Wire Inductance Research Articles

Analytical Models for Calculating the Inductances of Bond Wires in Dependence on their Shapes, Bonding Parameters, and Materials

Novel analytical models for accurately and efficiently calculating the inductances of bond wires in dependence on their shapes, bonding parameters, and materials are derived. For verification, the inductances of bond wires having different geometrical dimensions and material properties were analytically calculated using our proposed models, and compared to those numerically extracted using Ansys Q3D. An excellent correlation was obtained, with a maximum discrepancy of approximately 1%. These models can be applied to rapidly predict the impact of the bonding parameters and their process variations right at the beginning of the design process. For example, using the models, we could predict within seconds that the loop inductance of a ground-signal bond wire configuration can be reduced by approximately 14%, 19%, or 37%, respectively, if the loop height, pitch or the distance between the bonding positions is reduced by 50%. To quantify the impact of the reductions in inductance on realistic signal transmission characteristics of the wires, we fabricated and measured bond wire interconnects up to 40 GHz.

交流电速度可能超光速20倍—兼评郑翊等人的论文“电磁场的传播速度”

交流电源产生的电动势在电路内产生了交变电势差以及纵向电场。交变电场在金属导线内带动了电子运动，产生了电流和电功率。交流电(功率)的速度不是常数，它与电路参数相关。在大多数情况下，交流电的速度是低于光速的。可是在特定的电路参数情况下，交流电的速度可能超过光速20倍以上。我们实验的出发点是RL交流电路的电压方程,其中包含了欧姆定律。这个方程是与Maxwell方程相互独立的。本实验的关键是：RL电路中纵向交变电场的时间延迟是由直导线自身的电感引起的，导线自感量与长度有一定的相关性。实验表明，交流电在金属导线中可能以超光速传输信号和电能。光速不是一切物质运动的极限。 Alternating electromotive force generates alternating electrical potential difference and produces a longitudinal electric field in circuits. An alternating electric field within the metal wire leads the movement of electrons, resulting in a current and electric power. The speed of alternating elec-tricity is not constant, which is associated with the circuit parameters. In most cases, the speed of alternating electricity is less than the speed of light. However, under some specific circuit para-meters, the speed of alternating electricity may exceed more than 20 times the speed of light. The voltage equation of RL circuit involves the Ohm’s law. This equation is independent of Maxwell equations. The key in our experiment is: in RL circuits, the time delay of alternating electric field is caused by the wire inductance, which is related to the length of the wire. Our experimental results show that the speed of alternating electricity may be 20 times faster than the speed of light. The speed of light is not the up-limit in universe.

Resonant Power Supply Noise Reduction by STO Capacitors Fabricated on Interposer

This paper demonstrates the resonant power supply noise reduction effects of STO thin film decoupling capacitors, which are embedded in interposers. The on-interposer STO capacitor consists of SrTiO2 whose dielectric constant is about 20 and is sandwitched by Cu films in an interposer. The on-interposer STO capacitors are directly connected to the LSI PADs so that they provide large decoupling capacitance without package leadframe/bonding wire inductance, resulting in the reduction of the resonant power supply noise. The measured power supply waveforms show significant reduction of the power supply noise, and the Shmoo plots also show the contribution of the STO capacitors to the robust operations of LSIs.

A 4 × 2 switch matrix in QFN24 package for 0.5–3 GHz application

This paper presents a 4 × 2 switching matrix implemented in the Win 0.5 μm GaAs pseudomorphic high electron mobility transistor process, it covers the 0.5–3 GHz frequency range. The switch matrix is composed of 4 SPDT switch whose two output ports can simultaneously select the input port and a 4 to 8 bit digital decoder, both the radio frequency (RF) part and the digital part are integrated into one single chip. The chip is packaged in a low cost QFN24 plastic package. On chip shunt, capacitors at the input ports are taken to compensate for the bonding wire inductance effect. The designed switch matrix shows a good measured performance: the insertion loss is less than 5.5 dB, the isolation is no worse than 30 dB, the return loss of input ports and output ports is better than −10 dB, the input 1 dB compression point is better than 25.6 dBm, and the OIP3 is better than 37 dBm. The chip size of the switch matrix is only 1.45 × 1.45 mm2.

