Modeling for IGBTVineeta Agarwal, IEEE Member

Electrical Engineering Department, M.N.N.I.T. Allahabad, INDIAEmail: vineeta_agarwall23 Crediffmail.com

Abstract - A mathematical model has been developed for II PROPOSED MODELan Insulated Gate Bipolar Transistor (IGBT) bycompartmenting it into two diodes which are connected in Fig. 1 shows the basic architecture of an IGBT. It isseries with reverse configuration. One diode is an ordinary compartmented into two parts by segmenting with dotted linesdiode while other is a controlled diode. The performance as shown near the junction J1 in n- base region. By inspection,of the controlled diode depends upon the magnitude of the part of IGBT, between the dotted line and collectorGate Emitter, GE voltage and Collector Emitter (CE) terminal forms ap-n junction diode D1. The remaining part ofvoltage. A GE voltage Vg > Gate Emitter Threshold IGBT which accommodates the gate and emitter can beVoltage (VGET), modulates the conductivity of controlled viewed as a controlled diode, D2. Between the junction of twodiode together with hole injection from the p+ base near diodes and gate terminal, a parallel combination of RC circuitthe collector terminal. Parameters of these diodes are of constant values is added. This RC circuit is attributedestimated by applying curve fitting tool and power because of the insulation resistance and capacitance of SiO2invariance method. The validity of the model has been layer underlying the gate terminal. A non linear capacitancechecked by a simulation example. The results of Cix, between gate and emitter is also added which givessimulation show appreciable closeness with actual one. intermediate circuit of IGBT as shown in Fig. 2.

The final model can be obtained by replacing the diodes byI INTRODUCTION their equivalent circuit as shown in Fig. 3. In this model, the

ordinary diode has been replaced by a constant voltage sourceEver since the evolution of IGBT a number of models have Vdl in series with a parallel combination of a current source, i,been reported in literature namely IG Spice, PSpice [1], a variable resistance r, and a shunt capacitance Cc. Theanalytical [2] and EMTP [3]. Most of them explain both controlled diode is modeled as a variable capacitance Ce insteady-state and dynamic behavior of Insulated Gate Bipolar parallel to a series combination of variable voltage source Vd2Transistor, IGBT, with varying degree of accuracy. In utility and resistance re. At low frequencies all these capacitancesrelated applications such as flexible ac transmission systems become open circuit and the resultant circuit becomes the(FACTS) [4], requiring high power electronics, the system is steady state DC model of IGBT as shown in Fig. 4.generally described by means of differential/algebraicequations which are solved using any one of the several higher Emitter Gat (Vlevel computer languages such as FORTRAN, C, etc. For such Icases the detailed model of the devices will result a large o2layercomputation time, loss of accuracy and an overwhelmingamount of information which is difficult to digest [5]. In order

ba

to keep the execution time within reasonable limit, complexdevices in power electronics system such as IGBT etc. may berepresented by approximate models which may be represented n-basby standard algebraic equations [6].

~~~~~~~~~~0This paper proposes a simple mathematical model of IGBTconsisting of only diodes that are described by well known P+

algebraic equations. The model is illustrated with a controlleddiode characteristics whose performance depends on amodulation factor m which is function of the voltages appliedat different points across the device. The parameters of this Collectormodel are obtained by applying power invariance and curvefitting technique. The model is tested for an existing IGBT inFg.1BscCntuioofGTthe lab extracting required data from the instruction sheet.

1-4244-0726-5/06/$20.OO '2006 IEEE 563

c ~~~~~~~~Vd-V, -Vdl1

i) =I, (T){e VT -1} (1)

R QD, | where 10(T) reverse saturation current of diode at,G Temperature To K, ampere

0 _ ' °Vd Vdl =Threshold voltage of diode D1, Volt

VgS AC C Z2D2 1 VT = kT/q, Volt.

-o T O ERearrangement of (1), gives,

Fig. 2 Inter-mediate circuit of IGBT Vd - V+ = Vdl + (kT/q) In [1 + ic/IO(T)] (2)

Iic 0O C Differentiation of (2) with respect to ic gives the resistance ofthe diode

Vdl dd(Vd -V+) kT

lr = i +I (T)) (3)

v f TCCI To identify the current source, principle of power invariance isG V dd applied to the diode DI and its equivalent. Power consumed by

vL c vd2- t l l diode DI is given by,

;ix

r Ce i E(Vd - V+) ic = (Vdl+ (kT/q) In [I+ c ic (4)e Io~~~~~~~~~~~~~~1(T)

and its equivalent is given byFig. 3 Steady- State Model of IGBT

ic (Vdl + rc.ic- rc. i) ic. (5)C

Power invariance requiresVdl

kT(VdIt+ -) ln[]+

l

icr

