Wire Inductance Research Articles

An integral for self inductance of thin wires

Abstract I propose an elegant method of calculating the self inductance of a thin wire of arbitrary shape. The inductance is broken to into two parts - the inductance of a straight wire of the same length and cross section, and the remainder, the “curve inductance” due to the shape of the axial curve. The curve inductance is finite and can be calculated from a double integral by subtracting the straight wire singularity inside the integrand. Unlike all other methods, this does not involve a small parameter, and can be applied to any curve knowing its arc length parameterization. We use the circular arc and helix as examples and find that the integral is fast and accurate. The limits of the approximation are investigated for touching parallel wires.

Voltage‐controlled attenuator based on PIN diode and compensated gold wire inductors

AbstractThis paper proposes an innovative design approach for a voltage‐controlled (variable) attenuator that allows continuous control of attenuation through analog voltage. Different from fixed attenuators, this work employs PIN diodes and compensated gold wire inductors to configure the attenuation network. It is based in imperfect matching theory, ensuring to obtain the acceptable S‐parameters over the operating band. Measurement results demonstrate effective performance of the attenuator within the voltage range of 0.7–1.03 V. Return losses of the attenuator are all better than 15 dB in the operating range of 10.5–19 GHz. The insertion losses exhibit continuous variation from 2 to 15 dB, requiring only a single controlled voltage to adjust the attenuation value.

Design of CRLH-TL BPF with controllable attenuation poles

Compact and pole-controllable resonators and bandpass filter (BPF) using a composite right/left-handed transmission line (CRLH-TL) are designed in this study. The distributed constant line in the CRLH-TL has applied a tap-coupling technique, and one tap-coupled stub is loaded with the left-handed (LH) circuit. Attenuation poles are generated when the input susceptance of the stub diverges. In the tap-coupled CRLH-TL resonator, the attenuation pole is controlled at either the desired lower or higher region frequency than a resonant frequency by adjusting the circuit parameters. Also, the BPF constructed by the CRLH-TL resonators is designed based on a filter design theory, where the attenuation poles are located at lower and higher region frequencies than a negative-first-order frequency. The BPF with microstrip structure is fabricated using MEGTRON6 R-5775 (εr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon _\ ext {r}$$\\end{document}: 3.7, h: 0.63 mm, t: 18 μm), chip capacitors, and wire inductors. The simulated results show that the desired characteristics are approximately satisfied, i.e., we can design the CRLH-TL BPF which is controllable for the attenuation poles at both lower and higher region frequencies than a resonant frequency. The measured results are good agreement with the simulation. The negative-first-order frequency is generated at 2.00 GHz with 133 MHz bandwidth, i.e., the fractional bandwidth is 6.65 %. The resonator lengths in the BPF are shortened by 81.5 % and 75.0 % in comparison with a conventional half-wavelength (λ/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda /2$$\\end{document}) openstub, and the size of the fabricated BPF is 0.18 λg×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _\ ext {g} \ imes$$\\end{document} 0.17 λg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _\ ext {g}$$\\end{document}. Therefore, a compact BPF with two controllable attenuation poles is realized by the tap-coupled CRLH-TL.

Design, construction, and testing of an exploding wire pulsed plasma system for generating shock waves in industrial applications

Exploding Wire Pulsed Plasma System (EWPPS) used in oil recovery operations has been construct and developed with an initial energy release of 1.5 kJ in a fusion laboratory. Recently, the final experiments have been carried out on the purpose device operating in microsecond time scale in air and fluid medium successfully. In this setup, a single wire feeder is used for tests. Also, to study and develop the shock waves caused by wire explosions in the industry, the diagnostic tools of voltage probe, current coil, pressure probe and photodiode have been used. Choosing the optimal material of wire is one of the basic factors in creating a suitable shock wave. In addition, the impact of wire inductance on discharge current, voltage, pressure and shock wave strength has been investigated by applying two sets of wires, refractory (Cu, Cu-Ni, and Steel) and non-refractory (W, W-Al, Mo). The results show that the strongest shock wave is produced while the transition from warm wire to dense plasma happens. The soft X-ray intensity of both wire series has been measured using a photodiode BPX-65 (<10 keV). The comparison shows higher X-ray intensity for non-refractory wires than that for refractory wires. In good agreement, the maximum value of the shock wave was 8.7 and 6.6 MPa for non-refractory metals with high inductance and refractory metals with low inductance, respectively.

