Search Results(524)

2024-09-30
PIER M
Vol. 129, 53-64
Study of an Electric Vehicle WPT System with Ring-Series Passive Magnetic Shielding Based on Dual Transmitting Coils
Xueyi Zhang , Zhibang Luo , Sai Zhang , Bin Li , Ziyue Gan and Zhongqi Li
In the design of wireless power transfer (WPT) systems for electric vehicles, minimizing magnetic leakage while maintaining high transmission efficiency is a challenging problem. To this end, a novel structure featuring dual transmitting coils and a ring-series magnetic shielding coil (RMSDT) is proposed to reduce magnetic leakage during system charging, thereby enhancing system safety performance. Additionally, the Particle Swarm Optimization (PSO) algorithm is employed to optimize system parameters, aiming to achieve high transmission efficiency while maintaining low magnetic leakage. To validate the effectiveness of the proposed design, a shielded WPT system for electric vehicles has been developed. Its performance is verified through a combination of experiments and simulations. The results demonstrate that the PSO algorithm significantly enhances transmission efficiency compared to traditional optimization methods. At an output power of 3.7 kW, the peak transmission efficiency exceeds 95%, representing an improvement of 4.63% compared to the conventional for-loop algorithm. Furthermore, the leakage magnetic field of the RMSDT structure in the target region is only 16.08 μT, which is effectively reduced by 41.8% compared to the conventional WPT structure and sacrifices only 0.21% transmission efficiency. In summary, this paper can provide some references to the safety and efficiency of electric vehicle WPT.
2024-09-29
PIER Letters
Vol. 122, 101-105
On-Demand Single-Photon Extraction for Underwater Quantum Communication
Min Chen , Lian Shen , Yifei Hua , Zijian Qin and Huaping Wang
Single-photon sources with high repetition rates have been a focal point of modern research for decades. However, their application in underwater environments is significantly limited due to the absorption properties of water, which hinder the propagation of most optical wavelengths. This study addresses the challenge by reporting on-demand single-photon extraction suitable for underwater quantum communication. The use of plasmonic nanoantennas can significantly enhance the spontaneous emission of single-photon sources. Nonetheless, a primary challenge is the nanoscale guiding of emitted photons in underwater environments. To overcome this, a more sophisticated design is required to enhance photon emission and achieve momentum matching with water. Here, we present a topology-optimized design of underwater plasmonic nanoantennas to mitigate these limitations. The nanoantenna consists of an optimized gold pattern and a silicon nitride substrate. Consequently, the normalized extraction decay rate (γe⁄γ0) can reach 4.02 at a wavelength of 517 nm, which is within the blue-green spectral range, when using an objective lens with a numerical aperture of 0.6 (cross-section angle of 26.7°). The proposed design approach for plasmonic nanoantennas is versatile and holds promising potential for various applications, particularly in advancing single-photon technologies for quantum communication.
2024-09-26
PIER M
Vol. 129, 43-52
YOLOv8 -DEC: Enhancing Brain Tumor Object Detection Accuracy in Magnetic Resonance Imaging
Zekun Lin , Weiming Lin and Fuchun Jiang
Brain tumors are characterized by the fast growth of aberrant brain cells, which poses a considerable risk to an adult's health since it can result in severe organ malfunction or even death. Magnetic resonance imaging (MRI) provides vital information for comprehending the nature of brain tumors, directing treatment approaches, and enhancing diagnostic precision. It displays the diversity and heterogeneity of brain tumors in terms of size, texture, and location. However, manually identifying brain tumors is a difficult and time-consuming process that could result in errors. It is proposed that an enhanced You Only Look Once version 8 (YOLOv8) model aids in mitigating the drawbacks associated with manual tumor detection, with the objective of enhancing the accuracy of brain tumor detection. The model employs the C2f_DySnakeConv module to improve the perception and discrimination of tumors. Additionally, it integrates Content-Aware ReAssembly of FEatures (CARAFE) to efficiently expand the network's receptive area to integrate more global contextual information, and Efficient Multi-Scale Attention (EMA) to improve the network's sensitivity and resolution for lesion features. According to the experimental results, the improved model performs better for brain tumor detection than both the open-source model and the original YOLOv8 model. It also achieves higher detection accuracy on the brain tumor image dataset than the original YOLOv8 model in terms of precision, recall, mAP@0.5, and mAP@0.5~0.95 above, respectively, of 2.71%, 2.34%, 2.24%, and 3.73%.
