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Showing papers on "Filter capacitor published in 2005"


Journal ArticleDOI
TL;DR: These amplitudes are quantified for two modulation strategies that use nearest vectors to the reference vector and will help for the calculation of the dc-link capacitors in a given specific application.
Abstract: The nearest vectors to the reference vector are commonly used in space-vector modulation (SVM) strategies. The main advantages of these modulation strategies are the low switching frequencies of the devices, the good output voltage spectra, and the low electromagnetic interference. However, when these techniques are applied to the three-level neutral-point (NP)-clamped inverter, low-frequency oscillations appear in the NP voltage for some operating conditions. As a result, the value of the dc-link capacitors must be increased in order to attenuate such oscillations. In this paper, these amplitudes are quantified for two modulation strategies that use nearest vectors to the reference vector. Owing to the nondimensional variables used in the analysis, the information provided will help for the calculation of the dc-link capacitors in a given specific application. Simulated and experimental examples are presented.

279 citations


Proceedings ArticleDOI
M.L. Gasperi1
23 Jun 2005
TL;DR: In this paper, a multiple component model for capacitor impedance, a motor drive simulation to create ripple current waveforms, a heat transfer model based on bank geometry, and a capacitor life model derived from the device physics of failure is presented.
Abstract: Aluminum electrolytic capacitors are the leading choice for ac variable-frequency drive (VFD) bus filters. Predicting the expected life of these components in this application is complicated by four factors. First, the electrical impedance of aluminum electrolytic capacitors is nonlinear with both frequency and temperature. Second, motor drives produce a spectrally rich ripple current waveform that makes energy loss difficult to compute. Third, the heat transfer characteristic of capacitor banks is dependent on design geometry. Fourth, the expected life of aluminum electrolytic capacitors is extremely sensitive to operating temperature. This paper describes a method for predicting bus capacitor life that addresses these problems by using a multiple component model for capacitor impedance, a motor drive simulation to create ripple current waveforms, a heat transfer model based on bank geometry, and a capacitor life model derived from the device physics of failure. An example is given showing the effect of ac line impedance on the relative expected life.

189 citations


Proceedings ArticleDOI
16 Jun 2005
TL;DR: In this paper, a real-time diagnostic method of the ESR of the electrolytic capacitors in adjustable speed drives (ASD) and uninterruptible power supplies (UPS) is presented.
Abstract: Electrolytic capacitors are widely used in various power electronic systems, such as adjustable speed drives (ASD) or uninterruptible power supplies (UPS). Their high energy density (J/cm 3) features make them an attractive candidate for smoothing voltage ripple and pulse discharge circuitry. However, electrolytic capacitors have the shortest life span of components in power electronic circuits, usually due to their wear-out failure. The main wear-out mechanisms in electrolytic capacitors are the loss of the electrolyte by vapor diffusion trough the seals and the deterioration of the electrolyte. Both mechanisms can result in a fluctuation of the capacitor's internal equivalent series resistance (ESR). In this paper, a real time diagnostic method of the ESR of the electrolytic capacitors in ASDs and UPSs is presented. This method is employed satisfactorily to estimate their deterioration condition. An on board implementation of this method is proposed, which can be very helpful for preventing down time and alerting plant operators to needed maintenance and/or replacement. The approach does not involve removing the capacitor bank from its device and relies on the fact that in steady state, the power in the capacitor is only due to the power losses in the ESR. An analog-DSP based diagnostic system has been implemented and experimental results from a 3-phase 6 kVA/230 V ASD are presented

116 citations


Journal ArticleDOI
TL;DR: In this article, a cancellation inductor is integrated with capacitors to cancel the mutual coupling between two capacitors and the equivalent series inductance (ESL) of the integrated capacitor.
Abstract: In this paper, critical parasitic couplings in EMI filters are first identified. Based on the understanding of filter parasitics, methods are proposed to improve EMI filter performance by canceling critical couplings. A cancellation inductor is then integrated with capacitors to cancel the mutual coupling between two capacitors and the equivalent series inductance (ESL) of the integrated capacitor. The proposed method is applied to both rectangular and tubular capacitors. Two different integration approaches are also compared. Finally, prototypes are built and tested for both one-stage and two-stage EMI filters. Experimental results show the proposed mutual coupling cancellation technique can drastically improve EMI filter high frequency performance.

