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2020-06-14 PIER C Vol. 102, 265-281, 2020. doi:10.2528/PIERC20050602

Axial Ratio Bandwidth Enhancement of Asymmetrically Fed Microstrip Antenna

Kollannore Ukkuru Sam and Parambil Abdulla

Wide axial ratio bandwidth is imparted by placing rigorously designed radial slits on an asymmetrically fed circular radiating patch antenna with parallel bilateral truncations. A partial ground plane with beveling on both the upper corners and a double stepped notch embedded on it makes the antenna suitable for ultra-wideband and X-band applications. The antenna exhibits a −10 dB impedance bandwidth of 8.6 GHz from 3.4 GHz to 12 GHz (111.6%) and a 3 dB axial ratio bandwidth of 8.7 GHz from 3.3 GHz to 12 GHz (113.7%) thereby contributing an effective operating bandwidth of 8.6 GHz (111.6%). The prototype manifests an exceptional far-field radiation pattern and fair gain throughout the passband.

2020-06-10 PIER C Vol. 102, 253-264, 2020. doi:10.2528/PIERC20040703

Design of an Ultra-Wideband UHF RFID Reader Antenna for Wearable Ankle Tracking Applications

Khodor Jebbawi, Matthieu Egels, and Philippe Pannier

In this paper, a broadband reader antenna is designed and manufactured for wearable ankle strap applications. The frequency range covered for S11 < -10 dB is from 850 MHz to 1650 MHz with dipole like radiation pattern in free space. The proposed broadband antenna is manufactured with a semi-flex (Taconic RF-35) and flexible (Kapton) substrates. A good agreement between simulations and measurements has been achieved. Prototypes performances have been tested by measuring the reading distance. The maximum reading distance obtained is about 1.46 m at 865 MHz with an output power of the transmitter (PTX) of 25 dBm. Results of functional RFID test show that the proposed antenna can be used as an RFID reader antenna when it is placed on the ankle of the human body.

2020-06-10 PIER C Vol. 102, 241-251, 2020. doi:10.2528/PIERC20020603

A Computationally Efficient Modified MUSIC Spectrum for Resolving DOAs of Multiple Closely Spaced Non-Gaussian Sources

Chandrasekaran Ashok and Venkateswaran Narasimhan

The objective of this work is to estimate the Direction of Arrival (DOA) of signals from multiple closely spaced non-Gaussian sources corrupted by additive Gaussian noise. Generally, this is achieved by using higher order statistics (HoS) based MUSIC spectrum. In HoS, the Fourth order Cumulant is utilized because of its property of insensitivity to Gaussian process. But in the case of resolving closely spaced sources, a large number of sensor elements are required; otherwise, the resolution gets deteriorated. The large number of sensor elements leads to high computational burden. We propose a computationally efficient modified Spectrum that combines Fourth order Cumulants based MUSIC spectrum and its second-order differential counterparts. The proposed spectrum for DOA estimation offers good statistical performance and better accuracy the existing methods even in the case of extremely closely spaced signal sources. The improvement in the aspects of resolution and accuracy is substantiated by means of various simulation results such as Monte-Carlo simulations, spectral width, resolution with respect to angular separation, and comparison of RMSE with respect to number of array elements, number of snapshots, and SNR. The computational complexity analysis of the proposed method is also presented.

2020-06-10 PIER C Vol. 102, 225-240, 2020. doi:10.2528/PIERC19101401

Distribution Features of Underwater Static Electric Field Intensity of Warship in Typical Restricted Sea Areas

Cong Chen, Jingxuan Yang, Chuyang Du, and Lifeng Si

In order to study the distribution feature of the underwater electric field intensity produced by a ship in restricted seawaters, the horizontal DC electric dipole is used as the equivalent field source. Firstly, four kinds of field models are established. Secondly, the expressions of underwater electric field strength produced by a a horizontal DC electric dipole in the sea areas with upright bank is derived based on the mirror theory of static electric field. Then, based on this, the distribution features of the electric field intensity and the influence of the bank on the electric field are studied by numerical simulation. The simulated results show that the main characteristics of field strength distribution in restricted seawaters are consistent with those without bank, but it makes the absolute value of electric strength increased. The field point is closer to the vertical bank, and it generally presents greater influence on the absolute value of electric strength. But the influences of single vertical and parallel banks on the three-component field strength are different. The effect of bank on field intensity distribution in other restricted seawaters can be regarded as a superimposed effects of a series of vertical or parallel banks. Finally, the rectangle marine environment is simulated in laboratory, and the horizontal components of electric field intensity distribution on a certain depth plane under the simulated field source are measured. These theoretical derivation and analytical conclusions of simulation are further confirmed by comparing with the simulated results.