25-Gb/s Optical Transmitter with Si Ring Modulator and CMOS Driver

We present a 25-Gb/s optical transmitter composed of a Si ring modulator and CMOS driver circuit. The Si ring modulator is realized with 220-nm Si-on-insulator process and the driver circuit with 65-nm CMOS process. The modulator and the driver are hybrid-integrated on the printed circuit board with bonding wires. The driver is designed so that the parasitic bonding wire inductance provides enhanced driver bandwidth. The transmitter successfully demonstrates 25-Gb/s operation.

Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency.

Graphene can be utilized in designing tunable terahertz devices due to its tunability of sheet conductivity. In this paper, we combine the metamaterial having unit cell of cross-shaped metallic resonator with the double layer graphene wires to realize polarization independent absorber with spectral tuning at terahertz frequency. The absorption performance with a peak frequency tuning range of 15% and almost perfect peak absorption has been demonstrated by controlling the Fermi energy of the graphene that can be conveniently achieved by adjusting the bias voltage on the graphene double layers. The mechanism of the proposed absorber has been explored by a transmission line model and the tuning is explained by the changing of the effective inductance of the graphene wires under gate voltage biasing. Further more, we also propose a polarization modulation scheme of terahertz wave by applying similar polarization dependent absorbers. Through the proposed polarization modulator, it is able to electrically control the reflected wave with a linear polarization of continuously tunable azimuth angle of the major axis from 0° to 90° at the working frequency. These design approaches enable us to electrically control the absorption spectrum and the polarization state of terahertz waves more flexibly.

Improved Formulae for the Inductance of Straight Wires

The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires.

Investigation, Evaluation, and Optimization of Stray Inductance in Laminated Busbar

Wiring inductance has a critical effect on electrical, thermal, and electromagnetic compatibility (EMC) performances in inverters. Therefore, the low stray inductance laminated busbar, as a state-of-the-art pathway interface, is widely used in high-power inverters. However, the asymmetrical stray inductances of the laminated busbar may cause different voltage and thermal stresses for semiconductor devices of the same power stage. In order to achieve low and symmetrical stray inductances in the laminated busbar, this paper presents the investigation, evaluation, and optimization of the stray inductances of the laminated busbar. Based on the current commutation loop (CCL) analysis, the investigation of two-layer, three-layer, and multilayer laminated busbars is proposed through three-dimensional (3-D) finite element analysis (FEA) simulations. It can be found that the skin effect, mutual effect, CCL length, CCL separation distance, and split plate significantly influence the stray inductance of laminated busbars. Furthermore, the multilayer laminated busbar structure for multilevel neutral point clamped (NPC) inverter is derived. On the basis of the theoretical analysis, CCL stray inductances of a three-layer laminated busbar are extracted by means of FEA simulation and an improved impedance resonant measurement in a single-phase H-bridge high-power inverter. Insulated gate bipolar transistor (IGBT) voltage overshoot waveforms further validate the stray inductance asymmetry of the laminated busbar. A compromise between the stray inductance and symmetry is proposed in the three-layer laminated busbar. Finally, several feasible guidelines for the optimization of the laminated busbar design are introduced.

The Research of the Electric Vehicle Wiring Harness Dynamic Crosstalk Based on Statistical Simulation Method

In the actual situation, because of the shock of automobile in the movement process and the wire harness in undulating tube placement is random, leading to the relative position of the wire harness is not fixed, Thus lead to crosstalk value has certain dynamic range. In this paper, obtained the unit mutual inductance and mutual capacitance of wire with insulation layer using mirror image method, simulation and prediction of crosstalk dynamic interval by statistical simulation method, obtain harness near end crosstalk changes range within 3dB at a confidence level of 80%. This provides a reference for EMC design of automotive wiring harness.

