Loss Model Mosfet Matlab

Florence, Italy

Abstract— In this paper the effect of parasitic elements on the MOSFETs switching transient through a linear and time- varying electrical model is presented. In particular, the effect of non-linear junction capacitances and the stray inductances have been studied and compared in terms of switching loss and waveform overshoot and ringing. The results obtained with the proposed model are validated by comparison between the model implemented in Matlab/Simulink and LTspice simulations.

Considerations about the impact of stray inductances and switching energy losses are conducted and some observations to reduce energy losses are proposed.

Keywords — Power Mosfet; Switching Losses; Stray

Inductance; Junction Capacitance; Parasitic Elements.

Power Density Of Electronic Switching Devices Is

continuously increasing thanks to the introduction of components able to work at higher switching frequency.

Thanks To The Introduction Of Wide Bandgap (Wbg)

semiconductor power converters are nowadays able to work at

Than

conventional semiconductor material. In particular, the possibility to work at higher operating frequency allows higher power density and therefore save space, material and therefore reduce costs. Thus, if working at higher frequency brings several benefits, more attention must be placed during the design step. Predicting the power MOSFET losses is of primary importance for an optimum thermal design of the heatsink or cooling system, a fundamental aspect in many different high power sector such as automotive, railway and avionics -. Switching power converter are commonly based on PWM DC-DC converters which are simple, require a low number of components, and are widely investigated - . However the operations of these circuits is largely affected by parasitic components introduced by actual devices utilized in assembly the converter circuits -. When these parameters are takin into account the analysis of the circuit become cumbersome and require computer aided techniques -. In literature several studies were made to estimate the power losses with different degrees of approximation. In , a simple method to get a first and fast estimation of power losses is shown. This approach can be useful to get a rough estimation, but it does not consider the parasitic components.

In the impact of nonlinear junction capacitance on switching transient and its modeling for Silicon Carbide (SiC) MOSFET is shown. Experiments show that without full consideration of nonlinear junction capacitances, some significant deviations between simulated and measured results will emerge in the switching waveforms.

In A Detailed Study Of Sic Mosfet Switching

characteristics is shown. The switching performance of SiC MOSFETs are evaluated, in terms of turn on and turn off voltage and current in relation to gate driver maximum current, gate resistance, common source inductance and

Parameter Extraction Sequence Of A Sic Mosfet Is

presented. The procedure makes possible to find several characteristics parameters starting from electrical tests and datasheets information. In a circuit-level analytical model is shown. In particular, this model takes MOSFET parasitic capacitances and inductances, circuit stray inductances, and reverse current of the freewheeling diode into consideration is given to evaluate the MOSFET switching characteristics.

In this paper, starting from the information in - a state-space linear and time varying MOSFET model able to consider the non-linear junction capacitance and the stray inductance is proposed. This model is implemented in Matlab/Simulink. The results obtained are validated on LTspice using an accurate model of SiC MOSFET provided from the manufacturer. Since junction capacitances are characteristic of the MOSFET more attention is focused to the effect of the stray inductances and how they interact with the capacitances. The results show how each inductance affect the turn-on and turn off transient in terms overshoot, ringing and power losses. Some designing good practice observation to reduce the stray inductance are proposed.

Ii. Mosfets Switching Trasient Description

Fig. 1 shows the current, voltage and power waveforms during turn-on and turn off transient of a power MOSFET as derived in where a linear time-variant model of the device has been introduced to estimate the power losses starting from the characteristics reported in the datasheet. Both turn-on and turn-off can be divided in four main stages by considering the drain-to-source current IDS, the drain-to-source voltage VDS, the gate-to-source voltage VGS and the gate current IG. These This work is part of the OBELICS project which has received funding from the European Union Horizon 2020 research and innovation program

331

waveforms are useful to estimate the power losses due to both conduction and switching. Starting from , non-linear models of the parasitic capacitances of the MOSFET have been included in the switching model.

Iii. Analytical Model Of The Switching Transient

Every stage can be modelled by a state-space representation. Being a time-variant model, some continuity conditions are necessary when a transition from a stage to another one occurs.

Fig. 1 Stages during turn-on and turn-off switching transient. The general representation of the i-stage can be written as the

Following Time-Discrete Linear Time-Varying (Ltv)

dynamic system.

(1)

Where xk and uk are respectively the state and the input of the dynamic system at the instant time kT, for the integer index k ∈ ℕ and the sample time T. The state matrix is Ai and the input-to-state matrix is Bi.

The State variable used in this paper is a five element vector x = [VGS, VDS, VAK, IDS, IG] where VGS is the internal gate- to-source voltage, VDS is the internal drain-to-source voltage, VAK is the voltage of a diode placed between the drain and the main alimentation, IDS is the drain-to-source current and IG is the gate current. The input variable is u=[VTH, VTH,1,VDD, IDD, VGG], where VTH VTH,1 are the MOSFET threshold voltage , VDD is the voltage supply, IDD is the steady output current and VGG is the driver voltage.