2020-06-03 PIER C Vol. 102, 213-223, 2020. doi:10.2528/PIERC20041301

Design of on-Chip Compatible Concurrent Dual Band Millimeter Wave Antenna

Smriti Agarwal

This paper presents the design and analysis of an on-chip compatible millimeter wave (mmW) antenna concurrently operating at frequencies 60 GHz and 94 GHz. It is quite challenging to design an antenna at mmW frequency due to propagation of surface waves and use of high index Si substrate for system on-chip (SoC) applications. Hence, in this paper a micromachined mmW antenna design using suspended microstrip technology has been proposed for SoC applications. Dual band operation of the antenna has been achieved by reactive loading at the radiating edge. The designed antenna supports the fractional bandwidth of 3.7% & 5% and gain of 7.68 dBi & 8.22 dBi at 60 GHz and 94 GHz, respectively. The results were also compared using two different EM solvers HFSS and CST which were in close agreement. Parametric effects of different substrate and antenna design parameters have also been analyzed. As a proof of concept, a scaled prototype antenna was fabricated and compared with the proposed mmW antenna.

2020-06-01 PIER C Vol. 102, 203-212, 2020. doi:10.2528/PIERC20020304

A Compact Slot-Antenna with Tunable-Frequency for WLAN, WiMAX , LTE, and X-Band Applications

Fouad Fertas, Mouloud Challal, and Khelil Fertas

In this paper, a new monopole compact antenna with tunable frequency fed by a coplanar waveguide (CPW) for WiMAX, WLAN, LTE bands, and X-band satellite communication system is presented. This is achieved by adequate combination of a new radiating patch element along with slots and switches. The simulation and measurement results show that depending on ON/OFF states, the proposed reconfigurable antenna, printed on an FR4 substrate, can operate in four applicable frequency bands, i.e., [2.37-2.75 GHz], [3.15-4.08 GHz], [4.48-5.92 GHz], and [6.69-8.31 GHz]. Very interesting results for the reflection coefficient, current distribution, and radiation pattern of the antenna are presented and discussed. The measured results are in good agreement with the simulated ones.

2020-06-01 PIER C Vol. 102, 187-202, 2020. doi:10.2528/PIERC20040104

Design of Sub-THz Slotted Waveguide Array Antenna for the Broadside Circularly Polarized Applications Beyond 5G

Thevaruparambil Abdulnazer Nisamol, Parambil Abdulla, and Kunnath Kodakkat Ansha

This work presents the modelling of a highly efficient all-metal slotted waveguide array antenna (SLWA) at sub-THz frequencies for the 5th generation communication applications or beyond. The slotted waveguide array antenna is modified for the accomplishment of high gain, wide bandwidth, and circularly polarized broadside radiation pattern. The proposed double `T'-shaped slot (DTS) which acts as an active element in the whole antenna radiation and other elements after DTS contribute high directivity and gain. The designed slotted waveguide array antenna with DTS is modified for the reconfiguration of linear polarization into circular polarization and achieves the axial ratio (AR) below 3 dB for the bandwidth of 22.323 GHz with a maximum gain of 14.4 dBi. The length and shape of the slot are altered in the SLWA in-order to set up the advanced rectangular stepdown slots (RSDS) and cross stepdown slots (CSDS) for the circularly polarized beam scanning application. The RSDS SLWA, and CSDS SLWA provide wide impedance bandwidths of 56.506 GHz and 61.236 GHz with 3 dB AR range of 12.417 GHz and 9.688 GHz, respectively. The design and simulation of the proposed antenna are done in CST microwave suite and validated using HFSS software.