Influence of contact network parameters on value of current rise speed during short circuit in power circuits of electric rolling stock

Purpose. Influence investigation of contact system parameters on current rate of rise during short circuit, and the difference of these parameter values under different connection diagrams of traction motors in the power circuit. Methodology. The mathematical model and method for determining the effect of the contact system parameters, such as inductance and active resistance of the contact wire, on rise speed during the short circuit current were offered. Besides that, it is determined the influence of current speeds on their difference in power circuits of DC electric locomotive in different points of short circuit, different variants of traction electric engines connection and different distances of electric locomotives from the traction substation. The proposed model and method can be used for any type of electric DC locomotive at any point of a short circuit in traction engine circuit. Findings. Qualitative and quantitative influence of contact system parameters on values of current rise speed during short circuit and on the differences value of these parameters with different connection diagram of traction electric engines was established. Originality. The investigation method concerning determination of the influence of contact system parameters on current rise speed in short circuit and on the difference of these parameters on different distances of electric locomotives from traction substation was proposed. Practical value. The results can be used in selection of protective devices of rolling stock power circuits, where the main parameter is the current rise speed during the short circuit.

Wideband Bandpass Filters With SAW-Filter-Like Selectivity Using Chip SAW Resonators

Bandpass filters with surface acoustic wave (SAW)-filter-like selectivity and much wider bandwidth compared to conventional SAW filters are presented. The proposed topology consists of SAW resonator networks and parallel coupled lines. Each ladder type resonator network has a series resonator and two shunt resonators to define the upper and lower cutoff frequencies and realize the sharp passband selectivity. Analysis of the proposed SAW resonator network and a comparison with a traditional ladder type SAW filter is provided. Two filters are designed, fabricated, and measured using chip SAW resonators and microstrip coupled lines on Rogers RO4003C. As the available SAW resonators are discrete, they are connected together using 1-mil bond wires to form the SAW resonator network. The resonators are also wire bonded to the coupled lines and ground patch. The bandwidth of the two filters is 10.5% and 17%, respectively, which is much wider than conventional SAW filters with a bandwidth of a few percent. An analysis is provided for the bulk wave effects, ripples due to finite transducer, gratings of resonators, and second-order effects from series and parallel resonators, which cause deterioration of the passband performance. The impact of bond wire inductance and parasitic coupling, which cause spurious responses at the stopbands, are also discussed.

Adaptation of frequency-domain readout for Transition Edge Sensor bolometers for the POLARBEAR-2 Cosmic Microwave Background experiment

The POLARBEAR-2 Cosmic Microwave Background (CMB) experiment aims to observe B-mode polarization with high sensitivity to explore gravitational lensing of CMB and inflationary gravitational waves. POLARBEAR-2 is an upgraded experiment based on POLARBEAR-1, which had first light in January 2012. For POLARBEAR-2, we will build a receiver that has 7588 Transition Edge Sensor (TES) bolometers coupled to two-band (95 and 150GHz) polarization-sensitive antennas. For the large array's readout, we employ digital frequency-domain multiplexing and multiplex 32 bolometers through a single superconducting quantum interference device (SQUID). An 8-bolometer frequency-domain multiplexing readout has been deployed with the POLARBEAR-1 experiment. Extending that architecture to 32 bolometers requires an increase in the bandwidth of the SQUID electronics to 3MHz. To achieve this increase in bandwidth, we use Digital Active Nulling (DAN) on the digital frequency multiplexing platform. In this paper, we present requirements and improvements on parasitic inductance and resistance of cryogenic wiring and capacitors used for modulating bolometers. These components are problematic above 1MHz. We also show that our system is able to bias a bolometer in its superconducting transition at 3MHz.

Small size and low loss resonator type DMTL phase shifter

Two bit distributed coplanar waveguide phase shifter has been developed using bonding wire as an inductor. The idea is to remove all existent capacitances of an inductor, as it is in the planar inductor, and add controllable capacitor in parallel with pure inductor. The resonance condition of the bonding wire inductor and the added MAM capacitor creates wide range of working area to achieve large phase shifting per unit cell. The design utilizes MEMS switches in the DMTL phase shifter to change resonance condition. Using this method the number of cells is decreased considerably. As a result the size and loss are decreased. The design can be easily scaled to other frequencies for satellite and radar systems.