2024-09-24
PIER M
Vol. 129, 33-41
A Compact Four Port MIMO Antenna for n261 Millimeter Wave Band Applications
Reena Aggarwal , Ajay Roy and Rajeev Kumar
This article introduces a compact design for a four-element MIMO antenna for millimeter-wave (mmWave) communications for specifically n261 band having range from 27.5 GHz to 28.35 GHz with a bandwidth of 850 MHz. The single antenna structure uses a rectangular patch having four diamond-shaped slots in the feed-plane. On the ground plane, a dumbbell-shaped slot is positioned below the rectangular patch. A Rogers RT/Duroid 5880 substrate with ultra-thin thickness is used in this design. The optimized design for four-port MIMO antenna has small size with dimensions of 20 mm × 19 mm × 0.254 mm. The MIMO parameters such ECC is less than 0.011, and DG is greater than 9.90 dB in the mentioned band, which are within tolerance limits. The isolation between neighbouring MIMO elements is also less than -19.5 dB.
2024-09-23
PIER
Vol. 180, 55-60
Topology-Optimized Plasmonic Nanoantenna for Efficient Single-Photon Extraction
Min Chen , Lian Shen , Yifei Hua , Zijian Qin and Huaping Wang
Quantum emitters coupled to plasmonic nanostructures can act as extremely bright single-photon sources. Interestingly, the mode volumes supported by the plasmonic nanostructures can be several orders of magnitude smaller than the cubic wavelength, which leads to dramatically enhanced light-matter interactions and drastically increased photon emission. However, the requirements of a small mode volume for emission speed-up are always contradictory with a sufficiently large mode volume for efficient extraction, especially in a single architecture. Here, we report the design of a topology-optimized plasmonic nanoantenna to alleviate the above limitation which could greatly enhance far-field photon extraction. The plasmonic nanoantenna is composed of an optimized gold pattern and a silicon nitride substrate, with a nanohole in the center of the gold pattern. Our design is based on density-based topology optimization and is inherently robust to dimensions and fabrication errors. As a result, the normalized extraction decay rate (γe⁄γ0) can reach 5.48 at a wavelength of 517 nm if an objective lens with a numerical aperture of 0.45 is utilized. Plasmonic nanostructures can be obtained with a small mode volume of about 5 × 10-21 m3, while emission speed-up could still be achieved. The proposed method to alleviate the contradiction of plasmonic mode volume could brighten the prospects for future integration of single-photon sources into photonic quantum networks and applications in quantum information science.
2024-09-22
PIER M
Vol. 129, 23-32
Spoof Surface Plasmon Polaritons-Based Feeder for a Dielectric Rod Antenna at Microwave Frequencies
Rishitej Chaparla , Shaik Imamvali , Sreenivasulu Tupakula , Krishna Prakash , Shonak Bansal , Mohd Muzafar Ismail and Ahmed Jamal Abdullah Al-Gburi
This work explores the potential of spoof surface plasmon polaritons (SSPPs) for effectively feeding high-frequency antennas operating in the extremely high-frequency (EHF) range. An innovative approach is introduced in this study to utilize SSPP to feed a dielectric rod antenna. The design incorporates a straightforward dielectric rod antenna fabricated using FR-4 material with a relative permittivity of 4.3. Compared to conventional tapered dielectric rod antennas and their corresponding feeding configurations, this design presents the potential benefit of achieving an improved gain of up to 16.85 dBi using a specific antenna length of 7.6λ0. Through careful design optimization, we achieved impedance matching and directional radiation characteristics at a frequency of 7.3 GHz. To validate our design and assess its performance, we conducted simulations using the CST Microwave Studio. This study aims to demonstrate the effectiveness and practicality of the proposed dielectric rod antenna with an SSPP feed.
