Search Results(13732)

2024-11-05
PIER C
Vol. 150, 1-8
Monopole Antenna Loading Parasitic Metal Pillar Element with Suppression of Beam Upwarping to Improve Omnidirectional Radiation in Broadband
Jiemin Jing , Wen-Quan Cao , Hong Xue , Chuang Wang , Yangkun Zhu , Yixin Tong and Huangshu Zhou
Due to the presence of finite ground, the radiation pattern of a monopole antenna will upwarp, thereby affecting the communication quality in the horizontal direction. Loading parasitic metal pillar elements near monopole antenna is a common beam control method. In this paper, an inverted monopole antenna is used as the source antenna to analyze the effect and band of beam upwarping suppression in wide band. The working principle and parameter analysis of elements are also discussed. This antenna can achieve 1-24°of suppression from 360 to 570 MHz. At the same time, keeping the un-roundness almost unchanged, the horizontal plane gain is increased by 0.53-1.74dB. The omnidirectional pattern is improved, which provides a valuable candidate for vehicle communication.
2024-11-04
PIER C
Vol. 149, 177-186
Leakage Optimization of Active Magnetically Shielded Isotropic Coils for Electric Vehicle Wireless Charging Systems
Yonghong Long , Hui Li , Zhongqi Li , Bin Li and Ziyue Gan
In the field of wireless power transmission (WPT) for electric vehicles, the challenge of magnetic shielding technology is particularly prominent. Achieving effective magnetic shielding often comes at the cost of transmission efficiency, creating a significant technical bottleneck. As a result, research into improving transmission efficiency while minimizing magnetic leakage has become a primary focus in the industry. This is seen as critical for driving the sustainable development of the electric vehicle sector. In response to this challenge, this paper presents the construction of an active magnetic shield using an isotropic coil configuration, which not only optimizes system efficiency but also significantly reduces magnetic leakage in WPT systems. The paper begins by introducing the concept of an active magnetically shielded isotropic coil structure for wireless power transmission. Next, it details the design methodology and operational principles of the structure, followed by the derivation of the mathematical model and equivalent circuit. The effectiveness of the magnetic shielding mechanism is examined from a theoretical standpoint, and the influence of coil parameters on both shielding performance and transmission efficiency is analyzed. Finally, based on the optimized coil parameters, the design of the wireless charging system incorporating the magnetic shielding structure is completed. This includes relevant theoretical calculations, simulation analyses, and experimental validation to confirm the feasibility of the design. The results demonstrate that the active magnetically shielded isotropic coil significantly reduces magnetic leakage, lowering it by approximately 95.68% compared to traditional coils, while achieving a transmission efficiency of 95.68% in experiments.
2024-11-03
PIER C
Vol. 149, 165-176
Compact Dual-Band Monopole Antennas with Fractal-Based Half- and Quarter-Circular Folded Loops for WiMAX and WLAN Applications
Dhirgham Kamal Naji
In this paper, two new types of dual-band antennas are presented: a coplanar waveguide (CPW)-fed fractal monopole antenna (FMA) and an asymmetric coplanar strip (ACS)-fed fractal half-monopole antenna (FHMA). These antennas are designed to operate in two distinct bands suitable for 3.5/5.5 GHz WiMAX and 5.2/5.8 GHz WLAN applications. Both antennas possess the property of self-similarity by employing half- and quarter-circular folded loops, respectively, which represent the antennas' radiating elements. A design procedure based on a conventional circular patch antenna (CPA) is performed, with evolution steps leading to the achievement of the proposed two antennas with the above-mentioned features. To validate the design concept, two simulator programs (CST MWS and HFSS) were used to extract the simulated results regarding reflection coefficient S11, gain, efficiency, and radiation patterns. According to the agreement between the CST and HFSS simulated results, prototypes of the FMA and FHMA are fabricated on an FR4 substrate with a dielectric constant of 4.4, a height of 0.8 mm, and overall sizes of only 26×20 mm2 and 12×19 mm2, representing nearly 73% and 40% reduction in size, respectively, compared with the size of 26×33 mm2 for the CPA. The simulated and measured S11 results are in good agreement, illustrating the two antennas operating over the desired bands (S11 ≤ -10 dB): 3.5-/5.5-GHz (3.40-3.69 and 5.25-5.85 GHz) WiMAX and 5.2-/5.8-GHz (5.15-5.35 and 5.72-5.85 GHz) WLAN. Furthermore, the peak realized gain values are greater than 2 dBi, efficiency exceeding 90%, and nearly omnidirectional radiation at both bands. Based on the achieved results and antennas' compactness, they can be highly recommended for the use in WLAN and WiMAX applications.