A Physics-Based Causal Bond-Wire Model for RF Applications

A predictive causal physics-based compact model that describes the electrical behavior of multiple bond wires as a function of signal frequency and geometry of the wires is presented. It takes into account the inductive coupling between the wires, the frequency-dependent losses, and the capacitance between the wires and the ground plane. The model does not require any fitting parameters and places no restriction on the shape of the bond wires. Model predictions of resistance, of capacitance to the ground plane, and of self and mutual inductances of bond wires with different shapes were compared to the corresponding measured quantities. All inductive calculations use closed formulas that give a better approximations than the state-of-the-art. Furthermore, the causal nature of this model implies that it may be used for time-domain simulations.

Experimentally verified inductance extraction and parameter study for superconductive integrated circuit wires crossing ground plane holes

As the complexity of rapid single flux quantum (RSFQ) circuits increases, both current and power consumption of the circuits become important design criteria. Various new concepts such as inductive biasing for energy efficient RSFQ circuits and inductively coupled RSFQ cells for current recycling have been proposed to overcome increasingly severe design problems. Both of these techniques use ground plane holes to increase the inductance or coupling factor of superconducting integrated circuit wires. New design tools are consequently required to handle the new topographies. One important issue in such circuit design is the accurate calculation of networks of inductances even in the presence of finite holes in the ground plane. We show how a fast network extraction method using InductEx, which is a pre- and post-processor for the magnetoquasistatic field solver FastHenry, is used to calculate the inductances of a set of SQUIDs (superconducting quantum interference devices) with ground plane holes of different sizes. The results are compared to measurements of physical structures fabricated with the IPHT Jena 1 kA cm−2 RSFQ niobium process to verify accuracy. We then do a parameter study and derive empirical equations for fast and useful estimation of the inductance of wires surrounded by ground plane holes. We also investigate practical circuits and show excellent accuracy.

Proximity‐effect winding loss in different conductors using magnetic field averaging

PurposeThe purpose of this paper is twofold. First, it aims to study the proximity‐effect power loss in the foil, strip (rectangular), square, and solid‐round wire inductor windings. Second, it aims to optimize the thickness of the foil, strip, square wire windings, and the diameter of the solid‐round‐wire, the minimum of winding AC resistance and the minimum of winding AC power loss for sinusoidal inductor current.Design/methodology/approachThe methodology of the analysis is as follows. First, the winding resistance of the single‐layer foil winding with a single turn per layer and uniform magnetic flux density B is derived. Second, the single‐layer foil winding with uniform magnetic flux density B is converted for the case, where the magnetic flux density B is a function of x. Third, the single‐layer winding is replaced by the winding with multiple layers isolated from each other. Fourth, transformation of the multi‐layer foil winding into different conductor shapes is performed. For the solid‐round‐wire windings, the results of the derivation are compared to Dowell's equation and verified by measurements.FindingsClosed‐form analytical equations for the optimum normalized winding size (thickness or diameter) at the global or local minimum of winding AC resistance are derived. It has been shown that the AC‐to‐DC winding resistance ratio is equal to 4/3 (FRv=4/3) at the optimum normalized thickness of foil and strip wire winding hopt/δw. The AC‐to‐DC winding resistance ratio is equal to 2 (FRv=2) at the local minimum of the square wire and solid‐round‐wire winding AC resistances. Moreover, it has been shown that for the solid‐round wire winding, the proximity‐effect AC‐to‐DC winding resistance ratio is equal to Dowell's AC‐to‐DC winding resistance ratio at low and medium frequencies. The accuracy of equation for the winding AC resistance of the solid‐round wire winding inductors has been experimentally verified. The predicted results were in good agreement with the measured results.Research limitations/implicationsIt is assumed that the applied current density in the winding conductor is approximately constant and the magnetic flux density B is parallel to the winding conductor (b>>h). This implies that a low‐ and medium‐frequency 1‐D solution is considered and allows the winding size optimization. This is because the optimum normalized winding conductor size occurs in the low‐ and medium‐frequency range. The skin‐effect winding power loss is much lower than the proximity‐effect winding power loss and therefore, it is neglected.Originality/valueThis paper presents derivations of closed‐form analytical equations for the optimum size (thickness or diameter) that yields the global minimum or the local minimum of proximity‐effect loss. A significant advantage of these derivations is their simplicity. Moreover, the paper derives equations for the AC‐to‐DC winding resistance ratio for the different shape wire windings, i.e. foil, strip, square and solid‐round, respectively.