2024-09-19
PIER Letters
Vol. 122, 93-99
Miniaturized Filter Unit Based on Serpentine Microstrip Resonator and Half-Mode Substrate Integrated Waveguide and Its Application
Lianxin Li , Xiaohei Yan , Fupeng Wei , Guiqing Liao , Weijun Yv and Keyou He
In order to effectively reduce the loss of the filter, decrease its size, and improve its frequency selectivity, a miniature filter unit has been proposed. This unit offers enhanced frequency selectivity and facilitates adjustment of the center frequency. The filter unit is constructed by embedding a serpentine microstrip resonator in the upper metallic surface of a half-mode substrate-integrated waveguide (HMSIW). The center frequency of the filter unit is considerably lower than the cutoff frequency of the HMSIW, which contributes to the miniaturization of the filter. The center frequency of the filter unit can be adjusted solely by modifying the dimensions of the microstrip resonator, while the dimensions of the remaining components can be maintained at a constant value. A transmission zero has been incorporated into the upper resistance band with the objective of enhancing its frequency selectivity. A second-order filter with a center frequency of 3 GHz is accurately designed using this filter unit. The results demonstrate that a miniaturized filter with the desired center frequency and excellent performance can be rapidly achieved using this filter unit, which has potential applications in the 5G (sub-6G) band.
2024-09-18
PIER
Vol. 180, 25-53
Alternative Plasmonic Materials for Biochemical Sensing: A Review (Invited Review)
Leonid Yu. Beliaev , Andrei V. Lavrinenko and Osamu Takayama
Optical materials whose permittivity becomes negative for certain wavelength ranges, so-called plasmonic materials, have been widely used for biochemical sensing applications to detect a wide variety of analytes from chemical agents to protein biomarkers. Since many analytes are or contain nanoscale objects, they interact very weakly with light. Thus, light confinement is a key to improving sensitivity. Using metal or plasmonic nanostructures is a natural solution to confine light and boost light-matter interactions. As there are several different optical sensing schemes, such as refractometric sensing, fluorescence-labeled sensing, and vibrational spectroscopy, whose operating wavelength spans from ultraviolet to mid-infrared wavelength regions, some plasmonic materials are superior to others for certain wavelength regions. In this article, we review current progress on alternative plasmonic materials, other than gold, silver, and aluminum, used in biochemical sensing applications. We cover a wide variety of plasmonic material platforms, such as transparent conductive oxides, nitrides, doped semiconductors, polar materials, two-dimensional, van der Waals materials, transition metal dichalcogenides, and plasmonic materials for ultraviolet wavelengths.
2024-09-13
PIER M
Vol. 129, 11-22
A Dual Transmission Zero Bandpass Filter Employing Novel Hairpin-Coupled Resonators for Improved Stopband Characteristics Application the Vital Signs Detection Radar
Mingming Gao , Yunshu Yang , Jingchang Nan , Handong Wu , Xiaolin Wang and Xuanye Cui
Conventional hairpin band-pass filters (BPFs) typically have poor stopband performances. Therefore, this paper proposes a BPF with a center frequency of 24 GHz that employs a novel hairpin-coupled structure. An enhanced hairpin-coupled resonator topology is also introduced to improve the stopband suppression characteristics. Specifically, the proposed resonator and filter are configured through a hairpin structure and source-third resonator coupling, which afford a miniaturized size and coupling of the transmission zeros. Then, an equivalent circuit model is simulated to conduct loss analysis of the millimeter-wave (mm-wave) BPF, and the corresponding analytical parameters and result data are extracted. Furthermore, fast synthesis is achieved for the high stopband suppression mm-wave filter. The compact BPF developed is fabricated using the quart glass process, with the corresponding measurements revealing that the insertion Loss (IL) is less than 4.5 dB, and the return loss (RL) exceeds 9 dB within the passband. Meanwhile, the stopband suppression at 20.6 GHz and 28.6 GHz can reach 43 dB and 35 dB, respectively. Those advanced performances demonstrate the promising prospect of the proposed filter for its application in biological radar life feature monitoring.
2024-09-13
PIER M
Vol. 128, 145-153
Two-Port Hexagon-Shaped MIMO Antenna for UWB Applications Integrated with Four Frequently-Used Stopbands for Medical Domains
Liangliang Zhao , Aidong Li , Yongmao Wang , Dengyang Song , Mingxuan Zheng , Chenlu Liu , Chuwei Li , Yongtao Liang , Huiling Zhao and Chufeng Hu
A compact ultra-wideband (UWB) multiple-input multiple-output (MIMO) antenna with four stopbands is designed and experimentally investigated. By the method of coating, various T-shaped structures and split-ring resonators (SRRs) are used for suppressing the mutual coupling and introducing the band-notched characteristics, respectively. The actual design has an overall size of 46 × 37 × 1.57 mm3 across the whole UWB spectrum from 2 to 22 GHz except stopbands from 3.47 to 3.83 GHz, 5.2 to 5.85 GHz, 7.19 to 7.84 GHz, and 8.15 to 8.6 GHz, which prevent the interference of Microwave Access (WiMax), wireless local area network (WLAN), satellite downlink and satellite communications band (ITU 8 GHz) bands, respectively. Besides, the isolation of the most operating frequencies is higher than 20 dB, and the antenna obtains a fairly stable radiation pattern and gain, as well as a lower envelope correlation coefficient (ECC < 0.005). Additionally, using the antenna inserted in name badge of the doctor, the chance of infection will be greatly reduced. Ultimately, the proposed MIMO monopole antenna has a potential application in the medical domain.
