Equivalent Series Inductance Research Articles

Barium Strontium Titanate-based multilayer ceramic capacitors with excellent energy storage and charge-discharge performance

Energy storage capacitors for advanced pulse power systems and high-power electric devices is a kind of important electronic components, the demand continues to grow, specifications are constantly being upgraded, and performance boundaries are continuously being pushed. Multilayer ceramic capacitors (MLCCs) for energy storage applications have received increasing attention due to the advantages of ultralow equivalent series inductance, equivalent series resistance, good frequency characteristics, strong voltage overload ability, and stable operability at high temperatures. However, the relatively low energy storage density significantly limits its broader applications. Here, 0.4Ba0.55Sr0.45TiO3-0.4Bi0.5Na0.5TiO3-0.2SrZrO3 (0.4BST-0.4BNT-0.2SZ) relaxor ferroelectric MLCCs are prepared at different heating rates. Excellent recoverable energy storage density of 10.3 J cm−3 and high energy efficiency of 93 % are achieved in fast-fired MLCCs under the electric field of 106.3 V μm−1. The impedance spectroscopy and thermally stimulated depolarization current technologies are employed to investigate the conductance mechanism of MLCCs, and the results can explain the effect of heating rate on the performance of MLCCs. In addition, the charge-discharge performances of fast-fired MLCCs are also thoroughly investigated, exhibiting great thermal and fatigue stability.

Challenges in Measurement of Low-Value ESL and ESR of High-Performance PFN Capacitors for Klystron Modulator

In the high voltage line type pulse modulators, Pulse Forming Network (PFN) capacitors are one of the important components. These capacitors operate at peak kilo ampere current range and at repetition rate in the range of a few hundred hertz. The performance of these capacitors is critical w.r.t. overall system performance, and they are required to operate at high power density and low losses with high reliability. The Equivalent Series Inductance (ESL) and Equivalent Series Resistance (ESR) are two critical parameters that affect the performance of these capacitors. PFN modulator demands a capacitor of very low ESL and ESR for reliable operation and generation of high-voltage pulses. Higher ESR value adversely affects the performance of the capacitor by raising its temperature and thus deteriorating its life. ESL value does not directly affect life, but it affects the quality of high voltage pulse. In RRCAT, the PFN capacitors purchased from Indian manufacturers were showing high-temperature rise and failures. Therefore, new capacitors were designed to have lower ESL and ESR values. Measurement of ESL and ESR is important to evaluate the performance of the capacitors. The low value of these parameters makes their measurement a challenging task and requires special techniques. For low values of ESL and ESR (less than 100 mΩ) measurement, a differential measurement technique was used in which modification and different layouts were explored to improve the repetitive accuracy of the measurements. The differential ESR and ESL measurement techniques with more emphasis on the low-value ESR measurement will be discussed in the paper.

The impact of DC-bus impedance on the switching performance of low-voltage silicon power MOSFETs

Typical DC-bus stabilization for low-voltage power circuits consists primarily of ceramic capacitors due to the capacity density and low equivalent series resistance (ESR) resulting in low conduction losses. Particularly in hard-switching and hard-commutation operation, the low ESR and high equivalent series inductance (ESL) of the capacitors in the commutation path restrict the damping of the switch node voltage overshoot and introduce high-frequency ringing, reducing the voltage margin of the transistor. Therefore, this paper analyzes the impact of the DC-bus impedance and proposes a DC-bus snubber based on an RC network to form the DC-bus impedance’s characteristic, which minimizes the overshoot voltage. A comprehensive simulation using measurement-derived component models is shown, which is verified by an in-situ measurement on a test PCB. Furthermore, transient measurements using a double pulse test setup show the effectiveness of the proposed approach.

Beam–Wave Interaction Analysis Inside an Azimuthally Partitioned Axially Periodic Disk-Loaded Coaxial Structure for Bifrequency MILO

In this article, the electromagnetic (or RF) behavior of the azimuthally partitioned axially periodic metal disk-loaded coaxial structure was investigated using an equivalent circuit approach in the presence of the electron beam. In the analysis, the linearized Maxwell's fluid equation (also known as Vlasov-Maxwell's equation) was used to analyze the region in which the electron beam was present. The expression for the equivalent series inductance and shunt capacitance per unit length for the equivalent transmission line was derived in the electron beam present and absent case. The derived expressions include all the harmonics effects present inside the structure. Furthermore, the expression of the dispersion relation and temporal growth rate (TGR) was derived using the calculated equivalent series inductance and equivalent shunt capacitance. The output RF power and energy were also calculated analytically and validated through the PIC simulation. The results were compared with the already reported literature, and the relative error between them was below 5%. In addition, the effect of different beam parameters on the TGR behavior was also analyzed.

