2021 Vol. 30, No. 1

Special Focus: Data-Driven Industrial Intelligence
A Review of FPGA-Based Custom Computing Architecture for Convolutional Neural Network Inference
PENG Xiyuan, YU Jinxiang, YAO Bowen, LIU Liansheng, PENG Yu
2021, 30(1): 1-17. doi: 10.1049/cje.2020.11.002
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Convolutional neural network (CNN) has been widely adopted in many tasks. Its inference process is usually applied on edge devices where the computing resources and power consumption are limited. At present, the performance of general processors cannot meet the requirement for CNN models with high computation complexity and large number of parameters. Field-programmable gate array (FPGA)-based custom computing architecture is a promising solution to further enhance the CNN inference performance. The software/hardware co-design can effectively reduce the computing overhead, and improve the inference performance while ensuring accuracy. In this paper, the mainstream methods of CNN structure design, hardware-oriented model compression and FPGA-based custom architecture design are summarized, and the improvement of CNN inference performance is demonstrated through an example. Challenges and possible research directions in the future are concluded to foster research efforts in this domain.
Induction Motor Fault Diagnosis Based on Transfer Principal Component Analysis
YAN Ruqiang, SHEN Fei, ZHOU Mengjie
2021, 30(1): 18-25. doi: 10.1049/cje.2020.11.003
Abstract(26) HTML (12) PDF(2)
This paper presents a transfer learning-based approach for induction motor fault diagnosis, where the Transfer principal component analysis (TPCA) is proposed to improve diagnostic performance of the induction motors under various working conditions. TPCA is developed to minimize the distribution difference between training and testing data by mapping cross-domain data into a shared latent space in which domain difference can be reduced. The trained model can achieve a good performance in testing data by using the learned features consisting of common latent principal components. Experimental results show that the proposed approach outperforms traditional machine learning techniques and can diagnose induction motor fault under various working conditions effectively.
Multi-Scale Prediction of RUL and SOH for Lithium-Ion Batteries Based on WNN-UPF Combined Model
JIA Jianfang, WANG Keke, PANG Xiaoqiong, SHI Yuanhao, WEN Jie, ZENG Jianchao
2021, 30(1): 26-35. doi: 10.1049/cje.2020.10.012
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The prediction of Remaining useful life (RUL) and the estimation of State of health (SOH) are extremely important issues for operating performance of Lithium-ion (Li-ion) batteries in the Battery management system (BMS). A multi-scale prediction approach of RUL and SOH is presented, which combines Wavelet neural network (WNN) with Unscented particle filter (UPF) model. The capacity degradation data of Li-ion batteries are decomposed into the low-frequency degradation trend and high-frequency fluctuation components by Discrete wavelet transform (DWT). Based on the WNN-UPF model, the long-term RUL of Li-ion batteries is predicted with the low-frequency degradation trend data. The high-frequency fluctuation data and RUL prediction results are integrated effectively to estimate the short-term SOH of Li-ion batteries. The experimental results show that the proposed method achieves high accuracy and strong robustness, even if the prediction starting point is set to the early stage of Li-ion batteries' lifespan.
A New Dynamic-Copula Based Correlated Degradation Feature for Remaining Useful Life Prediction
LI Juan, DAI Hongde, JING Bo, JIAO Xiaoxuan
2021, 30(1): 36-44. doi: 10.1049/cje.2020.11.004
Abstract(34) HTML (17) PDF(2)
Feature extraction plays an important role in Remaining useful life (RUL) prediction. Feature extraction mainly depends on the performance degradation signal in the previous study, in which the dynamic correlations among different signals are ignored, and the RUL accuracy is affected. A new dynamic feature based on the correlations of the performance degradation signal is proposed. First, dynamic correlation coefficients are calculated by copula function as the multivariate correlation performance degradation features. Second, the random effect Wiener process is used for RUL prediction based on the new features, and the maximum likelihood estimation is adopted to calculate the unknown parameters of the Wiener process. Finally, the RUL estimation for solder joints under vibration load is carried out compared with the quantile and quantile-Principal component analysis (PCA) mixed feature extraction method. The research results show that the proposed method improved the prediction accuracy of RUL.