2024-09-12
PIER M
Vol. 129, 1-10
A Compact High-Isolation Tri-Band MIMO Antenna Based on Characteristic Mode Analysis
Jinrong Su , Shiqi Di , Chunhui Yao and Xinwei Chen
This paper presents a compact 3-port multiple-input multiple-output (MIMO) antenna for 5G wireless communication, covering the 2.6 GHz, 3.5 GHz, and 4.8 GHz bands. Three orthogonal modes (TMsub>10, TMsub>01, and TMsub>20 modes) are excited to realize tri-band operation and high isolation simultaneously. Using characteristic mode analysis (CMA), dual-slot structures and I-shaped patches are introduced to block coupling path, and the isolation is improved. Simulated and measured results show that the proposed antenna operates in the frequency bands of 2.57 to 2.64 GHz, 3.4 to 3.5 GHz, and 4.8 to 4.9 GHz with isolation better than 20.6 dB. In addition, it can be calculated that Envelope Correlation Coefficient (ECC) (<0.06), Diversity Gain (DG) (>9.99 dB), Total Active Reflection Coefficient (TARC) (<-10 dB), and Channel Capacity Loss (CCL) (<0.45 bits/Hz/sec) are in acceptable level, implying excellent diversity performance and data transmission quality. It is worth noting that the evolution of the antenna is entirely based on the CMA, which greatly simplifies the design process. The antenna has the advantages of high isolation, compact structure, easy processing, and low cost, positioning it as a compelling candidate for integration into 5G wireless communication systems.
2024-09-11
PIER Letters
Vol. 122, 87-92
Bio-Electromagnetic Safety Assessment of Wireless Charging Environment for Electric Vehicles
Haoran Zheng and Xiaohe Zhao
Wireless power charging technology has been developed rapidly and is extensively utilized for electric vehicle wireless charging due to its numerous over plug-in charging. The electromagnetic bio-safety of the human body in charging environment has become a significant public concern. To address this issue, this paper employes the finite element analysis method to assess the electromagnetic safety of crucial organs in a typical charging environment. Firstly, human-vehicle models in various typical postures were constructed in COMSOL, and the spatial distribution of electromagnetic fields in the critical organs was calculated in a 7.7 kW, 85 kHz charging environment. Subsequently, the electromagnetic radiation dose of each organ was calculated and compared with the ICNIRP standards. The results indicated that the electromagnetic radiation dose received by different organs is influenced by both the electromagnetic parameters and position of the organs. When the human body is positioned flat in the car, the electromagnetic radiation exposure to various organs is at its highest. Additionally, the maximum radiation dose for each organ is significantly below ICNIRP standard in a low-power wireless charging environment, supporting the commercial adoption of wireless charging technology for electric vehicles.
2024-09-09
PIER Letters
Vol. 122, 81-86
Multi-Band Band-Pass Filter with Independently Controlled Asymmetric Dual-Band Response Based on Metacell
Shobha Hugar , Jambunath S. Baligar , Veerendra Dakulagi and Kashipura Manjanaik Vanitha
The key challenges in the design of multi-band filters are realizing highly independent, controlled asymmetric-wide and narrow dual-band response. To address these challenges, this paper proposes the design and development of a dual-band band-pass filter (BPF) with highly independent, controlled wide and narrow band responses. The proposed filter is constructed using only two resonator structures, asymmetric step impedance resonator (A-SIR) and metacell. The wide and narrow band responses are independent and are controlled independently by impedance ratio (R) and the number of cells (N) in metacell structure, respectively. Additionally quasistatic circuit model of the metacell is used to analyze independently controlled narrow passband response. The prototype of the filter is fabricated, and the simulation results are validated through experimental measurements.