Design and Construction of High-Quality Capacitor for High Frequency and Power Application

The paper proposes a design and construction of a special plated capacitor exhibiting very good high-frequency characteristics. The capacitor is designed to minimize the parasitic parameters like ESR (equivalent series resistance) and ESL (equivalent series inductance) and to be suitable for power industry applications. The paper describes the fabrication process and discusses technical issues related to technology of manufacturing and assembling. It also provides an experimental verification and the quality evaluation based on frequency characteristics compared to existing commercial high-quality capacitor.

Analysis of Azimuthal Partition Periodic Disk-Loaded Coaxial Structure for Bifrequency MILO Using Equivalent Circuit Approach

In this article, an equivalent circuit approach has been used to study the bifrequency generation by the azimuthally partitioned axially periodic metal disk-loaded coaxial structure. Considering the effect of all harmonics present within the structure and using an equivalent circuit approach, the expression of the equivalent series inductance per unit length and equivalent shunt capacitance per unit length has been obtained for this equivalent transmission line. In addition, with the help of computed equivalent series induction and equivalent shunt capacitance, expressions for the dispersion relation, phase velocity, and characteristic impedance have been obtained. The maximum possible frequency difference (i.e., bandwidth) between the modes (i.e., resonating frequency) and its region of operation have also been analytically computed. Finally, the parametric studies have been performed to find out the effect of structural parameter variation on dispersion behavior. In order to validate the numerical analysis, the structure has been first simulated with the help of CST microwave studio, and then, the analytically obtained results (such as dispersion behavior and phase velocity) have been compared with the results obtained from simulation. The comparison of results shows that the relative error is below than 5%, which shows a good agreement between them.

Accurate Inductance Models of Mounted Two-Terminal Decoupling Capacitors

The inductance associated with a decoupling capacitor is typically represented with a constant equivalent series inductance (ESL). In reality, this inductance depends on how the capacitor is mounted and on coupling to closely located structures, including the traces and vias connecting the capacitor to the power and return planes. Here, a method is proposed to quickly and accurately compute the inductance associated with decoupling capacitors and their connections to the power planes. We call this equivalent inductance L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">above,decap</sub> . It is calculated by partitioning the geometry into sub-models for the connections to the power and return planes and for the mounted capacitor and pads. The accuracy of the partitioning approach is demonstrated in simulation and experiments using two common decoupling capacitor layouts. Simulations are performed using the finite element method (FEM) and the partial element equivalent circuit (PEEC) method. The partitioning approach estimates the overall inductance associated with the decoupling capacitor and its connections to the power bus within 16% if the distance between the capacitor and reference plane (dielectric thickness) is not more than 6 mils. A simplified PEEC model was further developed which allows a user to estimate the inductance associated with the capacitor using closed-form expressions. This simplified model estimates the capacitor's inductance within 14% of the results found using FEM. The models presented in this work should help both the power distribution network tool designer as well as the design engineer to obtain more accurate inductance estimates than is possible using the manufacturer's ESL value.

Transient pulse‐based impedance characterisation of DC‐link capacitor for EV systems

In this study, a method for impedance characterisation of DC-link capacitors based on transient pulse analysis is proposed. The fundamentals of the concept are presented and design considerations are discussed. The functionality of the proposed approach is supported by SPICE simulation with two different commercial capacitors from different manufacturers and validated with experimental results. Experimental results for equivalent series resistance, equivalent series inductance (ESL) and capacitance estimation are presented for commercial DC-link capacitors and compared with component analyser results. The simulation and experimental results show that the proposed method is a promising candidate for capacitance and ESL estimation of capacitors in EV traction systems.