A Robust LC-π Matching Network for 112 Gb/s PAM4 Receiver in 28 nm CMOS

This article presents analysis, design details, and simulation results of an impedance matching network designed for a 112 Gb/s pulse-amplitude-modulation-4 (PAM4) receiver using an LC-π structure. We designed the bonding wire as a part of the matching network, which reduced design pressure on the equalizer as there will be no need to compensate the loss of the chip package. To avoid robustness issues caused by the fluctuation of the bonding wire inductance, the matching network is designed to bw adjustable by the capacitance on PCB and the terminal resistance. We analyzed the parasitics in the layout and the influence of nearby and dummy metals and obtained reliable simulation results through electromagnetic field simulation. This matching network is designed with a 28 nm CMOS process. Post-layout simulation results show that with bonding wire inductance changing from 150 pH to 250 pH, it can always meet CEI-112G-XSR-PAM4 Extra Short Reach Interface requirements.

Over-85-GHz-Bandwidth InP-Based Coherent Driver Modulator Capable of 1-Tb/s/λ-Class Operation

We developed an InP-based coherent driver modulator (CDM) with a flexible printed circuit (FPC) RF interface. The CDM has a 3-dB electro-optic (EO) bandwidth of over 85 GHz, including the evaluation board loss, which is sufficient for 1-Tb/s/λ-class operation. Furthermore, we obtained good back-to-back bit-error-rate (BER) performance in modulations up to 144-Gbaud dual-polarization 16-QAM, and we confirmed the CDM's capability for operation over the 150-Gbaud class. With the FPC RF interface, a package's roll-off frequency above 100 GHz was demonstrated in both measured and simulated results. The CDM includes an InP-based n-i-p-n heterostructure modulator chip with a differential capacitively loaded traveling-wave electrode (CL-TWE) and a 4-channel linear SiGe BiCMOS driver IC with an open-collector configuration and low wire inductance. The modulator chip has an EO 3-dB bandwidth of over 70 GHz, which is an improvement of about 30 GHz over that of a conventional p-i-n structure. In addition, to facilitate future 200-Gbaud-class operation, a simulation with a reduced GND via diameter confirmed that the package's roll-off frequency can be improved to more than 120 GHz. Moreover, by reducing the CL-TWE period and the metal's DC resistance, the n-i-p-n modulator chip achieve an EO 3-dB bandwidth of 90 GHz or more.

High Bandwidth Active Gate Driver for Simultaneous Reduction of Switching Surge and Switching Loss of SiC-MOSFET

This study investigates an active gate driver (AGD) for an SiC-MOSFET. The source current feedback type AGD utilizes the induced voltage of the source wire inductance as a negative feedback signal to regulate the source current di/dt. Recent improvements in the switching performance of the AGD is limited due to the feedback system bandwidth. In this paper, a high bandwidth current feedback type power operational amplifier is applied as the gate drive circuit. Switching characteristics of the conventional resistive gate driver and AGD are experimentally investigated via a double pulse test setup. The switching setup condition is 700 V / 80 A. This paper describes the development of the AGD circuit and experimental results. The over-shoot and ringing of the Vds and Is are reduced using the AGD. Moreover, the switching loss is simultaneously reduced.

Back Flashover Probability of the Overhead Power Line Insulation Taking into Account the Soil Ionization and Frequency Response Features

Back flashovers caused by a lightning strike on an overhead power line tower or overhead ground wire give rise to voltage surges dangerous for the insulation of power substation electrical equipment. A pulse back flashover turns into a short-circuit arc leading to the power line tripping. Calculations of voltage surges in a single–circuit 110 kV power line are carried out using the methods of the grounding devices theory, and the back flashover probability is estimated based on the curve of dangerous currents. The insulation back flashover probability for a power line tower with a ground wire in areas with high-resistance soil is determined by the grounding conductor surge impedance. It is shown that the analysis carried out with taking into account the soil ionization and frequency response features yields an essentially lower back flashover probability. The second ground wire placed under the power line wires reduces the inductance of the ground wires, thereby intensifying the spread of current through the grounding conductors of neighboring towers. This leads to a decreased tower voltage and an increased voltage induced on the wires, thus resulting in a decreased voltage across the insulation voltage and, hence, lower back flashover probability. The factors governing a positive effect from using grounding counterpoises of an overhead power line in areas with high-resistance soil are shown, and the conditions under which this effect is achieved are determined.