2024-09-07
PIER M
Vol. 128, 135-144
Artificial Magnetic Conductor Based Improved Radiation Properties of Fractal MIMO Antenna for UWB Applications
Deshpande Ramesh , Usha Devi Yalavarthi and Boddapati Taraka Phani Madhav
A novel artificial magnetic conductor (AMC) structure as a reflector is presented to enhance the gain of a fractal ultra-wideband (UWB) multi-input multi-output (MIMO) antenna. Unit cell of proposed AMC structure is achieved through 4 iterations to obtain better characteristics as reflector. An in-phase reflection from 2-16 GHz is achieved by the unit cell. The proposed AMC structure 6 × 6 array and 6 × 12 array are examined with single element and 2 element fractal MIMO antennas respectively. The fractal MIMO antenna backed with an AMC structure achieved an operating band from 2.2 to 15.8 GHz, and the isolation between the elements is greater than 23 dB. The proposed AMC is structure is fabricated, and experimental results are analysed in comparison with simulation ones. An average gain improvement of 6.1 dB is observed by the proposed AMC structure in the operating band. Surface current distributions, EM fields, and radiation patterns are investigated at various frequencies. MIMO performance parameters such as diversity gain, total active reflection coefficient, envelope correlation coefficient, and channel capacity loss characteristics are analyzed in this paper. The fractal MIMO antenna backed with an AMC structure exhibits good diversity performance characteristics with improved radiation properties for UWB applications.
2024-09-04
PIER
Vol. 180, 13-24
Measurement of Time-Range-Angle-Dependent Beam Patterns of Frequency Diverse Arrays (Invited)
Haochi Zhang , Lepeng Zhang , Shengheng Liu , Zihuan Mao , Yahui Ma , Pei Hang He , Wen Yi Cui , Yi Fei Huang , Qi Yang and Tie-Jun Cui
Frequency diverse arrays (FDAs) have drawn great attention because they can provide a time-range-angle-dependent beam pattern that has many promising potential applications in navigation and radar systems. However, due to the limitations of measurement systems, this attractive beam pattern has not been experimentally observed. Here, a far-field measurement system for the time-range-angle beam pattern of FDA is proposed by improving the existing near-field mapping system. Without loss of generality, two types of time-range-angle-dependent beam patterns for FDA systems with different frequency sets are observed using the proposed far-field measurement system. The high efficiency and accuracy of the proposed system is verified by good agreement between the measured and simulated results. This work marks significant progress toward the practical implementation and application of FDAs.
2024-09-02
PIER M
Vol. 128, 127-134
3D-Printing of Slanted Corrugated Horn Antennas for the E-Band
Markus Tafertshofer , Maximilian Binder and Erwin M. Biebl
In this paper, the feasibility of using additive manufacturing (AM) technologies for the fabrication of corrugated horn antennas for the E-band (60 to 90 GHz) is investigated. Stereolithography apparatus (SLA) and selective laser melting (SLM) are identified as the most suitable technologies for manufacturing horn antennas in this frequency range. To ensure good manufacturing, slanted corrugations are utilized. The antennas have a gain of 13 dBi at 72 GHz and are designed in CST Microwave Studio. For the fabrication of the plastic parts, SLA and the finer-scaled projection micro stereolithography (PμSL) technology are applied. The metal antennas are printed with direct metal laser sintering (DMLS) from the aluminum alloy AlSi10Mg and the finer scaled micro metal laser sintering (μMLS) from 316L stainless steel. Overall, four antennas are fabricated. The plastic antennas are plated with copper. Dimensional tolerances and surface roughness of the antennas are evaluated. The antennas are investigated considering H- and E-plane beam shapes, input reflection, and realized gain. The measurement is conducted in an anechoic chamber using the Single-Antenna method. The μMLS antenna supplies the best results.