Circuit Models for the Inductance of Eight-Terminal Decoupling Capacitors

The series inductance associated with decoupling capacitors can contribute significantly to the impedance of the power distribution network. The eight-terminal capacitors considered in this article have a lower self-inductance than two-terminal capacitors and are commonly used in IC packages. Manufacturers typically specify the inductance of the capacitor using some type of equivalent series inductance (ESL), but this ESL may not accurately predict the inductance seen during use because it does not account for the coupling between the capacitor and nearby structures like the return plane. To adequately determine the inductance associated with an eight-terminal capacitor, models of typical eight-terminal capacitors were developed in Dassault Systemes CST Studio Suite. The partial element equivalent circuit (PEEC) method was used to construct simple models that can be simulated in SPICE. PEEC provides analytic insight into the source of inductance. Modeling the electrode stack as a solid block rather than a multilayer structure was shown to only change the computed inductance by 3% (~1 pH) and to substantially reduce the compute time. CST and PEEC models agreed within 9% (~3 pH), demonstrating the adequacy of the simpler PEEC models. Studies of the impact of the design parameters demonstrate that the distance between the capacitor and the reference plane has the greatest influence on inductance and that the placement of vias within the pads is important.

Continuously Tunable True-Time-Delay Phase Shifter Based on Transmission Lines With Simultaneously Reconfigurable Impedance and Phase Constant

This article reports on the design of continuously tunable true-time-delay (TTD) phase shifter using transmission lines with simultaneously reconfigurable impedance and phase constant. The reconfigurable transmission lines are designed with an independent control of equivalent series inductance and capacitance, which thus can achieve tunable phase constant (i.e., phase shift) while maintaining constant characteristic impedance. With the perfect matching property for all tuning states of phase constant, the proposed reconfigurable transmission-line units are cascaded to construct a tunable TTD phase shifter. For the proof-of-concept demonstration, three TTD phase shifters based on the proposed reconfigurable transmission lines with phase shifts of 45°, 90°, and 180° at center frequency of 1 GHz ( $f_{0}$ ) are designed and fabricated. The measured 2-unit phase shifter is tuned from −128° to −175° at $f_{0}$ while the insertion loss is better than 0.8 dB. The return loss is better than 15 dB from dc to $1.28f_{0}$ . For the 4-unit phase shifter, the phase shift tuning range is 93° at $f_{0}$ with insertion loss better than 1.4 dB. The return loss is better than 15 dB from dc to $1.03f_{0}$ for all states. The 8-unit phase shifter shows a measured tuning range of 183° at $f_{0}$ with insertion loss better than 2.0 dB. The return loss is better than 15 dB from dc to $1.03~ f_{0}$ for all states. The measured continuously tunable delay time is 507 ps. The measured 1-dB compression point is better than 12 dBm at $f_{0}$ for all states. As compared with the state-of-the-arts, the main merits of the proposed phase shifter are large phase shift/unit and wide matching bandwidth.

Z-Directed Component (ZDC) Technology for Power Integrity Applications

An important aspect of ensuring the power integrity of a power distribution network (PDN) design is to determine the layout, value, package size, and number of decoupling capacitors. To solve the limitation of the vertical connection of the surface-mounting-type capacitor to the power net area fill, a new concept of a capacitor denoted the Z-directed component (ZDC) is proposed in this paper. There are many applications possible with the ZDC with the first implementation as a decoupling capacitor. The ZDC capacitors can be integrated within the printed circuit board (PCB) substrate directly below the package ball and eliminate the integrated circuit (IC) to decoupling capacitor horizontal distance across the power net area fill. Furthermore, the inductance associated with the vertical current paths on the vias from the IC package to the horizontal power net area fill and similarly for the surface-mounted technology decoupling capacitors is eliminated. Since only the inductance of the ZDC capacitor itself remains, there is the possibility of using far fewer capacitors to achieve a high-frequency target impedance specification. The ZDC is a promising technology that gives the PCB designer the opportunity to integrate low equivalent series inductance decoupling capacitors much closer to the noise source than traditional surface-mount capacitors. In addition, in this paper, a high-order model is introduced for the ZDC capacitor to better understand the high-frequency characteristics of the component and is verified with measurements.