2020-06-01 PIER C Vol. 102, 175-185, 2020. doi:10.2528/PIERC20041102

Dual-Feed, Dipole Antenna System for 2.4/5.2/5.8-GHz , Tri-Band WLAN Laptop Applications

Che-Chi Wan and Saou-Wen Su

A low-profile, printed dipole antenna having two feed ports with two parasitic strips for tri-band operation in the 2.4 GHz (2400-2484 MHz), 5.2 GHz (5150-5350 MHz), and 5.8 GHz (5725-5825 MHz) wireless local area network (WLAN) bands is presented. The strip dipole is coupled-fed via a chip capacitor connected to a dual-feed network and generates the 2.4 and 5.2 GHz bands with the aid of the tuning stubs in the feed network. The two parasitic strips are further employed to introduce additional resonance to cover the 5.8 GHz band. It was found that by loading the chip capacitor with proper values between the strip dipole and the dual-feed network, the port decoupling in both the 2.4 and 5.2 GHz bands can be improved, making a dual-feed and yet single antenna system possible. The design with constant strip width is simple in structure and occupies a compact size of 5 mm × 40 mm (about 0.04-λ × 0.32-λ at 2.4 GHz), which is well-suited to current narrow-bezel laptop computers.

2020-05-27 PIER C Vol. 102, 163-174, 2020. doi:10.2528/PIERC20021501

High Permittivity Substrate and DGS Technique for Dual-Band Star-Shape Slotted Microstrip Patch Antenna Miniaturization

Zhor Bendahmane, Souheyla Ferouani, and Choukria Sayah

Three miniaturization techniques were combined in this work to achieve compact size while maintaining optimal performances of a dual-band star shape slotted Microstrip Patch Antenna (MPA) operating at 2.4 and 5 GHz resonant frequencies. High permittivity substrate and slot techniques were used for miniaturization and impedance matching improvement, while DGS technique was necessary for bandwidth enhancement and further miniaturization of the reference MPA. The miniaturized antenna shows a planar structure and occupies very small area of 15.55 x 19.80 mm2 achieving patch size area reduction of 71.24% and overall size reduction of 75.42%. Respectable positive gains were maintained with radiation efficiency exceeding 83% and 68% at 2.4 GHz and 5 GHz, respectively. The reference and miniaturized MPAs were fabricated, then their performances were measured and compared to the simulated ones. The measured impedance bandwidths of the miniaturized MPA were around 38% and 13% at the two resonant frequencies respectively, which confirm the originality and suitability of the miniaturized MPA for Wireless Local Area Network WLAN and ISM applications.

2020-05-26 PIER C Vol. 102, 149-162, 2020. doi:10.2528/PIERC20022503

Frequency Reconfigurable Multiband Antenna for IoT Applications in WLAN, Wi-Max, and C-Band

Prem Pal Singh, Pankaj Kumar Goswami, Sudhir Kumar Sharma, and Garima Goswami

Due to the upsurge in internet connected devices in everyday life, a compact embedded wireless device becomes essential to cater multiple frequency-based applications at common platform. Reconfigurability is the best solution to enhance the device utility at many technical interfaces. Wireless compatibility among different devices via internet elicits the importance of antenna unit. In this paper, a compact size 25×25 mm2, five-band frequency reconfigurable antenna is presented. The antenna exhibits the choice-based optimized frequency responses of slot structures, corner truncation and parasitic loading. These individual responses comprise the high frequency switching characteristics in synchronized module of three PIN diodes. The antenna is designed to operate among five different frequencies i.e. 3.85 GHz, 4.14 GHz, 4.43 GHz, 4.91 GHz, and 6.01 GHz. The work emphasizes the compact design and wide switching ability of the antenna, which validates its unique feasibility for high speed multiple applications of Internet of Things (IoT) through a common embedded platform under WLAN, Wi-Max, and C-band applications as per the FCC standards.

2020-05-25 PIER C Vol. 102, 139-148, 2020. doi:10.2528/PIERC20031805

Radar Target Discrimination of Real Size Aircraft with Minor Structural Variations: Challenges and Solutions