Learning a Deep Metric: A Lightweight Relation Network for Loop Closure in Complex Industrial Scenarios
JIN Sheng, CHEN Liang, GAO Yu, SHEN Changqing, SUN Rongchuan
2021, 30(1): 45-54. doi: 10.1049/cje.2020.11.005
Abstract(30) HTML (14) PDF(6)
The similarity metric in Loop closure detection (LCD) is still considered in an old fashioned way, i.e. to pre-define a fixed distance function, leading to a limited performance. This paper proposes a general framework named LRN-LCD, i.e. a Lightweight relation network for LCD, which combines the feature extraction module and similarity metric module into a simple and lightweight network. The LRN-LCD, an end-to-end framework, can learn a non-linear deep similarity metric to detect loop closures from different scenes. Moreover, the LRN-LCD supports image sequences as input to speed up the similarity metric in real-time applications. Extensive experiments on several open datasets illustrate that LRN-LCD is more robust to strong condition variations and viewpoint variations than the mainstream methods.
Computers and Microelectronics
Are Similar Bugs Fixed with Similar Change Operations? An Empirical Study
BO Lili, ZHU Xuanrui, SUN Xiaobing, NI Zhen, LI Bin
2021, 30(1): 55-63. doi: 10.1049/cje.2020.10.010
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Fine-grained change operations can help software developers fix software bugs more accurately and efficiently. However, the current fine-grained change operations are only used in specific fixing process, such as fixing of If statement. In this paper, we conducted an empirical study to explore the fine-grained change operations for bug fixing. Based on the Mozilla bug data, we examined whether similar bugs are fixed with similar change operations. The results show that: First, for bug reports with similar descriptions or bug-fix commits with similar descriptions, their corresponding fine-grained change operations are not related; Second, in the case where the descriptions of both bug reports and bug-fix commits are similar, the fine-grained change operations in patch code are not related; Third, by classifying bug reports, we find that the change operations in the same bug report category are similar; Finally, by analyzing the fine-grained change operations for each bug, we present some combined patterns that are often used together.
On the p-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences
JING Xiaoyan, XU Zhefeng, YANG Minghui, FENG Keqin
2021, 30(1): 64-71. doi: 10.1049/cje.2020.08.016
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The purpose of this paper is to determine the $p$-adic complexity of the Ding-Helleseth-Martinsen (DHM) sequences with period $N=2q$, where $q \equiv 5\pmod 8$ is a prime number. We firstly use the $p$-adic exponential valuation, cyclotomic numbers of order four, "Gauss periods" and "quadratic Gauss sums" on finite field $\mathbb{F_q}$ and valued in $\mathbb{Z_{p.N-1}}$ to determine the $p$-adic complexity of the DHM sequences.
One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes
LI Tiantian, SHI Minjia, LIN Bo, WU Wenting
2021, 30(1): 72-76. doi: 10.1049/cje.2020.10.011
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This paper is devoted to the construction of one and two-weight $\mathbb{Z}_{2}R_{2}$ additive codes, where $R_{2}=\mathbb{F}_{2}[v]/\langle v.{4}\rangle$. It is a generalization towards another direction of $\mathbb{Z}_{2}\mathbb{Z}_{4}$ codes (S.T. Dougherty, H.W. Liu and L. Yu, "One weight $\mathbb{Z}_{2}\mathbb{Z}_{4}$ additive codes", \textit{Applicable Algebra in Engineering, Communication and Computing}, Vol.27, No.2, pp.123--138, 2016). A MacWilliams identity which connects the weight enumerator of an additive code over $\mathbb{Z}_{2}R_{2}$ and its dual is established. Several construction methods of one-weight and two-weight additive codes over $\mathbb{Z}_{2}R_{2}$ are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.