CMOS LC voltage controlled oscillator design using multiwalled and single-walled carbon nanotube wire inductors

We have utilized our Multiwalled Carbon NanoTube (MWCNT) and Single-Walled Carbon NanoTube (SWCNT) bundle interconnects model in a widely used π model to study the performances of MWCNT and SWCNT bundle wire inductors and compared these with copper (Cu) inductors. The calculation results show that the Q-factors of Carbon NanoTube (CNT) wire (SWCNT bundle and MWCNT) inductors are higher than that of the Cu wire inductor. This is mainly due to much lower resistance of CNT and negligible skin effect in carbon nanotubes at higher frequencies. The application of CNT wire inductor in LC VCO is also studied and the Cadence/Spectre simulations show that VCOs with CNT bundle wire inductors have significantly improved performance such as the higher oscillation frequency and lower phase noise due to their smaller resistances and higher Q-factors. It is also noticed that CMOS LC VCO using a SWCNT bundle wire inductor has better performance when compared with the performance of LC VCO using the MWCNT wire inductor due to its lower resistance and higher Q-factor.

Improvement of modulation bandwidth in electroabsorption-modulated laser by utilizing the resonance property in bonding wire

We present and demonstrate a simple and cost-effective technique for improving the modulation bandwidth of electroabsorption-modulated laser (EML). This technique utilizes the RF resonance caused by the EML chip (i.e., junction capacitance) and bonding wire (i.e, wire inductance). We analyze the effects of the lengths of the bonding wires on the frequency responses of EML by using an equivalent circuit model. To verify this analysis, we package a lumped EML chip on the sub-mount and measure its frequency responses. The results show that, by using the proposed technique, we can increase the modulation bandwidth of EML from ~16 GHz to ~28 GHz.

Wideband ZVS half-bridge circuit for piezoelectric transformers with small inductance

A wideband zero-voltage-switching (ZVS) half-bridge circuit for piezoelectric transformers is introduced. The proposed circuit topology is the extension of the inductor-less half-bridge driver for the piezoelectric transformers. Two auxiliary shunt circuits are connected to the input terminal PT to ensure the ZVS condition in a wide bandwidth. Each auxiliary shunt circuit includes a diode, a switch and an inductor. The auxiliary inductor exhibits a small inductance and is not in the path of the major power flow, thus it can be implemented by the parasitic inductance of the connection wires or by PCB tracks. A 80kHz piezoelectric transformer was tested by the proposed circuit from 20 to 160 kHz to verify the ZVS condition.

Winding resistance of litz-wire and multi-strand inductors

This study presents an approximate model for multi-strand wire winding, including litz-wire winding. The proposed model is evaluated using Dowell's equation. The model takes into account the existence of proximity effect within the litz-wire bundle between the strands and between the bundles, as well the skin effect. The expressions for optimum strand diameter and number of strands at which minimum winding AC resistance is obtained for the litz-wire windings are derived. The boundary frequency between the low-frequency and the medium-frequency ranges are given for both litz-wire and solid-round wire inductors. Hence, the low-frequency ranges of both wire windings are determined. It is shown that litz-wire is better than the solid wire only in specific frequency range. The model has been verified by the measurements, and the theoretical results were in good agreement with those experimentally measured. Comparison of the theoretical predictions of the proposed approximate litz-wire model with models proposed in other publications and with experimental results is given.