Sathyamurthy Anuradha and Jyothi Balakrishnan

A novel aspect independent resonance based radar target discrimination method has been developed in a previous work, and is found to be effective in discriminating canonical shape closely resembling objects with minor structural variations. The method utilizes the Radar Cross Section (RCS) of the unknown target to be identified and the distinction polynomial stored in the database (built from the dominant resonances of the known target). In this paper, the method is implemented successfully to discriminate two real size F5 aircraft with minor structural variations between them. This study involving real size targets poses some challenges that are overcome in this paper. The foremost challenge is the accurate computation of resonance range RCS of electrically large sized target considered (> 10λ), which is computationally demanding. The second challenge is in selecting the dominant resonances (features) of the complex target, useful for discrimination, from a large set of resonances representing the target. The accuracy of the discrimination result is dictated by the accuracy with which the features of the targets are identified. This in turn is dependent on the accuracy with which RCS is determined. To achieve accurate results, the exact Computational Electromagnetic (CEM) method - the Method of Moments (MoM) is used for computing the RCS of real size aircraft. The procedure to choose an optimal number of dominant natural resonant frequencies (NRFs) from a pool of NRFs for real size complex target is presented in this paper. The discrimination quantifying function `Risk' is shown to be effective in discriminating F5 aircraft - with and without missile attached underneath. The two targets have been successfully discriminated at all aspects, which is yet another challenge, establishing the aspect independent discrimination capability of the technique.

2020-05-25 PIER C Vol. 102, 127-137, 2020. doi:10.2528/PIERC20020302

Low Reflection Coefficient Ku-Band Antenna Array for FMCW Radar Application

Laxmikant Minz, Hyunseong Kang, and Seong-Ook Park

A radar for decisive target detection and tracking requires wideband, high return loss and high efficiency antenna array. In this paper, a 16 element staked-patch microstrip antenna array is presented at Ku-band with very low reflection coefficient for radar system. An aperture coupled feeding approach for a stack patch antenna is employed for wide bandwidth. A thin and low-loss tangent material, Taconic TLY-5, is used in the design of an antenna array to minimize the surface current loss and dielectric loss. Moreover, the antenna is designed with good impedance match, -30 dB, for high efficiency, by optimizing the stacked patches and utilizing reactive loading from u-slit on patch. For a low reflection coefficient antenna array over a wide bandwidth, an adequate feeding network consists of a compact and meandering stripline with metal-post around it is developed. The stripline configuration with metal-post minimizes crosstalk and lateral leakage. The feeding network developed has low reflection coefficient of -30 dB for the target band. The simulated feeding network loss is also low, 0.5 dB. The overall size of the 16 element array is compact, 295 mm x 30 mm (14λ x 1.425λ). The antenna array performance gives a reflection coefficient of -30 dB in the range of 14-14.5 GHz and total efficiency of 80%. The gain of the array is 21.54 dBi at 14.25 GHz.

2020-05-21 PIER C Vol. 102, 109-125, 2020. doi:10.2528/PIERC20022707

Applications of the Random Coupling Model to Assess Induced Currents or Voltages in Reverberant Environment

Valentin Houchouas, Muriel Darces, Marc Hélier, Emmanuel Cottais, and José Lopes Esteves

Coupling in electronic devices may be a threat for the security of the information they process. Indeed, a current flowing into a conductor may radiate an electromagnetic field that will couple onto other conductors creating parasitic signals. If this current conveys sensitive information, its confidentiality may not be guaranteed. Moreover, depending on the amplitude of these parasitic signals, dysfunction may occur. It is thus valuable to assess the coupling effects in order to evaluate the probability that a current or a voltage reaches a given magnitude. This relevant quantity may be an input for a risk analysis process. In this study, we will focus on the study of couplings in reverberant cavities, and especially into the chassis of desktop computers. We will highlight that the Random Coupling Model (RCM) may be applied to determine statistical quantities related to induced currents or voltages between several ports placed inside a reverberant environment. Comparisons with experimental data, for several system configurations, show that the application of this model is relevant and allows to rapidly obtain the percentiles of the induced currents. At first, the coupling between two monopoles is studied, and then the coupling between printed circuit boards that are stacked together is investigated. Finally, the effect of adding broadband absorbers in casings is assessed.