2024-11-02
PIER C
Vol. 149, 155-163
Design a Dual-Band with CSRR Cascaded Patch Antenna Array for Wireless Communications
Maloth Chandrasekhar and Ketavath Kumar Naik
This paper presents a dual-band cascaded rectangular microstrip patch antenna array with a complementary split ring resonator (CSRR) for narrow-band wireless communication applications. The antenna array is fed with a microstrip feed line for proper impedance matching, and CSRR is loaded to generate dual-band characteristics. The CSRR-based proposed antenna radiators operate over two frequency bands, i.e. 100 MHz (3.06-3.16 GHz) and 110 MHz (4.36-4.47 GHz) with reflection coefficients (S11 < -10 dB) of -23 dB and -32 dB. The gain of the proposed antenna array with CSRR is 5.03 dBi and 6.34 dBi at 3.1 GHz and 4.4 GHz respectively. In addition, S-parameters, radiation patterns, 3D gain characteristics, and surface current distribution at resonating frequencies are observed. The proposed antenna array is miniaturized in size and suitable for wireless communication applications.
2024-11-02
PIER C
Vol. 149, 143-154
Modeling the Compression of Modulated Electromagnetic Pulses in a Straight Waveguiding Defect of Two-Dimensional Photonic Crystal
Vadym Pazynin , Kostyantyn Sirenko , Maksym Maiboroda , Miramgul Tokasheva , Akbota Tolegenova and Wilhelm Keusgen
The paper presents the results of numerical modeling of the compression of a frequency-modulated electromagnetic pulse in a straight waveguiding defect of a finite two-dimensional photonic crystal. For the first time, the time reversal method was used to accurately compute the temporal profile of a current pulse that excites an electromagnetic wave that is being compressed in such a structure, given that its temporal profile (electric field intensity) has a specified shape at a given point in space. The photonic crystal consists of an array of sapphire bars with a square cross-section of 1 mm × 1 mm, arranged in free space at a distance of 1 mm from each other. In this model, the boundaries of the frequency range containing the crystal's band gap (from 35.6 to 46.5 GHz), the optimal width of the waveguiding defect (4 mm), and the shape of the excitation current pulse for the waveguiding defect with a length of 0.5 m were found. The obtained pulsed power amplification coefficient is approximately 7.48. A photonic-crystal analog of an H-plane horn antenna was used to radiate the compressed pulse into free space.
2024-11-02
PIER Letters
Vol. 123, 55-60
Advanced Compact High-Power InGaAs HEMT Self-Oscillator Active Integrated Antenna for IoT Applications
Hanaa El Moudden , Tajeddin Elhamadi , Moustapha El Bakkali and Naima Amar Touhami
This work presents a new negative resistance self-oscillator based on an integrated active antenna and InGaAs HEMT technology, specifically designed for Internet of Things (IoT) applications. A key aspect of this design lies in the series integration of the active circuit and the antenna patch. The fabrication and testing were carried out on an FR4 substrate with a thickness of 0.8 mm. The Harmonic Balance numerical method, implemented in the Advanced Design System tool, was used for the optimization and co-simulation of the system. After simulation and measurement, the proposed self-oscillator, with a compact size of 3.4 x 3 cm², produced very significant results. The simulated output power reached 12.87 dBm at a frequency of 3.07 GHz, while the measured output power was 12.85 dBm at 3.04 GHz, with a recorded phase noise of -78 dBc/Hz at 10 MHz. The qualitative and quantitative performance of the proposed self-oscillating antenna makes it particularly suitable for applications such as satellite mobile communications, GPS, telemetry, and telemedicine.