106 citations


Patent
09 Nov 2005
TL;DR: In this article, a maximum power point tracking charge controller for double layer capacitors intended for uses with non-ideal power sources such as photovoltaics is described.
Abstract: Disclosed is a maximum power point tracking charge controller for double layer capacitors intended for uses with non-ideal power sources such as photovoltaics.

81 citations


Book
30 Mar 2005

74 citations


Proceedings ArticleDOI
16 Jun 2005
TL;DR: In this paper, the authors analyzed the lifetime of electrolytic capacitors used in the DC link of an induction motor (IM) drive whose front end consists of a controlled rectifier.
Abstract: Electrolytic capacitors are normally used as the energy storage element in the DC link of voltage-source converters because of their high density. Unfortunately, they are bulky and their lifetime is significantly reduced by their operating temperatures. Thus, reducing, or even better eliminating, the amount of electrolytic capacitors is an important goal since the capacitor could be a single point of failure. This paper analyses the lifetime of electrolytic capacitors used in the DC link of an induction motor (IM) drive whose front end consists of a controlled rectifier. The latter controls the DC-link voltage and input power factor. Both, the inverter and rectifier operate under space vector modulation (SVM). The peak ripple voltage, ripple current, core temperature and lifetime of electrolytic capacitors ranging from 200 muF to 12000 muF are calculated for different values of the source inductance and the ambient temperature when the IM is operating at rated load. In addition, the IM ripple torque and speed response time are also calculated and an 8.2 muF ceramic capacitor case is included for completeness. The evaluation is based on Matlabtrade/Simulink simulation results of the IM drive that are used to calculate harmonic components of the different current waveforms. The results show that the lifetime of electrolytic capacitors is significantly reduced for decreasing capacitance values. The main reason is that the effective series resistance (ESR), and hence heat losses, increases for decreasing capacitance values leading to increased core temperatures that are detrimental to the capacitor lifetime

71 citations


Journal ArticleDOI
24 Oct 2005
TL;DR: In this paper, an Hinfin controller is designed for the voltage-source-inverter voltage control in a microgrid to compensate the capacitance-parameter variation.
Abstract: Capacitors are widely used for power-factor correction (PFC) in power systems. When a PFC capacitor is installed with a certain load in a microgrid, it may be in parallel with the filter capacitor of the inverter interfacing the utility grid and the local distributed-generation unit and, thus, change the effective filter capacitance. Another complication is the possibility of occurrence of resonance in the microgrid. This paper conducts an in-depth investigation of the effective shunt-filter-capacitance variation and resonance phenomena in a microgrid due to a connection of a PFC capacitor. To compensate the capacitance-parameter variation, an Hinfin controller is designed for the voltage-source- inverter voltage control. By properly choosing the weighting functions, the synthesized Hinfin controller would exhibit high gains at the vicinity of the line frequency, similar to traditional high- performance P+ resonant controller and, thus, would possess nearly zero steady-state error. However, with the robust Hinfin controller, it will be possible to explicitly specify the degree of robustness in face of parameter variations. Furthermore, a thorough investigation is carried out to study the performance of inner current-loop feedback variables under resonance conditions. It reveals that filter-inductor current feedback is more effective in damping the resonance. This resonance can be further attenuated by employing the dual-inverter microgrid conditioner and controlling the series inverter as a virtual resistor affecting only harmonic components without interference with the fundamental power flow. And finally, the study in this paper has been tested experimentally using an experimental microgrid prototype.

70 citations


Journal ArticleDOI
24 Oct 2005
TL;DR: In this paper, the authors proposed to integrate the matrix converter with filters, which provide lower electromagnetic interference (EMI), lower common-mode current, lower shaft voltage, and sinusoidal output voltage waveforms.
Abstract: A matrix converter has a topology that inherently exhibits sinusoidal input current waveforms and has small output voltage steps. This paper proposes to integrate the matrix converter with filters, which provide lower electromagnetic interference (EMI), lower common-mode current, lower shaft voltage, and sinusoidal output voltage waveforms. A salient aspect of the proposed integration is its ability to significantly reduce the value of the input EMI filter capacitors and still meet strict EMI regulations. This helps in reducing the ground leakage current, which in the past has been a serious limitation in applying EMI filters with low ground currents for human and cattle safety