~~~~q Io (T)

tR Id =( dl + rc ic-rc i) ic. (6)

Vd2 F Above equality should hold for all value of ic This implies thatVg I differentiation of (6) for both side with respect to ic does not

re affect the equality or

rkiTqln(Il+ IoC)T) =Fig.4 DC Model of IGBT (-ln(l '())

dIII PARAMETER IDENTIFICATION ((r ic -ti))ic (7)

d(ic)In order to identify the parameters of the proposed model, twostrategies are resorted: 1) the principle of invariance of power Substituting the value of rc and drc/dic in (7) and simplifying itin the components and 2) mathematical tool of curve fitting. givesLet a positive voltage Vd is applied at collector with respect toemitter. Also a gate emitter voltage Vg > VGET is applied at d igate terminal. If V+ is the potential of point 'o' which is + - =junction of two diodes then the voltage Vd - V+ will appear d(iC) ic ic + I,(T)across the diode D1. If ic is the current flowing through the I (T) __circuit, then the voltage-current relation of diode D1 can be 1- i 10 10Inll(T)) (8)expressed as,

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i___ Equation (14) reveals that m becomes sole function of Vg foror i = ic - (ic +I0(T)) Iln ( 1 + C ) (9) large value of Vd. That is what IGBT characteristics shows at

Io(T) higher value of Vd. From (13), m can be written as follows:

In order to investigate the mathematical description of V -Vcontrolled diode D2 a functional relationship between ic, Vg m(Vg, Vd) = d bi (15)and Vd is required. Since IGBT model has been approximated Vdkic + ___log_I+i_to consist of mainly diodes, therefore, it is appropriate to rjqb q I,+Jg (T)jdescribe CE voltage drop equal to product of ordinary diodevoltage drop multiplied by a modulating factor m which Basically IGBT is dual input single output device. The inputshould of course be function of CE voltage and GE voltage. ordered pair (Vg, Vd) corresponds to the output ic. Thus (15)Thus, overall, IGBT can be described with a modified diode transforms above mentioned correspondence into (Vg, Vd) andcharacteristics as given below m (Vg, Vd).Vd= m(Vg, Vd) VTln (1+ ) + VCET (10)

IO (T) IV MODEL VALIDATIONHere, m (Vg, Vd) = modulating factor depending upon Vg

and Vd, dimensionless To identify m as function of (Vg, Vd) a table is generated fromVCET = collector emitter threshold voltage the characteristics sheet of IGBT [1] by extracting the data10(T) = IO 11+ 2 (T- To)} required for the model. For 4 distinct values of Vg and 7

distinct values of Vd the value of m is calculated from (15)Thermo-dynamic equation governing the temperature of IGBT knowing corresponding value of ic. This covers almost all theis given by operating range of IGBT. Table 1 is thus obtained which gives

the different parameter of IGBT. From this table it is observeddT that as the value of Vd is increased, m increases

M.S. d + b( T- To) = Vd ic ( 1) correspondingly whereas for an increase of Vg, m decreases.To obtain exact relation between m and Vd for a given value of

where S equivalent specific heat of IGBT Vg, the method of least square curve fitting [7] is used. Let m

M = Total mass of IGBT be approximated by one dimensional polynomial given byb = incremental wattage of IGBT which (16)

raises temperature by 1° C m = ao+ a, Vd (16)

dT Then, for V equal to 7, the coefficients ao and a, will beFor steady state analysis -= 0 therefore from (I11) 9

dt calculated as -0.714 and 1.115 respectively and the above

VdiC polynomial will be given by (17)T= To + b (12)

m = 1.115 Vd - 0.714 (17)

Substituting the value of T in (10) and rearranging the terms Similarly, for Vg equal to 8, 9 and 10 the above polynomialwe get may be written, respectively, as

mkT miM = 0.852 Vd -0.526 (18)VqIqn ET ' m = 0.502 Vd+ l.098 (19)

Vd =( ) + (13) m = 0.346 Vd + 1.3748 (20)