2024-10-31
PIER Letters
Vol. 123, 47-54
A Dual-Band High-Isolated MIMO Antenna Based on Compensation Network for 5G Coal Mine Applications
Yanhong Xu , Nanyue Li , Can Cui , Xuhui Fan , Jianqiang Hou and Anyi Wang
A dual-band MIMO antenna with high isolation is designed in this paper for coal mine applications. Each of the two elements in the designed MIMO antenna is composed of a bident-shaped monopole structure which is designed to cover the 5G NR frequency region (2.51-2.67 GHz, 3.4-3.6 GHz) allocated for coal mine scenario. The two elements are symmetrically placed to achieve high isolation at lower frequency region with an element spacing of 0.09λ at the lowest operating frequency. To further reduce the mutual coupling between the two elements, the decoupling network technique is utilized. In particular, a neutralization line is loaded with an adjustable capacitor and two adjustable inductors on the ground. In this way, an isolation of higher than 20 dB is achieved over the two operating frequency bands for the MIMO antenna, i.e., the isolation is increased by more than 11 dB and 10 dB for the lower and higher bands, respectively. Besides, the good performance of the designed MIMO antenna in terms of correlation values and diversity gain makes it a suitable candidate for 5G MIMO applications under coal mine scenarios.
2024-10-30
PIER C
Vol. 149, 131-141
Digital Non-Foster Impedance Design for Wideband Electrically Small Antennas Beyond the Chu Limit
Christopher Daniel Jr. and Thomas Weldon
Although initial results for the digital implementation of non-Foster impedances showed promise for increasing the bandwidth of electrically small antennas beyond the Chu limit, earlier approximate design methods were inadequate to fully describe the complexity of digital impedance circuits. Recently, the input impedance of such digital impedance circuits was discovered to be dependent on the external source impedance of the driving source. Furthermore, this dependence on the driving source impedance was shown to be extraordinarily complicated, even for a purely resistive driving source. Consequently, the digital non-Foster impedance match of an antenna is considerably more complicated, even with a lumped-element antenna model. In this paper, we present a method for designing a stable wideband digital non-Foster circuit to match the impedance of an electrically small dipole antenna. Simulation results confirm the theoretical predictions and the efficacy of the design method in producing VSWR bandwidth beyond the Wheeler-Chu limit. An RLC model of a 10 MHz electrically small dipole with Q of 215 and passive-tuned bandwidth of 46.5 kHz is chosen to demonstrate the proposed method. For this antenna with Wheeler-Chu bandwidth limit of 442 kHz and size parameter ka = 0.42 rad, the proposed method results in achieving an impedance bandwidth of 2.3 MHz, or more than five times the Wheeler-Chu limit and 48 times the passive-tuned bandwidth. Lastly, the mid-band noise figure is 12.7 dB when the proposed design is combined with a receiver having 3 dB noise figure.
2024-10-29
PIER C
Vol. 149, 123-130
Research on the Combination of IE3-IE5 Series Energy-Efficient Three-Phase Induction Motor
Chaohui Zhao , Huoda Hu and Wendong Zhang
Motor energy efficiency has gradually become a research hotspot. In this paper, the optimization analysis of motor energy efficiency is carried out for the widely used three-phase induction motors. Based on keeping the stator and rotor structure parameters unchanged, a reasonable combination of motor steel material, winding type, and bar conductor material can realize the change in motor energy efficiency class. Firstly, the influence of stator and rotor steel materials on iron consumption is analyzed using the triple equation of iron consumption. And the loss distribution and efficiency of DW540, DW470, DW360, DW310, DW270, 1J22, and amorphous alloy materials are discussed. Secondly, the effect of different winding types on the no-load reverse electromotive force is analyzed and discussed, and its simulation model is constructed. The corresponding motor efficiency is summarized. Then, the impact of cast copper and aluminum rotors on energy efficiency is compared and analyzed. Finally, the steel material combinations, winding type, and bar conductor material are classified according to the IE3, IE4, and IE5 energy-efficiency classes. The results show that by choosing the right combination, the motor's energy efficiency can be increased by up to 95.3%.