58 citations


Patent
13 Dec 2005
TL;DR: In this paper, a bridgeless PFC boost converter with a boost inductor and a filter capacitor is proposed to improve EMI noise performance in a bridged-PFC PFC converter.
Abstract: A circuit and method for improving EMI noise performance in a bridgeless PFC boost converter. Such a converter comprises a boost inductor having a first end connected to a first AC input terminal and a second end connected to a first junction defined between the anode of a first diode and a first terminal of a first switch; a second terminal of the first switch connected to a common line; a parallel circuit of a capacitance and a load connected between the cathode of the first diode and the common line; a series circuit of a second diode and a second switch connected between the cathode of the first diode and the common line; and a second AC input terminal connected to a second junction defined between the anode of the second diode and the second switch. High-frequency EMI noise is bypassed by placing a first filter capacitor between the first AC terminal and the common line. A second boost inductor may be connected between the second AC input terminal and the second junction, and a second filter capacitor may be connected between the second AC terminal and the common line. The first and/or second filter capacitor has a lower impedance in a high frequency range than the corresponding first or second boost inductor. Preferably the first and second capacitors have substantially the same capacitance.

49 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the microwave characteristics of the liquid crystal tunable capacitors for the first time, and demonstrated the potential applications of liquid crystals as dielectric materials for capacitors with high quality factors and wide tuning ranges at high frequencies.
Abstract: This letter investigates the microwave characteristics of the liquid crystal tunable capacitors for the first time. With the dielectric anisotropy properties, the liquid crystal capacitors present very different characteristics compared to the semiconductor or MEMS tunable capacitors. A quality factor of 310 with a control voltage of 5 V was achieved at 4 GHz. A tuning range of 25.3% for the control voltages from 0 to 5 V was obtained at 5 GHz. The results demonstrate the potential applications of liquid crystals as dielectric materials for capacitors with high quality factors and wide tuning ranges at high frequencies, particularly suitable for the future flexible electronics with transparent substrates.

Patent
06 Jan 2005
TL;DR: In this article, a printed circuit board including embedded capacitors, composed of a polymer condenser laminate including a plurality of polymer con-enser layers, each of which has a polymer sheet and a conductor pattern formed on the polymer sheet, and a via hole for interlayer connection therethrough.
Abstract: Disclosed herein is a printed circuit board including embedded capacitors, composed of a polymer condenser laminate including a plurality of polymer condenser layers, each of which has a polymer sheet and a conductor pattern formed on the polymer sheet, and a via hole for interlayer connection therethrough, and a circuit layer formed on either surface or both surfaces of the polymer condenser laminate and having a circuit pattern and a via hole for interlayer connection therethrough. The printed circuit board of the current invention has higher capacitance density per unit area than conventional embedded capacitor printed circuit boards, whereby capacitors having various capacitance values, such as multilayered ceramic capacitors having high capacitance, can be embedded in the printed circuit board, instead of being mounted thereon. Also, a method of manufacturing the printed circuit board including embedded capacitors is provided.

Proceedings ArticleDOI
05 Dec 2005
TL;DR: The use of ultra high voltage direct current (UHVDC) has been found to be economically attractive for power blocks up to 6000 MW for distances above 1000 km, Furthermore the use of 800 kV as transmission voltage will be achievable within the near future with a limited amount of development work none of the AC equipment, auxiliary equipment or control and protection will be affected by the increase of DC voltage as mentioned in this paper.
Abstract: The use of ultra high voltage direct current (UHVDC), i.e. voltages above the highest in use, 600 kV, has been found to be economically attractive for power blocks up to 6000 MW for distances above 1000 km, Furthermore the use of 800 kV as transmission voltage will be achievable within the near future with a limited amount of development work none of the AC equipment, auxiliary equipment or control and protection will be affected by the increase of DC voltage. Also most of the DC equipment is easily modified for 800 kV, such as thyristor valves and DC filter capacitors. However, equipment without resistive DC grading, like bushings and converter transformers, need additional R&D and verification. Also station external insulation and line insulation must be carefully considered. In order to meet the demands, ABB has started an R&D program with the goal to develop and test equipment needed for 800 kV HVDC

Proceedings ArticleDOI
27 Dec 2005
TL;DR: In this paper, the effect of chip, package and board capacitors on the performance of digital systems is analyzed taking into account the parasitic effects of power/ground planes, vias and solder balls.
Abstract: Surface mount technology (SMT) decoupling capacitors fail to provide decoupling above 100MHz. This paper presents the use of embedded thin film capacitors to provide decoupling in the mid frequency range from 100MHz to 2GHz. On-chip capacitance provides decoupling above 2GHz. The effect of chip, package and board capacitors on the performance of digital systems is analyzed taking into account the parasitic effects of power/ground planes, vias and solder balls. A synthesis and selection methodology for embedded package capacitors is also presented.

