### ETC AN5001

```AN5001 Application Note
AN5001
Use Of The VTO, rT On-state Characteristic Model
Application Note
Replaces February 2003 version, AN5001-6.0
AN5001-7.0 February 2004
The use of the VTO, rT on-state characteristic model and a
more accurate alternative.
where A, B, C and D are constants with values specific to the
device in question.
The inclusion of the theoretical terms VTO and rT in power
semiconductor data sheets allows a simple means of calculating
power loss, but this can lead to many incorrect assumptions.
The terms in question are the two coefficients of a simple straight
line model of the device on-state characteristic curve. To
calculate the power the following formula is used:
The use of this model is described below.
P = VT0 IT(AV) + rT k2 IT(AV)2
[1]
where k is the current waveform form factor, eg 1.57 for half
sine wave.
The use of VTO and rT to approximate to the forward volt drop
curve of a power semiconductor originates from pre-computer
days when engineers used slide rules, calculators and, later
on, simple computers for their calculations. The use of modern
computers means that better approximations to the characteristic
can easily be used. The most popular of these is the model
proposed by General Electric:
[2]
VTM = A + B*lnI + C*I + D*sqrt(I)
VT0, rT DEFINITIONS
Although the straight line model is basically simple, variations in
definition can lead to significant differences in calculated powers.
Different manufacturers of power semiconductors have defined
VT0 and rT in different ways. Here are 4 variations:
1) As fig. 1, where the line is the tangent to the VTM vs IT curve
at the average current.
2) As fig. 2, where a chord is drawn through IT(AV) and 3xIT(AV).
This variation is the one used by Dynex for the calculation of
data sheet power losses and current ratings. The definition
is commonly used for thyristors. For rectifier diodes a chord
through 3xIT(AV) and 5xIT(AV) sometimes gives a better result.
3) A variation of 2 which uses two straight lines instead of one
to approximate to the true curve. In this version the lines
IT
IT
rT
rT
3x IT(AV)
IT(AV)
IT(AV)
VTO
Fig.1
VT
VTO
VTM
Fig.2
1/5
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AN5001 Application Note
and 4 give adequate accuracy up to 3 x IT(AV).
IT
For improved accuracy a mathematical model is needed which
approximates better to the true curve.
A FOUR COEFFICIENT MODEL
The GE four term curve-fit equation given above has been
shown to be a good isothermal approximation and is being
increasingly adopted by several manufacturers of power
semiconductors for inclusion in their datasheets. For the user,
the one problem with the equation
rT
[4]
VTM = A + B*lnI + C*I + D*sqrt(I)
is that, when multiplied by the equation for the current, it is not
easily integratable to give the power loss. However, the equation
is solvable by numerical integration, now easily possible with
computers.
IT(AV)
VTO
VT
Fig.3
The following equation for half sine waves uses the A, B, C, D
coefficients used in the VTM equation above, their numerical
values depending on the device type.
P = [(A*(I/E) + B*(I/E)* ln(I/E))*F + B*(I/E)*G + C*(I/E)2 *H+ D*(I/E)3/2*J]
pass through 1/6IT(AV) and πIT(AV) and also πIT(AV) and 20 x IT(AV).
4) As Fig 3. A tangential point constructed such that the value
of IT(AV) calculated from:IT(AV) = (–VTO ± ÷ (VTO2 + 4*k2*rT*P)) / 2*k2*rT
[3]
is the same as that calculated by more exacting methods. This
method is a variation of method 1). It has been used to
retrospectively calculate meaningful values of VT0 and rT where
more accurate current rating data already exists.
LIMITATIONS OF THE VT0, RT MODEL
Using any one of the four definitions gives the correct value of
the conduction losses at one or at most two points on the VTM
vs IT curve, ie where the straight line meets the true curve. It can
be seen that depending on where a point is taken on the curve
the answers will be optimistic or pessimistic. Definitions 1, 2
[5]
where I is the peak value of the half sine wave current.