Characteristics of Output Filters Providing Electromagnetic Compatibility of the Frequency Converter of an Electric Drive with Asynchronous Motors

An analysis of the characteristics of the output filters of electromagnetic compatibility of a frequency converter, including their logarithmic amplitude-frequency characteristics, is carried out by mathematical modeling. The filters with the different parameters, are considered in the steady operation mode at the carrier frequency of pulse-duration modulation of 2.5 kHz and basic frequency of supply voltage of the asynchronous motor of 50 Hz, including with the different connection diagrams of the damping resistors—with parallel connection of inductance in the longitudinal filter branch and series connection of the capacity in the transverse filter branch. In addition, the filter is studied, not including the damping resistors. The losses in the filters are considered. A conclusion is drawn that it is necessary to consider the parasitic parameters of the capacitors: equivalent series inductance, equivalent series resistance, equivalent parallel resistance considering the leakage current through the capacitor, and voltage regulator diode simulating the behavior of the capacitor under the overvoltages.

Folded Feedthrough Multilayer Ceramic Capacitor EMI Filter

A chip three-terminal multilayer ceramic capacitor (MLCC) electromagnetic interference (EMI) filter with a good stopband characteristic was designed. Parasitic effects on the internal signal electrode, including equivalent parallel capacitance and series inductance, were utilized to form a tunable transmission zero in stopband by folding the traditional chip three-terminal feedthrough MLCC. Based on a network theory, an equivalent circuit was constructed in ADS to explain the operating mechanism of the proposed structure. The ADS and HFSS were utilized to simulate the proposed structure, and the measured results corresponded to the simulation results. The structure of the proposed EMI filter presents a new method to improve the stopband characteristic of capacitor EMI filters.

Analytical multi‐parametric stability boundaries of DC‐DC buck converters under V1 control concept

SummaryTwo main methods for controlling switching converters exist in the literature. The direct one is the voltage mode control, which suffers from some disadvantages such as slow response to load variations and an input voltage‐dependent total loop gain. The current mode control can overcome these problems but at the expense of extra cost and more complex control design. V1 concept is a new promising control technique for designing voltage mode control of buck‐type converters with an optimal response similar to current mode control. In this paper, the dynamics and the stability of buck converters under V1 control are studied. In particular, subharmonic oscillation limits in the parameter space are addressed. First, a closed‐loop state‐space model is derived and then used to formulate an analytical matrix‐form expression for predicting the stability limit of the system. Using this expression, multi‐parametric stability boundaries are obtained. It is shown that the equivalent series inductance of the output capacitor can narrow the stability region. It is also demonstrated that the integral action in the feedback loop of a V1‐controlled buck converter has a negligible effect on the subharmonic oscillation boundary. The theoretical analysis is validated through numerical simulation of the circuit‐level switched model of the system. Copyright © 2017 John Wiley &amp; Sons, Ltd.

Ultrahigh-Sensitivity Mediator-Free Biosensor Based on a Microfabricated Microwave Resonator for the Detection of Micromolar Glucose Concentrations

This paper presents a miniaturized microwave-resonator-based ultrahigh sensitivity mediator-free biosensor for determining the level of glucose in deionized-water glucose solutions and human sera using integrated passive device technology on a gallium–arsenide substrate. The proposed glucose biosensor, which consists of cross-coupled stepped-impedance resonators (SIRs), strongly concentrates electromagnetic energy between the coupling regions at a central frequency of 6.53 GHz. The changes in effective permeability $(\mu_{\rm eff})$ and permittivity $(\varepsilon_{\rm eff})$ , which correlate with the variations in the glucose concentration, effectively change the equivalent series inductance and shunt capacitance of the biosensor resonator. This concept was used for the first time to develop an ultrahigh-sensitivity biosensor based on a low $-$ Q microwave resonator. The length of each SIR was meandered width wise, and a meandered-line stub-load was embedded inside the SIR to utilize the equivalent high series inductance and shunt capacitance, respectively. The newly designed present biosensor, which linearly detected glucose level within a wide range of concentration, exhibited an ultrahigh sensitivity (978.7 ${\hbox{MHz/mgmL}}^{-1}$ for sera) at least 4.918 times higher than that of previously reported microwave-resonator-based glucose biosensors, a lower detection limit of 0.01928 $\mu{\hbox{M}}$ , and a rapid detection time of less than 5 s. Supported by S-parameter-based effective-medium-parameter analysis and a sensitivity enhancement principle, the detection accuracy of the proposed biosensor was increased using its glucose-level-dependent spreading of propagation constant $(\gamma)$ and self-resonances of impedance $(Z)$ .