2020-05-21 PIER C Vol. 102, 93-107, 2020. doi:10.2528/PIERC20041501

Pilot Contamination Mitigation Based on Interfering User's Angle of Arrival in Massive MIMO Systems

Parfait Ifede Tebe, Guangjun Wen, and Kwadwo Ntiamoah-Sarpong

A new approach to mitigate pilot contamination in massive MIMO systems is proposed in this paper. We consider two cells from the first tier of copilot cells of a cellular network where the base stations (BSs) are equipped with uniform linear arrays with hybrid beamforming adopted. We consider one cell as the cell of interest containing a typical desired user, and the other cell contains an interfering user sending data and contaminating pilot signals to the BS of the cell of interest. We derive a closed-form expression for the desired user's achievable rate as a function of the interfering user's angle of arrival (AoA). We model the ray propagation from the interfering user to the BS of the cell of interest and its related AoA as Gaussian distribution. Based on the model, we derive closed-form expressions for the pilot contamination level in the cell of interest, and for the desired user's data path gain estimation error due to pilot contamination. A perfect agreement is found between theoretical and Monte Carlo simulation results which show that when the interfering user's AoA is increased the pilot contamination level is significantly minimized, the desired user's data path gain estimation error also minimized, and hence its data rate is significantly increased. Moreover, we show in our analysis that the interfering user's AoA can be effectively controlled and increased by reducing the copilot cells' radius.

2020-05-20 PIER C Vol. 102, 79-91, 2020. doi:10.2528/PIERC20022901

Design, Analysis, and Optimization of Dual Side Printed Multiband Antenna for RF Energy Harvesting Applications

Rashmi Pandey, Ashok Kumar Shankhwar, and Ashutosh Singh

In this paper, the performance of a compact, multiband, and dual side printed microstrip patch antenna is introduced. The proposed antenna configuration is designed using a nested triangular patch and defected ground structure (DGS). A simple rectangular DGS is constituted in the ground plane, which helps to enhance the multiband characteristics of the antenna with its size. The proposed design exhibits compact size, better radiation, and reflection characteristics over a multiband frequency ranging from 1 GHz to 6 GHz. These entire bands are allied with various wireless communication services, such as GSM 1400 MHz and 1900 MHz, ISM, WLAN, Bluetooth, LTE, Wi-Fi, and GPS applications. The receiving Triangular Nested Patch (TNP) antenna offers omnidirectional radiation with 4.45 dBi gain and maximum return loss -34.31 dB at 3.75 GHz. Moreover, extraction of parameters has been presented in this paper with the variation of feed width and ground length. The proposed design shows the enhancement of gain and improved return loss. A comparative analysis has also been shown with the four different antennas parameters. Furthermore, this paper also presents the compact structure to cover efficient frequency ranging from 1400 MHz to 5.8 GHz for radiofrequency energy harvesting applications.

2020-05-18 PIER C Vol. 102, 63-77, 2020. doi:10.2528/PIERC20030402

Compact Two-Port MIMO Antenna with High Isolation Using Parasitic Reflectors for UWB, X and Ku Band Applications

Tathababu Addepalli and Vaddinuri Rajareddy Anitha

In this communication, a compact two-port multiple input multiple output (MIMO) antenna with high isolation is presented for multiband applications. The size of the proposed structure is 0.15λ0x 0.27λ00, measured at lower frequency, is 2.95 GHz), and the antenna elements are separated by a distance of 0.04λ0. The truncated partial ground offers good impedance performance with a fractional bandwidth of 136.5% from 2.95 to 15.65 GHz and covers the uninterrupted ultra-wideband (UWB), X and Ku band applications. High isolation of more than 25 dB is attained by placing parasitic elements between the antennas in a precise manner. The proposed structure is simulated, fabricated, tested, and verified practically. The radiation efficiency is more than 90% of the entire band. The peak gain values vary from 1.2 to 6.8 dB in the desired band, and its maximum value is 6.8 dB at 11.6 GHz. Diversity performance is also studied. The proposed structure offers an envelope correlation coefficient (ECC) of less than 0.04, diversity gain (DG) of greater than 9.996 dB, total active reflection coefficient (TARC) of below -10 dB, mean effective gain (MEG) of around -3 dB, and channel capacity losses (CCL) values are below 0.2 bits/sec/Hz. The measured and simulation results are in good concord.

2020-05-15 PIER C Vol. 102, 47-62, 2020. doi:10.2528/PIERC20031204

Compressed Sensing DOA Estimation in the Presence of Unknown Noise

Amgad A. Salama, M. Omair Ahmad, and M. N. S. Swamy

A new compressive sensing-based direction of arrival (DOA) estimation technique for source signal detection in the presence of unknown noise, based on the generalized correlation decomposition (GCD) algorithm, is presented. The proposed algorithm does not depend on the singular value decomposition nor on the orthogonality of the signal and the noise subspaces. Hence, the DOA estimation can be done without an a priori knowledge of the number of sources. The proposed algorithm can estimate more sources than the number of physical sensors used without any constraints or assumptions about the nature of the signal sources. It can estimate coherent source signals as well as closely-spaced sources using a small number of snapshots.