Iv. Improved Cds And Cgd Non-Linear Model

The proposed model is time-varying since the parasitic capacitances are dependent from the applied voltage. These dependences can be found from the MOSFET datasheet and it is shown in Fig. 2. From the input capacitance CISS, the output capacitance COSS and the reverse transfer capacitance CRSS can be found the gate-to-drain capacitance CGD=CRSS, the drain-to- source capacitance CDS=COSS-CRSS and the gate-to-source capacitance CGS= CISS-CRSS. In are modelled the effect of the non-linear capacitances on the transient characteristics of the switching process. The effect of the nonlinearity of CGS can be neglected, therefore it is assumed constant . On the other hand, if CDS is assumed simply constant, there will be a serious deviation between the simulation and experimental results in switching transient. The factor that made the CDS changes are substantially two: the drain-to-source voltage VDS and the gate-to-drain voltage VGD. In fact, as a junction capacitance, CDS decreases significantly with the increase of VDS since the depletion width changes with bias voltage.

However, when MOSFET is turned ON or in the switching transient, CDS will be impacted by the conductive channel and the non-uniform distribution of electrons caused by the gate- to-drain voltage VGD, which is the second factor mentioned above. As shown in , the CDS can be view as a linear combination of two parameters, CDS,vds, a hyperbolic function of VDS, and δ, which is a function of VGS.

(4)

While δds0 can be approximately regarded as the attenuation ratio of CDS on the condition that MOSFET is fully turned- ON, α is an adjustable parameter. Unfortunately, the actual value of CDS in ON-state is difficult to measure as it is almost

On-State Resistance. Thus, The Two

undetermined parameters δds0 and α, probably only can be obtained by finite-element analysis or experience at present. Regarding the gate-to-drain modelling, its non-linearity is faced up in where, in transient equations section of table 1, the value of the capacity is related directly to the drain-gate voltage.

(5)

Where Coxd is the Gate-drain overlap oxide capacitance and Cgdj is the gate-drain depletion capacitance and VTd is the gate-drain overlap depletion threshold.

(C)

Fig. 2 Non-linear capacitances (a) Non-linear capacitances varying drain-to source voltage. Gate-to-drain capacitance CGD, the drain-to-source capacitance CDS and the gate-to-source. (b) Dependence of CGD from gate to source voltage. (c) Difference between classical model presented in and the new proposed model dependent from the Gate-to-Source voltage.

(6)

where Agd is the Gate-drain overlap area, εsemi is the semiconductor dielectric constant and Wgdj is the gate to drain depletion width body junction and can be calculates as

(7)

With q fundamental electronic charge and Nb base dopant density.

The Analytical Model Of Power Mosfet Mentioned In

Section II-III-IV was implemented in Matlab-Simulink software. To validate the results obtained with the analytical model, several simulations were performed on LTspice. The chosen component is the SiC power MOSFET SCT3022AL since the manufacturer provide an accurate LTspice Model.

This MOSFET has a conduction resistance rDS=22mΩ, a drain-source breakdown voltage VDSS=650V and a continuous drain current IDD=93A. The MOSFET behaviour is analysed in a typical double pulse test system as shown in Fig. 3.

Compared to the circuit presented in , the body diode of

An Sct3022Al Is Used Instead Of A Schottky Diode

(C4D10120D). When the component is connected to the PCB, some parasitic inductances are created at the electric terminations. In this paper, it is assumed as nominal value LS=9 nH, LD=5 nH and LG=15 nH. The comparison between the analytical model assuming VDD=420V and IDD=40A and the LTspice simulations are shown in Fig. 4. It’s noticeable that the analytical model implemented in Matlab/Simulink is

Validated By The Comparison Between Output Mosfet

current, voltage and power delivered.

Transient

After validating the model, a study on how the parasitic inductances affect the turn-on and turn-off transient is carried out. In the following analysis a single inductance is changed maintaining constant the other two to the nominal values.

A. Effect Of The Parasitic Gate Inductance Lg

The waveforms for three values of gate inductance LG are shown in Fig. 5, while the energy dissipated during a turn-ON and turn-OFF transient are summarized in Table I. This inductance tends to resonate with the MOSFET input capacitance, causing oscillations in the gate-to-source voltage

87 Μj

For this reason, it is recommended to minimize LG placing the gate driver as close as possible to the power device, ensuring the correct gating of the device and avoiding its spurious operation leading to undesirable faults. Apart from this recommendation, the influence of LG on the VDS and IDS is limited if compared to the effect of the other two inductances.

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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