Journal ArticleDOI
TL;DR: In this paper, multilayer ceramic capacitors (MLC) of low rated voltage have been used for power decoupling and bypass in telecommunication equipment for many years.
Abstract: High energy density capacitor is a very important component to supply energy in pulse power source. Owing to its high dielectric constant (up to 10/sup 5/ or more), ceramic material is regarded as a sound dielectric for producing high energy density capacitors. With the energy density under the same order of several hundred J/L, ceramic capacitors can endure higher inverse voltage (>70%) and have longer life (shot times >10/sup 6/) compared with metallized film. Multilayer ceramic capacitors (MLC) of low rated voltage have been used for power decoupling and bypass in telecommunication equipment for many years. In this paper, MCL samples of high voltage have been produced, and their electrical characteristics tested in a pulse energy discharge circuit. From the result, the relations between the changes of capacitance, dielectric loss, the charge frequency, and the lifetime have been deduced. The features in discharge wave are also presented. Some failure mechanisms for these capacitors are put forward in this paper. In conclusion, MLC is suitable for making high energy density capacitor, which can endure high reverse voltage, high current, and possesses long lifetime.

Patent
20 Jul 2005
TL;DR: In this paper, a high-energy storage and high-capacity capacitors are implemented over conventional electrolytic capacitor anode substrates using highly conformal contact layers deposited by atomic layer deposition.
Abstract: Electrostatic capacitors with high capacitance density and high-energy storage are implemented over conventional electrolytic capacitor anode substrates using highly conformal contact layers deposited by atomic layer deposition. Capacitor films that are suitable for energy storage, electrical and electronics circuits, and for integration onto PC boards endure long lifetime and high-temperature operation range.

Proceedings ArticleDOI
03 Oct 2005
TL;DR: In this article, the authors discuss strategies for locating and mounting decoupling capacitors in various situations as well as methods for estimating the total amount of decoupled capacitance required.
Abstract: Power bus decoupling is an important part of digital printed circuit board design. Effective strategies for implementing power bus decoupling depend on the board construction as well as the demands that the circuits place on the power distribution network. This paper discusses strategies for locating and mounting decoupling capacitors in various situations as well as methods for estimating the total amount of decoupling capacitance required

Patent
26 Jan 2005
TL;DR: In this paper, a high electrical energy storage system consisting of arrays of high energy capacitors and their charging and discharging protocols is described. Butler et al. present an array of capacitors are conductively connected together and connected to an energy source.
Abstract: The invention is a high electrical energy storage system consisting of arrays of high energy capacitors and their charging and discharging protocols. An array of capacitors are conductively connected together and connected to an energy source. A computer and software control the charging and discharging of the capacitor banks.

Patent
06 Sep 2005
TL;DR: In this paper, one or more capacitors are selectively switched into or out of an inductive-capacitive resonant circuit portion of an integrated circuit filter to alter the resonant frequency based on a phase difference between the resonance frequency and a reference frequency.
Abstract: Using low impedance switches and coupling to a virtual ground, one or more capacitors are selectively switched into or out of an inductive-capacitive resonant circuit portion of an integrated circuit filter to alter the resonant frequency based on a phase difference between the resonant frequency and a reference frequency. The capacitors are sized for a sequence of total capacitances proceeding by halves or doubles between values corresponding to minimum and maximum desired frequency adjustments, allowing a binary count of pulses representative of the phase difference to address the correct combination of capacitors. An exact or ratioed replica of the inductive-capacitive resonant circuit, controlled by the same capacitance selection signal, may be used as a frequency-selective amplifier load or matching network, or to form a ladder filter.