In Situ Diagnosis of Multichip IGBT Module Wire Bonding Faults Based on Collector Voltage Undershoot

Condition monitoring of insulated gate bipolar transistor (IGBT) modules is an effective way to improve the transient performance and reliability of modular multilevel converters (MMC). This article proposes a novel bond wire failure monitoring method for the multichip IGBT modules in the MMC half-bridge submodule (SM) structure. The collector voltage undershoot <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CA(np)</sub> of the complementary IGBT switch is measured during the turn- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> switching transition of the controlled IGBT switch. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CA(np)</sub> is sensitive to the induced voltage over the stray inductance of the IGBT bond wires and provides high sensitivity as a health indicator. The non-intrusive measurement technique is demonstrated using a half-bridge circuit during the turn- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> transition of the controlled IGBT, while its complementary switch (i.e., the device under test) is in the <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> state. Theoretical analysis and experimental results show that the parametric drift due to wire bonding failures can be effectively monitored with high specific relative sensitivity and granularity. To ensure its effectiveness in practical applications, the influence of load current, SM capacitor voltage, and junction temperature is discussed. In addition, a readout circuit is designed featuring the integrated desaturation detection and voltage peak detection, which offers both the short-term overcurrent fault protection and long-term bond wire aging monitoring functions.

Equivalent circuit modeling in GaN wireless power transmission including stray inductance and capacitance by measuring radiated emission

We establish the method for estimating the stray elements of the GaN-WPT circuit by measuring the radiated emission around the GaN switching device. By controlling the circuit supply voltage, the spectrum peak shift due to the output capacitance of the GaN-HEMT is observed. It is found that these peak shift characteristics include the influence of both the stray wire inductance and stray capacitance. By fitting using the series resonance model, the value of the stray inductance and stray capacitance can be estimated in the non-destructive measurement in the GaN-WPT circuit.

Current distribution at underwater electrical explosion of wires with different diameter connected in parallel

Underwater electrical wire explosion is usually used as a source of underwater shock waves, and the generated shock wave intensity can be regulated by adopting a wire array. In this paper, the dynamics of the electrical explosion of two wires with different diameters connected in parallel were studied. The current flowing through each wire was measured to study the current distribution, and the self-emission image and laser backlight shadow image was obtained to observe the evolution of the wires. A numerical model was built to make explanations and predictions. The results showed that due to the presence of wire inductance and contact resistance between the wire and electrode, the wires are with different current densities and undergo asynchronous heating from the beginning of the discharge. Furthermore, the variation of current distribution among the wires was divided into six stages according to the moment the wire melted and exploded, and analyzed stage by stage. The unbalanced energy deposition results in obvious differences in thermal dynamic parameters, which explains the gradual “extinguishment” of the thinner wire in the self-emission image.

Diagnostic performance of intravascular ultrasound-based fractional flow reserve versus angiography-based quantitative flow ratio measurements for evaluating left main coronary artery stenosis.

We compared the diagnostic performance of the ultrasonic flow ratio (UFR) and quantitative flow ratio (QFR) for left main coronary artery (LMCA) stenosis. Evaluation of LMCA stenosis remains challenging because of its complex pathogenesis and severity. Computing QFR allows rapid determination of fractional flow reserve (FFR) from coronary angiograms. A novel intravascular ultrasound (IVUS)-based FFR (UFR) allows rapid FFR computation from IVUS images. Neither of the computational approaches required a pressure wire or hyperemia induction. Previous studies have validated the good diagnostic accuracy of QFR and UFR in identifying hemodynamically significant coronary stenosis using FFR as the reference standard. This retrospective observational study enrolled consecutive patients with intermediate-grade LMCA stenosis who underwent IVUS evaluation. UFR and QFR of all LMCA stenosis patients were assessed, their correlation and agreement were analyzed, and diagnostic performance of UFR in LMCA stenosis was evaluated. Eighty-three paired comparisons between UFR and QFR were obtained. UFR excellently correlated with QFR (r = 0.74, p < 0.01). The Bland-Altman plot showed good agreement between UFR and QFR (mean differences: 0.01 ± 0.05, p = 0.34). The area under the curve of UFR for identifying physiological LMCA stenosis was 0.97 (95% confidence interval [CI]: 0.93-1.00, p < 0.01). The overall UFR diagnostic accuracy was 0.95 (95% CI: 0.88-0.99). UFR showed excellent correlation and good agreement with QFR in LMCA stenosis assessment, indicating that it is highly feasible to use UFR for functional evaluation of LMCA stenosis.