2024-10-29
PIER C
Vol. 149, 111-121
Multi-Objective Optimization Design of PMa-BSynRM Rotor Structure Based on Macroscopic Parameters and DPCA
Bo Mao , Xiaoyan Diao , Huangqiu Zhu and Jintao Ju
The rotor of PMa-BSynRM, with its multi-layer barriers and permanent magnet, poses a challenge in the design process as both torque system and suspension force system performance need to be considered comprehensively. To solve this problem, a multi-objective optimization method for the rotor structure of PMa-BSynRM is proposed in this paper. Firstly, the harmonic characteristics of PMa-BSynRM air gap magnetic field are analyzed based on the magnetic potential and magnetic permeability method. The expression for suspension force under the coupled magnetic field is derived by combining Maxwell tensor method. This analysis reveals the relationship between magnetic field characteristics and suspension force, providing guidance for subsequent optimization design. Secondly, through the analysis of the rotor structure, the macroscopic parameters related to the micro and detailed geometric optimization of the PMa-BSynRM rotor are proposed. Based on these macroscopic parameters, the response surface method and dual-population-based co-evolutionary algorithm (DPCA) are applied to realize a compromise among the optimization objectives. Finally, the proposed optimization method is comprehensively analyzed through simulation analysis and prototype experiment. The simulation and experimental results demonstrate a reduction of 51% in optimized torque ripple and 74% in suspension force ripple, as well as a decrease of 3.2˚ in the suspension force error angle. After optimization, the performance of the motor torque and suspension force system is significantly improved, thus verifying the effectiveness and superiority of the proposed optimization method.
2024-10-29
PIER C
Vol. 149, 105-109
A Low Profile 20-Bit Frequency-Coded L-Shape Multi-Slot Resonator for Chipless RFID Applications
Narayanan Saranya , Thangarasu Deepa , Periyasamy Raja , Kumar Paayal , Arunagiri Sofiya and Raju Swetha
This research work investigates the performance of a novel low profile 20-bit frequency coded L-shape slot loaded resonator for chipless RFID applications. The proposed chipless RFID comprises a CPW-fed UWB radiator and an L-shaped multi-slot resonator to achieve 20-bit data capacity. CPW technique is implemented to enhance antenna bandwidth and radiation characteristics. The designed UWB radiator covers the entire band from 3 to 12 GHz with better return loss. Also, the peak gain is measured as 6 dBi in the respective frequency spectrum. The proposed L-shaped frequency-coded multi-slot resonator is developed with a compact size of 23.6×14.1×1.6 mm3. Moreover, the frequency coding technique allows for a wide range of frequency combinations for data representation, as well as contributes to reducing the RFID tag size. The research holds significance in propelling RFID technology forward and ushering in a new era of small, efficient, and flexible data encoding solutions.
2024-10-28
PIER C
Vol. 149, 95-103
A Compact UHF RFID Tag Antenna with Tunable Double Interdigitated Structures
Luoxin Cai , Zibin Shi , Yanwei Qiu and Jiade Yuan
A compact and tunable ultra-high frequency (UHF) radio frequency identification (RFID) tag antenna is proposed. The antenna comprises a rectangular ring, two symmetrical radiating arms formed by multiple L-shaped stubs, and two interdigitated structures. By adjusting the parameters of double interdigitated structures, the resonant frequency of the antenna can be tuned coarsely and finely, while maintaining a nearly constant maximum power transmission coefficient. The proposed tag antenna has a size of 28 mm x 16 mm (0.086λ x 0.049λ at 920 MHz). Measurement results show that the proposed antenna can achieve the maximum reading distance of 6.8 m at 920 MHz under the condition of 3.28 W effective isotropic radiated power. The proposed RFID tag antenna offers several advantages, including compact size and frequency tunability, making it well-suited for various RFID system applications.
2024-10-28
PIER C
Vol. 149, 87-94
Small Size Radially Embedded Probe-Fed Dielectric Resonator Antenna for Ultra-Wideband Applications
Abinash Thakur and Satyajib Bhattacharyya
Radially embedded probe-fed circular disc dielectric resonator antenna (DRA) for ultrawideband applications is investigated. Initially, a single-layer probe fed DRA is developed. The probe length is adjusted to optimize S11 performance. For a probe length of 10 mm, a measured -10 dB bandwidth of 47.8% (4.75-7.74 GHz) is obtained. The design is modified with two concentric rings of different dielectric materials with a hollow center. The modified configuration improves the matching from an S11 value of -18 dB at 5.23 GHz to -24.2 dB at 4.56 GHz. However, the measured -10 dB bandwidth reduces to some extent to 38.4% (4.2-6.2 GHz). In another modified design, an air gap is introduced between two inner discs of Alumina supported by a solid outer ring of Teflon. The radially embedded feeding probe, therefore, protrudes into the circular air pocket sandwiched between the two Alumina discs. An improved measured bandwidth of 55.9% (6.66-11.83 GHz) is obtained. Measured S11 of -24.1 dB is similar to that obtained for the concentric ring design but at a higher frequency of 9 GHz. All the three antenna designs feature a reduced size having a volume of approximately 1963.5 mm3, wider bandwidth and consistent radiation pattern over the operating frequency band. It makes the proposed designs suitable for ultra-wideband (UWB) applications.