1- mkic. llog I1+ 'cqb Io

The coefficients a, and a, are plotted in Fig. 5 for differentFrom (13) it is clear that for very large value of Vd, values of Vg. It is observed that if these points are joineddenominator of (13) approaches to zero. This implies that together it will result a straight line which can be extended on

bq both axis. These lines will provide the value of coefficients aom(Vg) = (14) and a, for any other value of Vg not calculated in the above

kic log I+ lc equations.Io5(T)

TABLE 1

VARIOUS PARAMETERS OF IGBT

Vd =1.0 Vd =2.0 Vd= 4.0 Vd= 6.0 Vd= 8.0 Vd =lO.0 Vd =20.0

Vg=7 ic=0.5 ic=2 ic=3.33 ic=3.33 ic=3.33 ic=3.33 ic=3.33m=0.392 m=1.633 m=4.056 m=4.456 m=8.794 m=11.069 m=21.497

Vg =8 ic= 0.9 ic= 5.5 ic= 12.2 ic=12.2 ic= 12.2 ic= 12.2 ic=12.2m=0.385 m=1.58 m=3.677 m = 5.58 m=7.31 m=8.87 m=14.84

Vg =9 ic= 0.95 ic= 6 ic=16.4 ic= 23.3 ic= 25 ic= 25 ic= 25m=0.384 m=1.57 m=3.45 m=4.78 m=5.89 m=6.91 m=10.27

Vg =10 ic= 1 ic= 6.25 ic=20.8 ic= 34.2 ic= 39.6 ic= 40.5 ic=40.5m=0.384 m=1.57 m=3.34 m=4.19 m=4.83 m=5.46 m=7.49

Now if the value of ao and a, are known for a specified (13). Table 2 shows the value of m (m,) calculated fromvalue of Vg, then the value of m may be calculated for a (16) and compared with the value obtained in Table 1 for aspecified value of Vd and Vg. using (16). Once the value of known value of ic. Both of them found in close agreement.m is known, the current ic is directly calculated from

1.6 V CONCLUSIONS

1.4 A simple mathematical model has been developed for IGBTa I O in terms of a modified diode characteristics where total

1.2 0 I a1 voltage drop across the diode is equal to the product of

1.0 ordinary diode voltage drop multiplied by a modulatingfactor m.

0.8 -TABLE 2

0.6 CALCULATED VALUE OF MODULATING FACTOR (mc)

0.4

Vg Vd c m M0.2-

7 4 3.33 4.05 4.0

0.2 7 12 3.33 13.28 2.96

8 6 5.50 1.57 1.50.4-

9 2 40.0 7.49 7.40.6

10 20 47.7 4.39 4.00.8

Gate Emitter Voltage (V) 10 6 45.5 3.744 3.4

F;g@ 5RCIatOn bOtOOn V & a(}and V &a,11 8 |12.2 |5.575 | 5.57

12 6 34.2 4.19 4.19

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To identify the modulating factor, the input variables Vg and [3] Chuck Wong, "EMTP Modeling of IGBT Dynamic Performance forVd are transformed appropriately. In order to identify the Power Dissipation Estimation", IEEE Trans. On Industrial

circuit parameters power invariance and curve fitting Application, vol. 3, No.1 January/ February 1997

technique has been used. For curve fitting data are extracted [4] N.G Hingorani, "Flexible ac Transmission," IEEE Spectrum, vol.30,from the data sheet of IGBT. The proposed model is simple pp 40-45, April 1993accurate and integrates DC behaviour into single formula [5] N. Mohan, W.P. Robbins, T.M. Undeland, R. Nilssen and Olve Mo,

"Simulation of Power Electronics and Motion Control Systems-AnOverview," Proceeding of IEEE vol. 82, No. 8, August 1994

REFERENCES[6] V. J. Thottuvelil, D. Chin, and G.C Verghese, "Hierarchical

[1] F. Mihalic, K. Jezenik, K. Krishan & Manfred Rentmister, "IGBT approaches in modeling high power factor ac-dc converters," IEEESPICE Model" IEEE Trans. On Industrial Electronics, vol. 42, No.1 Trrans. Power Electronics, vol. 6, pp. 179-187, April 1991February 1995

[7] S. S. Sastry, " Introductory Methods of Numerical Analysis", PHI,[2] Allen R. Hefiner, "Analytrical Modeling of Device Circuit Interaction 2002

for the Power Insulated Gate Bipolar Transistor" IEEE Trans. OnIndustrial Application, vol. 26, No.6 November/December 1990

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