The values of E, F, G, H and J depend on the conduction angle
and are given in the table 1, and for Rectangular waves :
P = [ A + B*ln(I*360/θ) + C*(I*360/θ) + D*÷(I*360/θ) ]*(I*360/θ)]
[6]
where I is the average current (not the peak current) and θ is
the conduction angle in degrees.
Dynex Semiconductor has determined the values of A, B, C and
D and these are given in the attached table 2.
Conduction Angle
(degrees)
E
F
G
H
J
180
1
0.31830986
– 0.0976260
0.25
0.27820862
120
1
0.23752350
– 0.0522407
0.02000795
0.21579720
90
0.75
0.15776190
– 0.0488128
0.12361100
0.13771530
60
0.45
0.08077821
– 0.0453849
0.04992036
0.06241130
30
0.25
0.02062772
– 0.0245605
0.00686488
0.01166912
15
0.067
0.00506346
– 0.0095093
0.00084797
0.00203133
Table 1
2/5
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AN5001 Application Note
Device Type Number
DCR504ST
DCR604SE
A
B
C
0.351374
0.171814
0.000964
D
– 0.020616
– 5
– 0.173031
0.2366
0.1182
0.0005
– 0.0019
DCR803SG
0.464203
0.051516
0.000249
0.005951
DCR806SG
0.6102629
0.08049203
7.189037 x 10– 4
– 0.01028328
DCR818SG
0.650046
– 0.018621
0.000589
0.063601
DCR820SG
– 0.759775
0.639225
0.004376
– 0.092153
6.698580464
– 1.571103736
– 0.001210868
0.239948957
– 0.6475
0.3079
0.0002787
– 0.02311
DCR720E
DCR840F
DCR1002SF
DCR1003SF
– 1.191257
0.4149784
– 3.307461 x 10
0.056345
1.086551
3.623888 x 10
– 4
– 0.02991257
– 4
– 0.04905585
DCR1006SF
– 1.456962
0.5361379
DCR1008SF
1.458475
– 0.098355
0.000484
0.012565
DCR1020SF
0.25863
0.322589
0.002564
– 0.061059
DCR1021SF
– 0.3126
0.2744
0.001
– 0.0143
DCR1050F
1.458475
– 0.098355
0.000484
0.012565
DCR1374SBA
0.4846543
0.05408984
8.508026 x 10– 5
1.863019 x 10– 3
DCR1375SBA
1.149986
– 0.09990939
7.993598 x 10– 5
0.02290949
1.459103
– 0.07503561
– 4
3.442677 x 10
7.82981 x 10– 3
DCR1474SY / DCR1474SV
0.7635305
8.73036 x 10– 3
8.568357 x 10– 5
1.537158 x 10– 3
DCR1475SY / DCR1475SV
0.9905546
– 0.044251168
0.00011976
0.009125351
DCR1476SY / DCR1476SV
0.8659641
0.03698496
3.245389 x 10– 4
– 2.597435 x 10– 3
DCR1574SY / DCR1476SV
1.328994
– 0.1381631
3.565973 x 10– 6
0.01786171
– 5
0.02837417
DCR1376SBA
6.639949 x 10
DCR1575SY / DCR1476SV
1.659647
– 0.2206499
7.427997 x 10
DCR1576SY / DCR1476SV
0.414672883
0.039124962
0.000288077
0.008514638
0.4624
0.0275
2.2501 x 10– 5
0.0032
DCR5980A
DCR1594SW
1.152158
– 0.08401428
3.351054 x 10
– 5
0.01199439
– 4
– 5.23298 x 10– 3
DCR1595SW
0.02866651
0.1590393
DCR1596SW
– 0.5011559
0.2638417
2.5367114 x 10– 4
– 0.01249303
DCR1673SZ / DCR1673SA
0.6180535
0.007965
4.57 x 10– 5
4.003 x 10– 3
DCR1674SZ / DCR1674SA
0.6844942
– 0.0108645
7.203702 x 10– 5
0.01015201
– 5
0.01334724
DCR1675SZ / DCR1675SA
0.8497627
– 0.03614853
1.947584 x 10
5.286579 x 10
Table 2 List of thyristor GE VTM coefficients
3/5
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AN5001 Application Note
Device Type Number
A
B
C
D
DS402ST
– 0.143917755
0.236902917
0.000989976
– 0.026033549
DS502ST