2024-10-27
PIER M
Vol. 130, 19-27
Designing Fabric-Based Broadband Metamaterial Absorbers for Radar Operating Frequency Bands
Baojun Chen , Hao Yuan , Yanjie Ju , Yanbing Xue , Tianyu Jiao , Qinghua Liu and Mengqiu Qian
With the increasing use of radar technology across various fields, electromagnetic pollution has become a growing concern, posing significant risks to human health. Consequently, there is a rising interest in developing wearable, flexible fabric-based absorbers that can efficiently absorb electromagnetic waves. However, the low dielectric constant of fabrics makes it challenging to achieve high absorption rates and broad bandwidth at low frequencies. To address this issue, in this study, we introduce a fabric-based broadband metamaterial absorber using felt as the dielectric substrate. The absorber features a centrosymmetric square block array design, incorporating a PU conductive film as the surface resonant material. By fine-tuning the parameters of each component in the absorber's equivalent circuit and optimizing structural parameters, the absorber achieves an extended bandwidth from 3.92 to 15.25 GHz, with a relative absorption bandwidth of 118.21%. Impressively, in the lower frequency C-band, the absorber maintains an efficiency of over 95%. The absorber was fabricated using the ``cut-transfer-paste patterning method.'' Testing results demonstrate that it is insensitive to incident angle and polarization and retains excellent absorption performance even when being bent.
2024-10-26
PIER C
Vol. 149, 81-86
Dual-Band RF Rectifier Using Stepped Microstrip Line Matching Network for IoT Sensors Application
Meghdad Khodaei , Halim Boutayeb , Larbi Talbi and Alireza Ghayekhloo
RF rectifier circuits are critical to powering IOT sensors through energy harvesting process, allowing devices to operate without conventional batteries. This paper presents an efficient and dual-band RF rectifier circuit working at 0.915 GHz and 2.45 GHz frequencies which could be used in IOT power sensor devices. The design of a dual-band matching circuit, which is a key element of the RF rectifier, is discussed, and closed-form expressions are derived to extract the most significant parameters. In order to simplify the matching circuit, only three microstrip line sections are required in this design. The first line makes the structure independent of frequency, and the second and third lines are used to transfer the desired impedance to 50 Ohm of the source. For validation, a dual-band RF rectifier circuit using SMS7621-079LF Schottky diode is fabricated. The measured results show that the fabricated rectifier can achieve power conversion efficiency (PCE) around 65.7% and 62.4% (with a load resistance of 2500 Ohm and 5 dBm input power) at 0.915 GHz and 2.45 GHz, respectively. The dual-band and high-efficiency features of the proposed rectifier make it suitable for energy harvesting (EH) systems to power IOT sensor devices.
2024-10-26
PIER B
Vol. 109, 1-16
Ultrawideband High-Gain Stacked Microstrip Antenna with Modified E-Shaped Active Exciter and Four Single-Sided Bowtie Passive Elements
Mikhail S. Shishkin
The article presents a method that allows for the high gain of a stacked microstrip antenna on an air substrate in an ultrawide frequency range. The method uses an active exciter in the form of a modified E-shaped patch, as well as four single-sided bowtie passive elements placed in the corners above the active one. The active element can match an antenna in an ultra-wide frequency range (up to 100%) with an impedance bandwidth matching of 10 dB or better, whereas passive elements are able to produce unidirectional radiation in the range of approximately 70-80% with a gain of more than 10 dBi. Based on the method under study, an ultrawideband antenna design was made which operates in a frequency band of 3,915 to 11,046 MHz (95.3%) with an impedance bandwidth matching of 10 dB and a bandwidth about 83% with |S11| ≤ -15 dB; the usable bandwidth with a gain of more than 10 dBi in the normal direction to the antenna plane with a cross-polar discrimination more than 55 dB is 77% (3,925-8,837 MHz). At frequencies below 4 GHz and above 9 GHz, the phase center shifts, and accordingly, the main lobe of the radiation pattern (radiation maximum) deflects. All antenna elements (one active and four passives) are made of sheet metal (e.g., stainless steel) and are connected to the conductive screen by steel or dielectric racks. The antenna dimensions are 1.05λmax × 1.2λmax × 0.1λmax (1.7λ0 × 1.9λ0 × 0.2λ0). Owing to its high performance, the antenna may be used as a measuring device in radio monitoring systems or in laboratories.