2020-05-14 PIER C Vol. 102, 31-46, 2020. doi:10.2528/PIERC20020403

A Review of Remotely Sensed Surface Urban Heat Islands from the Fresh Perspective of Comparisons Among Different Regions (Invited Review)

Zhao-Liang Li, Menglin Si, and Pei Leng

Urban heat islands (UHIs) threaten the ecological environment and human health. A large number of studies have focused on surface UHIs (SUHIs) across different spatial and temporal scales around the world with the development of satellite remote sensing technology. However, the influences of heterogeneous urbanization processes and background climates on SUHIs are still unclear and are important for targeted mitigation policies. A systematic review of the current status of SUHI studies, particularly from the perspective of comparisons among different regions, is urgently needed. We first introduce the commonly used satellite-retrieved data products and quantification methods used in SUHI studies. Subsequently, we summarize the potential driving factors of SUHI and compare the specific findings for different regions. Finally, we point out the deficiencies in the existing research and propose several prospects for the consideration of future SUHI studies. Additional global-scale research should be conducted using more advanced spatial statistical models. This can help better explore the spatially heterogeneous relationship between the SUHI and its associated driving factors. The effects of urbanization and climate from different regions should be further explored. Moreover, the problems of imperfections in the satellite data and from dynamic land use should not be ignored.

2020-05-13 PIER C Vol. 102, 13-30, 2020. doi:10.2528/PIERC20021101

Compact Dual-Band MIMO Antenna System for LTE Smartphone Applications

Haneen Sobhi Aziz and Dhirgham Kamal Naji

The design of an eight-port MIMO antenna at the sub-6-GHz (LTE 42/43 and 46) bandsfor fifth-generation (5G) smartphone is presented. First, based on the Babinet's principle, a microstrip slot antenna (MSA) is designed from its counterpart complementary structure, microstrip patch antenna (MPA) to operate over the LTE 46 band. In order to make the MSA to operate at the specified three LTE bands, a proposed single antenna, namely RMSA, is achieved by adding a strip-ring resonator within the grounded slot of MSA which shows a good measured impedance bandwidth (S11 ≤ -6 dB) of 3.28 ~ 3.84 GHz and 5.14 ~ > 6.0 GHz. Then, eight similar antenna elements of RMSA are printed on a smartphone printed circuit board (PCB). An FR4 substrate is used as the system PCB with an overall dimension of 80 × 150 × 0.8 mm3. Two techniques, namely polarization and pattern diversity, are exhibited by designing the MIMO system due to the orthogonal arrangement of microstrip lines feeding the RMSAs. Simulated and experimental results are conducted to examine the performance of the designed MIMO antenna. Good isolation, acceptable gain, and efficiency are obtained over the bands of interest which verify the suitability of the proposed system for MIMO smartphone applications.

2020-05-12 PIER C Vol. 102, 1-11, 2020. doi:10.2528/PIERC20031108

Multipole-Based Cable Braid Electromagnetic Penetration Model: Magnetic Penetration Case

Salvatore Campione, Larry Kevin Warne, and William L. Langston

The goal of this paper is to present, for the first time, calculations of the magnetic penetration case of a first principles multipole-based cable braid electromagnetic penetration model. As a first test case, a one-dimensional array of perfect electrically conducting wires, for which an analytical solution is known, is investigated: we compare both the self-inductance and the transfer inductance results from our first principles cable braid electromagnetic penetration model to those obtained using the analytical solution. These results are found in good agreement up to a radius to half spacing ratio of about 0.78, demonstrating a robustness needed for many commercial and non-commercial cables. We then analyze a second set of test cases of a square array of wires whose solution is the same as the one-dimensional array result and of a rhomboidal array whose solution can be estimated from Kley's model. As a final test case, we consider two layers of one-dimensional arrays of wires to investigate porpoising effects analytically. We find good agreement with analytical and Kley's results for these geometries, verifying our proposed multipole model. Note that only our multipole model accounts for the full dependence on the actual cable geometry which enables us to model more complicated cable geometries.