An Efficient SCF-PEKS Without Random Oracle Under Simple Assumption
WANG Guangbo, LI Feng, FAN Liwen, LIU Haicheng
2021, 30(1): 77-84. doi: 10.1049/cje.2020.11.006
Abstract(12) HTML (6) PDF(1)
The Public key encryption scheme with keyword search (PEKS), firstly put forward by Boneh et al., can achieve the keyword searching without revealing any information of the initial data. However, the original PEKS scheme was required to construct a secure channel, which was usually expensive. Aimed at resolving this problem, Baek et al. put forward an improved scheme, which tried to construct a Secure channel free PEKS (SCF-PEKS). Subsequently, several SCF-PEKS schemes were proposed, however most of them turned out only secure in the random oracle model, which possibly lead to the construction of insecure schemes. Therefore, Fang et al. put forward an enhanced SCF-PEKS construction, which was provably secure in the standard model, however this construction needed a strong and complicated assumption. Then Yang et al. put forward an SCF-PEKS construction under simple assumption, but their construction had a big reduction in efficiency. In this article, we propose an SCF-PEKS construction, which is provably secure under the same assumption as that of Yang et al.'s scheme, however, with better performance. Then we give its full security proof, along with the performance analysis. Finally, we improve the SCF-PEKS construction to resist Keyword guessing attack (KGA) and give its security demonstration.
Research on the Security Criterion of S-Boxes Against Division Property
WANG Senpeng, HU Bin, GUAN Jie, SHI Tairong, ZHANG Kai
2021, 30(1): 85-91. doi: 10.1049/cje.2020.10.013
Abstract(33) HTML (16) PDF(2)
As a generalized integral property, division property was proposed by Todo at EUROCRYPT 2015. We propose a new security criterion of S-boxes against division property and prove that it is invariant under permutation-xor equivalence. Based on the criterion, the division properties of some important 4-bit S-boxes are showed. Then, we apply it to improve the resistance of ciphers against division-property-based integral attacks while keeping the same security level against other attacks. Specifically, the resistance of the cipher PRESENT against division-property-based integral attack is improved by 2 rounds, and the resistance of the cipher LBlock against division-property-based integral attack is improved by 1 round.
Trust Evaluation Model Based on PSO and LSTM for Huge Information Environments
ZHANG Lin, HUANG Yanwen, XUAN Jie, FU Xiong, LIN Qiaomin, WANG Ruchuan
2021, 30(1): 92-101. doi: 10.1049/cje.2020.12.005
Abstract(19) HTML (10) PDF(3)
Due to the challenge of increasing data volume, the traditional trust model is unable to manage data with high efficiency and effectively extract useful information hidden in big data. To fully utilize big data and combine machine learning with trust evaluation, a trust evaluation model based on Long short-term memory (LSTM) is presented. The powerful learning ability, expressive ability and dynamic timing of LSTM can be applied to study data while avoiding the vanishing and exploding gradient phenomena of traditional Recurrent neural networks (RNNs) to ensure that the model can learn sequences of random length and provide accurate trust evaluation. Targeting the performance instability caused by the LSTM model's random initialization of weights and thresholds, Particle swarm optimization (PSO), one of the intelligent algorithms, is introduced to find global optimal initial weights and thresholds. Experiments proved that the trust model proposed in this paper has high accuracy and contributes a new idea for trust evaluation in big data environments.
An Improved Global Shutter Pixel with Extended Output Range and Linearity of Compensation for CMOS Image Sensor
GUO Zhongjie, YU Ningmei, WU Longsheng
2021, 30(1): 102-108. doi: 10.1049/cje.2020.11.007
Abstract(29) HTML (14) PDF(6)
An improved global shutter pixel structure with extended output range and linearity of compensation is proposed for CMOS image sensor. The potential switching of the sample and hold capacitor bottom plate outside the array is used to solve the problem of the serious swing limitation, which will attenuate the dynamic range of the image sensor. The non-linear problem caused by the substrate bias effect in the output process of the pixel source follower is solved by using the mirror FD point negative feedback self-establishment technology outside the array. The approach proposed in this paper has been verified in a global shutter CMOS image sensor with a scale of 1024×1024 pixels. The test results show that the output range is expanded from 0.95V to 2V, and the error introduced by the nonlinearity is sharply reduced from 280mV to 0.3mV. Most importantly, the output range expansion circuit does not increase the additional pixel area and the power consumption. The power consumption of linearity correction circuit is only 23.1μW, accounting for less than 0.01% of the whole chip power consumption.