Proceedings ArticleDOI
01 Jan 2005
TL;DR: In this article, the critical effects of parasitics, including component self-parasitics and their respective mutual coupling effects, are first identified and their impact to both differential and common mode noise are quantified.
Abstract: EMI filter design is critical for power electronics equipment to be in compliance with the EMI/EMC standards A good filter design realizes effective high frequency attenuation Such a design is often achieved empirically, with good common sense, and deemed, by and large, as an art rather than a science It is well known that the filter parasitics are detrimental to its ability to attenuate high frequency noise In this paper, the critical effects of parasitics, including component self-parasitics and their respective mutual coupling effects, are first identified and their impact to both differential and common mode noise are quantified Filter design techniques are proposed to mitigate these adverse effects due to self and mutual parasitics While reduction of certain critical parasitics such as, ESE of filter capacitors and certain mutual couplings can be realized relatively easily in the conventional discrete filter design practice, reduction of the winding capacitance of the common-mode/differential mode inductor can best be implemented in an integrated filter design Methods of reducing structural parasitics are investigated in this integrated filter design approach and a design technique proposed for canceling the winding capacitance of inductors that results in significant improvement of CM noise attenuation A unique class of integrated distributed interconnect EMI filter is introduced Experimental results are provided to substantiate all the claims made in the paper

Proceedings ArticleDOI
24 Oct 2005
TL;DR: A two-phase switched reluctance drive that employs a voltage doubler rectifier circuit charging a split dc supply made up of two low value film capacitors and novel control algorithms are presented to allow operation of the motor over a wide speed range despite the inevitable supply and motor frequency modulation of the dc link.
Abstract: This paper proposes a two-phase switched reluctance drive that employs a voltage doubler rectifier circuit charging a split dc supply made up of two low value film capacitors. The proposed converter not only uses a single-switch per phase topology, but also eliminates the unreliable electrolytic capacitors present in conventional split dc supply converters. The operation of the circuit is described and novel control algorithms are presented to allow operation of the motor over a wide speed range despite the inevitable supply and motor frequency modulation of the dc link. The implementation of the control algorithms is achieved using a low cost 8-bit microcontroller.

Patent
Bulent Sarlioglu1
15 Sep 2005
TL;DR: In this paper, a differential mode EMI filter was proposed for attenuating electromagnetic interference (EMI) of an autotransformer-based rectification system, which utilizes the leakage inductance of the auto-transformer and one or more capacitors (121-139) connected on the secondary side.
Abstract: A filter system (100) for attenuating electromagnetic interference (EMI) of an autotransformer-based rectification system that utilizes the leakage inductance of the autotransformer (110) and one or more capacitors (121-139) connected on the secondary side and optionally one or more differential mode inductors (104) and input capacitors (108A-108C) connected on the primary side to form a differential mode EMI filter. This configuration reduces the size, weight, and cost of the differential mode EMI filter when compared with a differential filter formed by placing the inductors and capacitors on the primary side.

Proceedings ArticleDOI
24 Oct 2005
TL;DR: In this article, the authors proposed a new method to detect the rise of equivalent series resistor (ESR) in order to realize the on-line failure prediction of the electrolytic capacitor for LC filter of switching-mode power converter.
Abstract: The objective of this paper is to propose a new method to detect the rise of equivalent series resistor (ESR) in order to realize the on-line failure prediction of the electrolytic capacitor for LC filter of switching-mode power converter. Characteristics of electrolytic capacitors are introduced in this paper. Different experimental measurements are conducted and shown to illustrate the properties of electrolytic capacitors. The proposed on-line failure prediction method has the merits of low cost and circuit simplicity. Hardware experimental results are shown to verify the performance of the proposed method.

Proceedings ArticleDOI
05 Dec 2005
TL;DR: In this paper, a combined power filter system consisting of the parallel operation of a hybrid active power filter (HAPF) and the passive power filters or capacitors is proposed. And the characteristics of the combined system and the harmonic current detection method are analyzed and simulated.
Abstract: Harmonic pollution and reactive power compensation are the important power quality problems. This paper proposes a combined power filter system consisting of the parallel operation of a hybrid active power filter (HAPF) and the passive power filters or capacitors. The HAPF is formed by a single tuned LC filter per phase and a small-rated three-phase active filter, which are directly connected in series. The characteristics of the combined system and the harmonic current detection method using the combination of load current and the mains current are analyzed and simulated. The simulation results show that good filter performance can be obtained by the combined system. Experimental results from a 100 kVA/380 V hardware prototype parallel operation with capacitors are presented to conform the validity and effectiveness of the combined system

