which gives each element a certain quantization phase error to find the beam pointing deviation. The novel method is then compared with previous methods. Examples show that a 32-element uniform linear array with 5-bit phase shifters using the proposed method can achieve a higher beam-steering accuracy than the same array with 11-bit phase shifters.
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  • Zhitao XU, Jun XU, Shuai LIU, Yaping ZHANG
    Article type: BRIEF PAPER
    Subject area: Microwaves, Millimeter-Waves
    2016 Volume E99.C Issue 7 Pages 895-898
    Published: July 01, 2016
    Released on J-STAGE: July 01, 2016
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    In this paper, a novel multilayer substrate integrated waveguide (SIW) four-way out-of-phase power divider is proposed. It is realized by 3D mode coupling, on multilayer substrates. The structure consists of vertical Y-junction, lateral T-junction of SIW and lateral Y-junction of half-mode SIW. The advantages of the proposed structure are its low cost and ease of fabrication. Also, it can be integrated easily with other planar circuits such as microstrip circuits. An experimental circuit is designed and fabricated using the traditional printed circuit board technology. The simulated and measured results show that the return loss of the input port is above 15 dB over 8 to 11.8 GHz and transmissions are about -7.6±1.6 dB in the passband. It is expected that the proposed the proposed power divider will play an important role in the future integration of compact multilayer SIW circuits and systems.
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