Signal Processing
Joint Feature Representation and Classifier Learning Based Unsupervised Domain Adaption ELM
WANG Xuesong, ZHAO Jijuan, CHENG Yuhu, YU Qiang
2021, 30(1): 109-118. doi: 10.1049/cje.2020.11.008
Abstract(17) HTML (9) PDF(1)
In the problem of unsupervised domain adaption Extreme learning machine (ELM), the output layer parameters need to have both classification and domain adaptation functions, which often cannot be simultaneously fully utilized. In addition, traditional matching method based on data probability distribution cannot find the common subspace of source and target domains under large difference between domains. In order to alleviate the pressure of double functions of classifier parameters, the entire ELM learning process is mainly divided into two stages: feature representation and adaptive classifier learning, thus a joint feature representation and classifier learning based unsupervised domain adaption ELM model is proposed. In the feature representation stage, the source and target domain data are projected to their respective subspace while minimizing the difference in probability distribution between the two domains. In the adaptive classifier learning stage, the smooth manifold regularization term of target domain is used to improve the parameter adaptive ability. Experiments on six different types of datasets show that the proposed model has higher cross-domain classification accuracy.
A Joint TDOA/FDOA Localization Algorithm Using Bi-iterative Method with Optimal Step Length
LIU Congfeng, YUN Jinwei
2021, 30(1): 119-126. doi: 10.1049/cje.2020.11.009
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In order to improve the estimation accuracy of multi-station joint Time difference of arrive / Frequency difference of arrive (TDOA/FDOA) location with Bi-Iterative method, a solution for the position of target with Gauss-Newton optimal step length is proposed in this paper. First, get the initial estimation of target based on Two-stage weighted least-squares (TSWLS) algorithm, and then alternately solve the position and velocity of the target with Bi-Iterative method. In this paper, Gauss-Newton method is applied to iteratively solve the target position, including the detailed equations of the descending direction and the optimal iterative step length in each iterative process. Simulations are carried out to examine the algorithm's performance by comparing it with TSWLS method and Gauss-Newton method regardless of the step length. The results show that when Gauss noise variance is small, the estimation accuracy is close to Cramer Rao lower bound (CRLB) and the proposed method performs better than the other two methods. In addition, because the model which includes the position and velocity of the observation station and the target is in line with the over-the-horizon reality scene in this paper, our research has certain practical value.
A Novel Dual Pointer Approach for Entity Mention Extraction
LIU Jie, PANG Yihe, ZHANG Kai, LIU Lizhen, YU Zhengtao
2021, 30(1): 127-133. doi: 10.1049/cje.2020.11.010
Abstract(9) HTML (4) PDF(1)
The named entity extraction task aims to extract entity mentions from the unstructured text, including names of people, places, institutions and so on. It plays an important role in many Natural language processing (NLP) tasks, such as knowledge bases construction, automatic question answering system and information extraction. Most of the existing entity extraction studies are based on the long text data, which are easier to annotate due to the sufficient contextual information. Extracting entities from short texts such as search queries, conversations is still a challenging task. This paper proposes a dual pointer approach for entity mention extraction, it extracts one entities by two position pointers of the input sentence. The end-to-end deep neural networks model based on the proposed approach can extract the entities by serially generating the dual pointers. The evaluation results on the Chinese public dataset show that the model achieves the state-of-the-art results over the baseline models.
Quantitative Method Based on Cotangent Similarity Degree in Three-Valued Ł ukasiewicz Logic
YU Peng
2021, 30(1): 134-144. doi: 10.1049/cje.2020.11.011
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The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued Ł ukasiewicz propositional logic system $\text{Ł}_{3}$. We introduce the concepts of the cotangent similarity degree, cotangent pseudo-distance and cotangent truth degree of the propositions, together with their basic properties in $\text{Ł}_{3}$. We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives $\neg, \vee$ and $\rightarrow$ in the $\text{Ł}_{3}$ logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F(S), and provide several examples and basic properties of it.
A Novel Quantum Entanglement-Inspired Meta-heuristic Framework for Solving Multimodal Optimization Problems
ZHAO Shijie, MA Shilin, GAO Leifu, YU Dongmei
2021, 30(1): 145-152. doi: 10.1049/cje.2020.11.012
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To solve Multimodal optimization problems (MOPs), a Novel Quantum entanglement-inspired meta-heuristic framework (NMF-QE) is proposed. Its main inspirations are two concepts of quantum physics: quantum entanglement and quantum superposition. When given Proto-born particles (PBPs) of a population, these two concepts are mathematically developed to generate twin-born and combination-born particles, respectively. And if any elite-born particles would be created by a local re-searching strategy. These three or four groups of particles come together as a whole search population of NMF-QE to realize exploration and exploitation of algorithms. To guarantee dynamical optimization capability of NMF-QE, the individual evolutionary mechanism of some existing meta-heuristics will be adopted to iteratively create PBPs. A selected meta-heuristic is coupled with NMF-QE to present its improved variant. Numerical results show that the proposed NMF-QE can effectively improve optimization performance of meta-heuristics on MOPs.