2024-10-25
PIER C
Vol. 149, 67-79
Multi Resonant Gap-Coupled Designs of E-Shape Microstrip Antenna for Wideband Response
Venkata A. P. Chavali and Amit A. Deshmukh
The wideband gap-coupled configuration of an E-shape microstrip antenna, with two C-shape microstrip patches and loaded with a parasitic printed rectangular loop element, is proposed. In 1200 MHz frequency range and on a substrate thickness of 0.11λg, with an optimum inter-spacing between the frequencies of TM10 and TM02 resonant modes of the rectangular patch along with TM20 resonant mode frequencies on the parasitic C-shape and printed rectangular loop element, the maximum reflection coefficient bandwidth of 945 MHz (68.11%) is achieved. The gap-coupled antenna offers broadside radiation characteristics across the complete bandwidth with a peak broadside gain of 9 dBi. Design methodology to realize wideband gap-coupled configuration in different frequency ranges is presented which yields similar result. The antenna response is experimentally verified, which yields close agreement against the simulated result.
2024-10-25
PIER C
Vol. 149, 59-65
Research on Wireless Signal Coverage Enhancement in Mine Tunnels with Different Turning Angle Based on PRIS
Bo Yin , Xiaoliang Li , Yun Li and Xiangdong Fu
Wireless communication is an essential part of future smart mines. However, the complex structure of mines, especially curved mine tunnels, makes the coverage of wireless signals drastically reduced compared to the ground, which increases the difficulty of wireless communication inside the mine. In order to improve the transmission characteristics of wireless signals in the underground non line of sight (NLOS) region, a new passive reconfigurable intelligent metasurface (PRIS) is proposed, which realises the reconfigurable characteristics of the PRIS beam through the principles of passive coding and splicing, and can be applied to different turning angle tunnels. Finally, the PRIS with different radiation directions is designed and simulated in the simulation software, and loaded into different turning angle tunnels for the simulation of tunnel power distribution. By comparing with the simulation results of unloaded PRIS, the PRIS is the most effective when the turning angle is 50˚. The overall power intensity of the tunnel is improved by 25 dBm, and the overall power intensity of the tunnel is improved by 14~17 dBm at other turning angles, which proves the effectiveness of passive splicing metasurface in the application of underground wireless communication blindness mending scenarios.
2024-10-25
PIER Letters
Vol. 123, 41-46
Design of X-Band Vertical Non-Standard Coaxial-Waveguide Converter
Bo Yan , Zibin Weng , Dalei Yuan and Youqian Su
A non-standard rectangular waveguide-to-coaxial converter designed for the X-band (9.3-9.5 GHz) is presented. This converter builds upon traditional coaxial probe coupling and stepped contact feeds by integrating a Chebyshev impedance transformer and stepped impedance matching technique. The proposed improved converter features a coupling probe combined with a stepped contact, enabling a vertical feed configuration from the bottom. This design offers an effective option for optimizing array antenna layouts. Simulation results indicate that within the operational frequency range, the rectangular waveguide-to-coaxial converter achieves |S11| less than -27 dB and |S21| greater than -0.04 dB. Practical measurements for non-standard rectangular waveguides show a VSWR below 1.1 across the working frequency band.
2024-10-25
PIER Letters
Vol. 123, 37-39
Broadside-Incidence Extinction Measurements of Thin Copper Circular Discs and the Extinction Paradox at 35 GHz
Charles W. Bruce and Sharhabeel Alyones
This article presents millimeter wavelength measurements of the mass normalized extinction cross section (extinction efficiency) of thin copper circular discs at broadside incidence. The extinction efficiencies of the discs were measured as a function of diameter and thickness at a fixed frequency of 35 GHz. The measurements cover a wide range of diameters and thicknesses and were compared with the approximate numerical solution of the problem provided by the CWW code. A good agreement between the measurements and CWW code was achieved after applying the extinction paradox for small particles with high index of refraction to the CWW code calculations.