Progress in the Reduction of Inductance in Three Kinds of High Voltage Energy Storage Capacitors

Today an energy storage capacitor having a lower equivalent series inductance (ESL) coupled with an improved terminal for better integration with the gas switch, will contribute to faster discharge times and lower driving impedance, making fast linear transformer driver more sensible and energy efficient. The ESL is an important parameter in the design and operation of pulsed power system and is sometimes difficult to obtain. A ringing discharge method and a differential method to measure, simply and accurately, the ESL of three different kinds of high voltage energy storage capacitors are described in this paper. An error analysis of the differential method is also discussed. The ringing discharge method requires the capacitor tested to be fitted with an adjustable external short circuit and spark gap, while the differential method measures the ESL over a wide range of inductance, including extremely low inductance values, without specialized equipment or intricate data interpretation. These work and results can give some advices to design or optimize linear transformer driver.

Cold isostatic pressing of screen-printed dielectric for power electronics passive component integration

This paper focuses on the study of high-capacitance embedded capacitors for power electronics applications, manufactured by the screen-printing technique. Thick film ferroelectric ceramic was printed on Ag/Al2O3 substrates and dried at 120 °C, then a pre-treatment was applied by cold isostatic pressing (CIP) before sintering. A comparison of the physico-chemical and electrical properties of the non-CIP and CIP samples is made. The results show that the thick film samples pre-treated by CIP have higher permittivity and higher dielectric strength compared to the untreated ones. The capacitor samples with CIP pre-treatment also exhibit higher capacitances, lower parasitic equivalent series inductance and series resistance; all key intrinsic dielectric properties relevant for applications. We propose the use of this process for obtaining the embedded capacitors that allow for high-capacitance values for decoupling and filtering in power electronics applications.

Modelling and Simulation of Variable Frequency Synchronous DC-DC Buck Converter

In this paper, novel small-signal averaged models for dc–dc converter operating at variable switching frequency are derived. This is achieved by separately considering the on-time and the off-time of the switching period. The derivation is shown in detail for a synchronous buck converter. The Enhanced Small Signal (ESSA) Model is derived for the synchronous buck converter. The equivalent series inductance (ESL) is also considered in this modelling. The buck converter model is also simulated in MATLAB and the result is also presented. DOI: http://dx.doi.org/10.11591/ijpeds.v5i2.6472

Development and Electrical Properties of (Ca&lt;sub&gt;0.7&lt;/sub&gt;Sr&lt;sub&gt;0.3&lt;/sub&gt;) (Zr&lt;sub&gt;0.8&lt;/sub&gt;Ti&lt;sub&gt;0.2&lt;/sub&gt;)O&lt;sub&gt;3&lt;/sub&gt; Thin Film Applied to Embedded Decoupling Capacitors

A formed device embedded-type 0402 sized (Ca <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.7</sub> Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.3</sub> ) (Zr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.8</sub> Ti <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.2</sub> )O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (CSZT) embedded capacitor was fabricated for use in embedded printed circuit board. The capacitance and dielectric loss of the CSZT embedded capacitor were 406.1 pF and 0.015, respectively, at 1 MHz. The CSZT embedded capacitor exhibits stable capacitance with varying applied voltage and C Zero G (-55 °C-125 °C, delta C/C = ±30 ppm/°C) properties. The measured values of equivalent series resistance and equivalent series inductance were 6.1 Ω and 62.39 μH, respectively. The leakage current density was 0.78 μA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at 3 V of applied voltage. These electrical properties indicate that the CSZT embedded capacitor holds promise for use as an embedded passive capacitor.

Characterization of Marx Generator

This paper discusses the characterization of 200 kV, 20 J mini Marx generator. Marx generators are extensively used in very high voltage fast pulse generation. Capacitors are the major components of Marx generator, apart from the capacitance of the capacitor the other parameters such as internal inductance (Equivalent series Inductance) and Equivalent series resistance (ESR) has significant effect on the output current waveform. The internal inductance of the capacitor, ESR and the discharge path to the load circuit has to be kept as minimum as possible so as to achieve lower characteristic impedance, higher peak current, faster rise time and reduced Full Width Half Maximum(FWHM). Therefore there is a need to determine the internal inductance and ESR of Marx generator. Short circuit discharge test is conducted on the Marx generator to determine the value of total inductance of Marx generator during erection. From the determined value of total inductance of Marx generator L T and erected capacitance of the Marx C T , ESR is estimated from the PSPICE circuit. Also maximum output of Marx is estimated using the PSPICE circuit.