A Short Text Classification Algorithm Based on Semantic Extension
ZHOU Yajian, DENG Dingpeng, CHI Junhui
2021, 30(1): 153-159. doi: 10.1049/cje.2020.11.014
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A semantic-extension-based algorithm for short texts is proposed, by involving the Word2vec and the LDA model, to improve the performance of classification, which is frequently deteriorated by semantic dependencies and scarcity of features. For every keyword within a short text, weighted synonyms and related words can be generated by the Word2Vec and LDA model, respectively, and subsequently be inserted to extend the short text to a reasonable length. We not only have established a criterion by means of similarity estimation to determine whether a sentence should be extended, we designed a scheme to choose the number of extended words. The extended text will be classified. Experimental results show that, the classification performance of the proposed algorithm, in terms of the precision rate, is approximately 5% higher than that of the TF-IDF model and approximately 10% higher than that of the VSM method.
Selected-Mapping Peak-to-Average Power Reduction Method with Orthogonal Pilot Sequences in Underwater Acoustic OFDM System Without Side Information
QIAO Gang, XING Siyu, ZHOU Feng
2021, 30(1): 160-163. doi: 10.1049/cje.2020.11.015
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A novel Selected-mapping (SLM) Peak-to-average power ratio (PAPR) reduction scheme requires no Side information (SI) in Underwater acoustic (UWA) OFDM system is proposed. In the proposed scheme, every distinct phase sequence is represented by a unique Orthogonal comb pilot sequence (OPS), and the orthogonal properties of the OPSs are used to distinguish the index of phase sequences at the receiver. Therefore, the proposed scheme does not need to reserve bits for transmitting SI, so that the data rate can be raised. Simulation results show that the PAPR reduction performance has almost 0.5dB gains comparing to the Conventional SLM (C-SLM) scheme and the Bit error ratio (BER) performance is approximately the same as the SLM scheme with perfect SI. Field experimental results also demonstrate that the proposed scheme can differentiate phase sequences, therefore significantly enhance the quality of the UWA OFDM communication system.
A Novel Collision Supervision and Avoidance Algorithm for Scalable MAC of Vehicular Networks
WANG Shuai, LU Yan, ZHU Jie, WANG Ping
2021, 30(1): 164-170. doi: 10.1049/cje.2020.12.001
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In order to meet low-latency and ultrareliable requirements on safety services in vehicular networks, this paper proposes a novel Collision supervision and avoidance (CSA) algorithm for the contention based scalable media access control protocol. The twodimensional Markov chain model of adaptive backoff state transition criterion in CSA has been built, which could efficiently match the backoff states of nodes to the dynamic changes of vehicular networks. The scalable transmissions can be achieved through supervised trend and matching backoff mechanisms with three adaptive backoff modes. The packet transmit probabilities for the backoff modes have been derived with the theoretical result of the enhanced throughput. The simulation results show the remarkable scalability performance such as normalized throughput > 0.92, PDR > 86% and delay < 6.5ms even in the high-density and high-mobility environment.
Microwave and Electronic System Engineering
Evaluation Model and Method of Margin in Electromagnetic Environmental Effects for Complex Systems
TANG Shiping, MAO Junfa
2021, 30(1): 171-179. doi: 10.1049/cje.2020.12.006
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Margin is an important index in the control of Electromagnetic environmental effects (E3) and Electromagnetic compatibility (EMC) design for systems. How to define and verify the E3 margins of complex systems such as ships and airplanes is a difficult problem. A new method of system-level E3 margin evaluation is proposed. Based on the theory of fault tree, the evaluation model of system-level margin is constructed. The complex system function is transformed into the equipment and subsystem that affect the function, and the relationship between margin of system-level and equipment is established. The change from margin of equipment to system-level margin is realized. According to the action process of Electromagnetic environment (EME), the verification and evaluation methods of EME domain, response domain and effect domain are put forward. The margin calculation formula of EME domain and typical electromagnetic energy coupling response are deduced. The problem of margin evaluation for equipment under different input parameters is solved. A typical application example is given. The verification test scheme is designed. The methods of electromagnetic energy radiation and injection are adopted. The system-level margin is analyzed by the data obtained from the effective test verification. The results show that the model and method are reasonable and feasible.