Measurement of the impedance for a hybrid X-pinch load

For a hybrid X-pinch load assembled in parallel with the return-current rods, the impedance of the hybrid X-pinch load is important for current division between the load and the current rods. In this paper, the experimental results of the investigation of the impedance of a hybrid X-pinch load on the Qiangguang facility (1.5 MA, 100 ns) were reported. The current of the X-pinch load was measured using a serial nickel foil resistor, and the voltage was measured using a two-stage resistive divider. The inductance of the X-pinch load was obtained by comparing the differential signal of the current with the voltage waveform, and it is about 4.7 nH, which is nearly equal to the calculated total inductance of the metal wire and the two X-pinch electrodes. The resistance of the X-pinch was determined by subtracting a part of the inductance from the measured voltage, and the following results were obtained. At the start of the current, the resistance of the X-pinch increases quickly from the metallic resistance of 0.16 Ω at room temperature for a 2-mm-length 30-μm-diameter Mo wire to 0.8 Ω in about 10 ns, and then, it falls fast to nearly zero, which suggests that the electrically exploding phase of the metal wire ends and the high conductive plasma is formed. As the current continues to flow through the Mo wire, the resistance increases once again from nearly zero to about 0.4 Ω at the moment when the X-pinch begins to burst x-ray radiation, which reflected that the micro-pinch dynamical process occurs and a hot and tight plasma zone is formed. Assuming that the tight plasma zone is 300 μm long with a 10 µm diameter and the temperature of the plasma is ∼1 keV, we can obtain that the resistance of the tight X-pinch spot is about 0.6 Ω, which is close to the value of 0.4 Ω obtained in the experiments.

Modelling and optimization of winding resistance for litz wire inductors

Optimization of winding resistance for litz wire inductors is essential to reduce losses and improve energy transfer efficiency in electrical power systems. In this study, an approximate model for the optimization of winding resistance in litz wire inductors based on Dowell's equation is developed in three frequency ranges. The proximity and skin effects are analysed separately and subsequently combined to obtain an approximation with minimum theoretical error. Two error functions are defined to determine the frequency ranges for which the approximation is valid. Based on this Dowell's model approximation, it is found that, with the other parameters of the inductors fixed, both the porosity factor and conductivity have an optimal value that minimizes AC resistance for the litz wire windings. Thus, expressions for the optimum porosity factor and conductivity are derived, the optimization schemes under different practical engineering conditions are also given. The theoretical results are in good agreement with the experimental measurements, which indicates that the proposed model is valid for three frequency ranges, and the proposed optimization method is practical and suitable.

Structure-Simplified Resonant-Tunneling-Diode Terahertz Oscillator Without Metal-Insulator-Metal Capacitors

We propose and fabricate a novel structure-simplified resonant tunneling diode (RTD) terahertz (THz) oscillator without metal-insulator-metal (MIM) capacitors. In conventional RTD THz oscillators, the DC and RF circuits are separated by MIM capacitors. In the proposed oscillator, the DC-to-RF separation is based on the difference between the impedances of the antenna and biasing wire inductances in the low-frequency range and those in the THz range. Thus, by removing MIM capacitors, we simplify the device structure. We also introduce an InP etch stopper layer in the RTD epitaxial structure for easy formation of an airbridge. Owing to the simple structure and the introduction of the etch stopper layer, the fabrication process is significantly simplified. We successfully fabricated novel RTD oscillators using a simple fabrication process. Oscillation frequency of up to 742 GHz and output power of ~ 10 μW up to 600 GHz were obtained, respectively. The novel RTD oscillator is expected to be suitable for massive array configurations that could enable a wide range of practical THz applications.

Evaluation of Surge Reduction Performance of a SiC Avalanche Diode with Mesa Structure in a Switching Power Supply

A p-n junction diode with mesa structure by silicon carbide (SiC) has been developed to utilize the avalanche breakdown in an excessed reverse bias condition to clamp the surge voltage in switch-mode power supplies. Static voltage-current correlation by pulsed reverse voltage has been measured. The increase of the breakdown voltage was measured to be 32 volts with increased current density up to 3900 A/cm2. The operational performance in suppressing the surge voltage in a step-down DC/DC converter has been evaluated. A superior performance in suppressing the surge voltage by the SiC p-n junction diode has been confirmed. It was also found that a resonant oscillation induced during clamping period limits the performance. By a circuit analysis with an equivalent circuit model, it was found that a parasitic wiring inductance between the diode and switching element induces the resonance. It was also found that a promising way to mitigate the disturbing effect is to minimize the inductance.