Proceedings ArticleDOI
06 Mar 2005
TL;DR: In this paper, an integrated traction and compressor drive is proposed to reduce the HVAC compressor drive cost in electric and hybrid electric vehicle (EV/HEV) applications, which employs a five-leg inverter to drive a three-phase traction motor and a two-phase compressor motor.
Abstract: This paper presents an integrated traction and compressor drive to reduce the HVAC compressor drive cost in electric and hybrid electric vehicle (EV/HEV) applications. The drive system employs a five-leg inverter to drive a three-phase traction motor and a two-phase compressor motor. The common terminal of the two-phase motor is tied to the neutral point of the three-phase traction motor to eliminate the requirement of a third phase leg. The cost of the compressor drive can be significantly lowered due to the elimination of one phase leg and additional part count reduction made possible by sharing the switching devices, DC bus filter capacitors, gate drive power supplies, and control circuit. Simulation and experimental results are included to verify that speed control of the two motors is independent from each other.

Journal ArticleDOI
TL;DR: In this article, the performance of polymer capacitors and certain ceramic capacitors is almost independent of the temperature, DC bias, and frequency of the capacitors, and they showed a dramatic decrease of capacitance at 77 K, possibly due to the electrolyte being frozen and losing its conductivity.

Patent
24 Feb 2005
TL;DR: In this paper, a switch circuit connects the input capacitor and one of the reference capacitors between an output and an input of an amplifier in a second period, which causes a feedback gain to be "1" in the second period.
Abstract: An input capacitor and a plurality of reference capacitors sample an input voltage and reference voltages in a first period. A switch circuit connects the input capacitor and one of the reference capacitors between an output and an input of an amplifier in a second period. This mechanism causes a feedback gain to be “1” in the second period. Therefore, it is possible to reduce power consumption and noise.

Patent
28 Jan 2005
TL;DR: In this article, the structural and functionalities for serially connecting at least two capacitors together are described. But they do not specify how many capacitors are incorporated in the device and what configuration the capacitor assembly will assume.
Abstract: Structures for serially connecting at least two capacitors together are described. Serially connecting capacitors together provides device manufactures, such as those selling implantable medical devices, with broad flexibility in terms of both how many capacitors are incorporated in the device and what configuration the capacitor assembly will assume.

Proceedings ArticleDOI
01 Nov 2005
TL;DR: An EDM power supply prototype utilizing the flyback topology for low power applications with minimal components count and inherent protection under short circuit conditions is developed.
Abstract: Electrical discharge machining (EDM) uses controlled electric sparks to erode the metal in a workpiece, and this method is now a well established machining process for high power applications. EDM power supplies utilizing different topologies for high power applications (e.g. full bridge configuration) are widely available. Through the years, EDM processes have increasingly been used in high precision machining and in manufacturing micromechanical components, with new low power topologies being investigated for the latter. We implemented a current mode flyback converter for use in low power EDM applications. This topology has an energy conservation feature and removes the need for output bulk capacitors. Energy used in the erosion process will come from the energy stored in the flyback transformer and will be transferred to the small output filter capacitors and the effective capacitance of the tool, workpiece, and dielectric combination. A servomechanism that controls the arc distance will determine the output voltage. We have developed an EDM power supply prototype utilizing the flyback topology for low power applications with minimal components count and inherent protection under short circuit conditions. Our work includes the design, fabrication, and characterization of the whole system. We compared the efficiency and quality of work of our proposed topology with that of a linear converter.

Proceedings ArticleDOI
16 Jun 2005
TL;DR: In this article, the authors proposed a method to reduce the capacitor ripple current, which leads to a reduced demand on DC link electrolytic capacitors, by applying an optimised switching pattern to the power transistors.
Abstract: The use of electrolytic capacitors in automotive applications is critical. High ambient temperatures lower lifetime and reliability, while further disadvantages arise from costs and installation space. The presented work shows a method to reduce the capacitor ripple current, which accordingly leads to a reduced demand on DC link electrolytic capacitors. The proposed method is based on applying an optimised switching pattern to the power transistors. Thereby, the ripple current can be reduced to approximately one third compared to conventional PWM signals. The optimisation is also described graphically, and measurements verify the practicability