Analysis of Dark Signal Degradation Caused by 1 MeV Neutron Irradiation on Backside-Illuminated CMOS Image Sensors
LIU Bingkai, LI Yudong, WEN Lin, ZHOU Dong, FENG Jie, ZHANG Xiang, CAI Yulong, FU Jing, GUO Qi
2021, 30(1): 180-184. doi: 10.1049/cje.2020.12.002
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The purpose of this work is to investigate the influence of the epitaxial layer thickness of Backside-illuminated CMOS image sensors (BSI CISs) on dark signal behaviors. BSI CISs with the high quantum efficiency and sensitivity were irradiated by 1 MeV neutron up to the fluences of 109cm−2. The displacement damage induced variations of the mean dark signal, Dark signal nonuniformity (DSNU), dark signal spikes and Random telegraph signal (RTS) on the different epitaxial layer thicknesses are analyzed. The experimental results show that there is no obvious correlation between the degradations of dark signal parameters and the epitaxial layer thickness, suggesting that the electric-optical performance of BSI CISs can be improved by optimizing the epitaxial layer thickness.
A Novel Quarter-Circular Arc Multi-Direction Piezoelectric VEH and Its Theoretical Model
ZHU Yucheng, HU Jiayang, BAI Yunshan, ZHAO Jiang, JI Xincun, WANG Debo
2021, 30(1): 185-191. doi: 10.1049/cje.2020.12.003
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A quarter-circular arc piezoelectric Vibration energy harvester (VEH) based on nonlinear geometry is proposed with both bending moment and torque deformation mode, so it can effectively absorb multi-directional vibration at the same resonance frequency. The theoretical model of quarter-circular arc piezoelectric VEH is established to study the resonance frequency and the output voltage. In order to demonstrate multi-directional performance of the quarter-circular arc VEH, the stress distribution is compared with that of the traditional piezoelectric VEH in multi-direction vibration, and the output voltage of the circular arc piezoelectric VEH are relatively increased 267.26% in X-direction, 463.18% in Y-direction, and 17.24% in Z-direction. The external load is equipped in circuit to measure output power, whose matching resistance is around 21k$\bm{\Omega}$, and the maximum output powers are 7.57mW in X-direction, 2.39mW in Y-direction, and 9.93mW in Z-direction.
A Miniaturized Bandwidth Reconfigurable Bandpass Chip Filter with Semi-lumped Topology and GaAs pHEMT Technology
LI Linqing, ZHU Haoran, NING Xingyu, LI Zunwen, WU Xianliang
2021, 30(1): 192-198. doi: 10.1049/cje.2020.12.004
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A miniaturized reconfigurable bandpass chip filter with semi-lumped topology and Gallium Arsenide pseudomorphic High electron mobility transistor (GaAs pHEMT) technology is proposed. Semi-lumped topology is employed to instead the traditional lumped inductor with microstrip transmission line, which can reduced the size of the tunable filter significantly. Three-order series and shunt resonated bandpass filter is implemented with shorted stubs and metal-insulator-metal capacitors. Two transmission zeros are introduced with the series resonator and the shunted GaAs FET. By tuning the gate bias circuit of the FET, the capacitance of the series resonator is changed and the bandwidth of the filter is adjusted correspondingly. An equivalent circuit model is developed to interpret the mechanism of the proposed filter circuit. A reconfigurable on chip filter sample operated at 10GHz is fabricated to validate the design. Two fractional bandwidth of 14.3% and 23.5% are tuned with bias voltage of the FET, while insertion loss of 2.4dB and 2.2dB are observed with the filter, respectively. The area of the chip filter is $ {{0.86 \times 0.96 \mathrm{mm}^{2}}} $ and is equivalent to an electrical length of $ {{0.08 \times 0.09 \lambda \mathrm{g}^{2} }}$ at center frequency. Measurement results agree well with the simulation ones.