The Geometry Effect of Regular Polygonal Wire on Its Inductance for Antenna Application

One important parameter of an antenna is its inductance. Inductance is the nature of a conductor which is related to its magnetic characteristics when alternating electric current is flowed. There are several factors that affect the inductance of a conductor wire, such as the size (dimension of the wire), the geometric shape of the wire, the permeability of material around the wire, and others. In this paper, we will discuss the effect of wire geometry on the value of the wire inductance. The wire diameter of regular polygonal wire is very thin. In determining the inductance of regular polygonal wire, some restrictions do for simplification in the calculation. Some of these restrictions are (1) the length of wire or circumferential polygon is fixed, (2) the diameter of the wire is considered very thin, (3) the distribution of the magnetic field is considered homogeneous, (4) the effect of external magnetic fields on the wire ignored. The results of calculations and analysis show that the change in geometry of regular polygonal wire from rectangular wire to decagonal wire causes the wire’s inductance value to increase.

Design and Development of Magnetostrictive Actuators and Sensors for Structural Health Monitoring.

Carbon Fibre Reinforced Polymer composite (CFRP) is widely used in the aerospace industry, but is prone to delamination, which is a major causes of failure. Structural Health Monitoring (SHM) systems need to be developed to determine the damage occurring within it. Our motivation is to design cost-effective new sensors and a data acquisition system for magnetostrictive structural health monitoring of aerospace composites using a simple RLC circuit. The developed system is tested on magnetostrictive FeSiB and CoSiB actuator ribbons using a bending rig. Our results show detectable sensitivity of inductors as low as 0.6 μH for a bending rig radii between 600 to 300 mm (equivalent to 0.8 to 1.7 mStrain), which show a strain sensitivity resolution of 0.01 μStrain (surface area: ~36 mm2). This value is at the detectability limit of our fabricated system. The best resolution (1.86 μStrain) was obtained from a 70-turn copper (~64 μH) wire inductor (surface area: ~400 mm2) that was paired with a FeSiB actuator.

Analysis of Discharge Faults Between Flanges Caused by Transient Enclosure Voltage

An increase in transient enclosure voltage can threaten the personal safety of workers and the normal operation of secondary equipment and may cause discharge between the flanges of gas insulated switchgear (GIS) enclosures. This study considered the spark–discharge fault between GIS enclosure flanges of a 500-kV nuclear power plant in China when the disconnect switch is operated in the background. The dynamic arc model during the operation of the disconnect switch was improved in this study, and the equivalent calculation model of transient enclosure voltage (TEV) caused by very fast transient overvoltage generated during the operation of the disconnect switch was established using the electromagnetic transient program ATP-EMTP. Suppression measures of the discharge phenomena were also discussed. The results demonstrated that the transient enclosure voltage caused by the operation of the disconnect switch can reach 75 kV in the most severe case, which causes discharge between the flanges. Reducing the residual charge on the island side of the disconnect switch, installing a metal oxide arrester, and reducing the inductance of the ground wire have different inhibitory effects on this discharge phenomenon, but they all have their limitations. The most simple and effective control measure is to use a short joint between two flanges. The study conclusions can be used as reference for preventing such discharge phenomena.

Calculation of Additional Losses in Windings of Permanent Magnet Motors Using the Femm Package

The calculation of additional losses in the windings of permanent magnet synchronous motors is proposed to be performed using the FEMM package. The article describes a system of equations that allows to determine the distribution of instantaneous values of currents in the elementary wires of the winding. As an example, a low-voltage permanent magnet motor with concentrated windings on a stator is considered. To determine the matrix of inductances of elementary phase wires, the FEMM program was used. To speed up the calculations, a control script for FEMM (in the lua scripting language) was used, which made it possible to automatically de-termine the matrix of own and mutual inductances for a given distribution of elementary wires in a slot. The re-sults of calculating the instantaneous values of the currents in the elementary wires of the winding are used to determine the additional losses. Variants of the distribution of elementary conductors in a slot are considered, the corresponding coefficients of increasing losses in the winding are determined.