2024-09-01
PIER
Vol. 180, 1-11
Highly Accurate and Efficient 3D Implementations Empowered by Deep Neural Network for 2DLMs -Based Metamaterials
Naixing Feng , Huan Wang , Xuan Wang , Yuxian Zhang , Chao Qian , Zhixiang Huang and Hongsheng Chen
Streamlining the on-demand design of metamaterials, both forward and inverse, is highly demanded for unearthing complex light-matter interaction. Deep learning, as a popular data-driven method, has recently found to largely alleviate the time-consuming and experience-orientated features in widely-used numerical simulations. In this work, we propose a convolution-based deep neural network to implement the inverse design and spectral prediction of a broadband absorber, and deep neural network (DNN) not only achieves highly-accurate results based on small data samples, but also converts the one-dimensional (1D) spectral sequence into a 2D picture by employing the Markov transition field method so as to enhance the variability between spectra. From the perspective of a single spectral sample, spectral samples carry not enough information for neural network due to the constraints of the number of sampling points; from the perspective of multiple spectral samples, the gap between different spectral samples is very small, which can hinder the performance of the reverse design framework. Markov transition field method can enhance the performance of the model from those two aspects. The experimental results show that the final value of the soft required accuracy of the one-dimensional fully connected neural network model and the two-dimensional residual neural network model differ by nearly 1%, the final value of the soft accuracy of the one-dimensional residual neural network model is 97.6%. The final value of the two-dimensional residual neural network model model is 98.5%. The model utilises a data enhancement approach to improve model accuracy and also provides a key reference for designing two-dimensional layered materials (2DLMs) based metamaterials with on-demand properties before they are put into manufacturing.
2024-08-28
PIER
Vol. 179, 113-124
Josephson Traveling Wave Parametric Amplifier as Quantum Source of Entangled Photons for Microwave Quantum Radar Applications (Invited)
Patrizia Livreri , Bernardo Galvano , Luca Fasolo , Luca Oberto and Emanuele Enrico
Josephson Traveling Wave Parametric Amplifier (JTWPA) has the potential to offer quantum limited noise and a large bandwidth. This amplifier is based on parametric amplification of microwaves traveling through a transmission line with embedded non-linear elements. In this paper, starting from the fabrication of the JTWPA, based on Quantum Electrodynamics (QEDs), operating as a nonclassical quantum source for generating a signal-idler entangled state, its characterization in terms of scattering parameters is presented. The cryogenic and room temperature experimental results are discussed. The good performance of the JTWPA in terms of wide bandwidth and increased transmitted power makes it an ideal candidate for Microwave Quantum Radar (MQR) applications. Finally, the performance of an MQR based on the JTWPA developed at INRiM is reported, showing a radar maximum range equal to 82.2 m, which represents a greater value than previously published works.
2024-08-28
PIER M
Vol. 128, 115-125
Design of a 3D Printed Wide Band Metasurface Antenna for High Power Applications
Mohamed Z. M. Hamdalla , Mashrur Zawad , Matthew Kunkle , Somen Baidya , Roy C. Allen , Peter J. Bland , Travis D. Fields and Ahmed M. Hassan
Weight-size optimization is the main challenge of high-power antenna design. This paper presents a low-profile, metasurface-based wideband antenna. The proposed antenna comprises an N-type-to-waveguide transition to excite the metasurfaces and handle high-power excitations. A metasurface array of 4×4-unit cells is integrated into the waveguide. The proposed waveguide is 3D printed, and its internal faces are covered by copper tape to maintain a low weight (less than 200 g). The prototype is experimentally tested, and the results confirm the prototype's functionality from 2.1 GHz to 3.6 GHz with a bandwidth of 52.6% and a peak gain of 8.5 dBi. Furthermore, the high-power handling capability of the proposed design has been experimentally confirmed by exciting it with a 7 kV pulsed source. These results demonstrate the applicability of the proposed antenna in satellite communication, radar applications, and wireless communication between Unmanned Aerial Vehicles (UAVs).
2024-08-28
PIER Letters
Vol. 122, 75-80
Deviation Analysis of Multiport VNA Hardware Specification-Related Nonideality
Nan Sun , Liang Ren , Zhi-Tao Yang , Ming Shen and Hong-Wei Deng
In this paper, the deviation generated by actual multiport vector network analyzer (MVNA) hardware specification is derived. Based on the error flowchart of the n-port VNA, the generalized matrix expression of the raw scattering parameters for each error term is solved by introducing the generalized node method. Combined with incremental method, the generalized matrix expression of the final relative scattering parameter measurement deviation is calculated after ignoring the infinitesimals above the second order. Thus, the method of variable controlling is applied to make difference so that the deviation associated with every error term can be obtained. The validness and effectiveness of this method are verified by utilizing Agilent N5230C to measure a 20 dB direction coupler. The data is processed with an algorithm in MATLAB.