0.50435325
0.056610963
0.000639419
– 0.001101334
DNB61
0.827165759
– 0.035964275
0.000111412
0.007187415
DNB63
0.517184167
0.035582615
4.93781 x 10– 5
– 0.001102222
DNB64
0.50649703
0.070975272
0.000219255
– 0.005527578
DNB65
– 0.369840129
0.292196574
0.000353522
– 0.0311127
DS1104SG
0.782526539
– 0.077708882
0.000120208
0.019499005
DS1107SG
0.616460694
– 0.014521148
0.00034868
0.009951883
DS1109SG
0.788645971
– 0.004501879
0.000591618
0.006984031
DS1112SG
1.249986249
– 0.1764565
0.000523815
0.041024446
DS2002SF
– 0.647732445
0.268580716
0.000160327
– 0.017958086
DS2004SF
– 0.231479628
0.20380136
0.000230067
– 0.01443255
DS2007SF
0.658789195
– 0.017063104
0.00019441
0.01035792
DS2009SF
0.290476453
0.064490173
0.000335017
0.004080104
5.73018 x 10
– 5
0.042435146
DS2012SF
0.819644816
– 0.136726285
DS2101SY / DS2101SV
0.081706784
0.100348872
5.71812 x 10– 5
– 0.005290799
DS2102SY / DS2102SV
0.402090735
0.011717664
6.48045 x 10– 6
0.005977122
– 5
– 0.518264054
0.195880942
DS2106SY / DS2106SY
– 0.153571217
0.177571072
0.000178862
– 0.012942108
DS2107SY / DS2107SY
0.671710935
0.011005871
0.000158152
0.000604348
– 0.015914444
0.11368224
8.04212 x 10– 5
– 0.002839595
DS2906SZ
6.39322 x 10
– 0.005435085
DS2103SY / DS2103SV
Table 3 List of diode GE VFM coefficients
4/5
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POWER ASSEMBLY CAPABILITY
The Power Assembly group was set up to provide a support service for those customers requiring more than the basic
semiconductor, and has developed a flexible range of heatsink and clamping systems in line with advances in device voltages
and current capability of our semiconductors.
We offer an extensive range of air and liquid cooled assemblies covering the full range of circuit designs in general use today.
The Assembly group offers high quality engineering support dedicated to designing new units to satisfy the growing needs of
our customers.
Using the latest CAD methods our team of design and applications engineers aim to provide the Power Assembly Complete
Solution (PACs).
HEATSINKS
The Power Assembly group has its own proprietary range of extruded aluminium heatsinks which have been designed to
optimise the performance of Dynex semiconductors. Data with respect to air natural, forced air and liquid cooling (with flow
rates) is available on request.
For further information on device clamps, heatsinks and assemblies, please contact your nearest sales representative or
Customer Services.
http://www.dynexsemi.com
e-mail: [email protected]
HEADQUARTERS OPERATIONS
DYNEX SEMICONDUCTOR LTD
Doddington Road, Lincoln.
Lincolnshire. LN6 3LF. United Kingdom.
Tel: +44-(0)1522-500500
Fax: +44-(0)1522-500550
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These offices are supported by Representatives and Distributors in many countries world-wide.
© Dynex Semiconductor 2003 TECHNICAL DOCUMENTATION – NOT FOR RESALE. PRODUCED IN
UNITED KINGDOM
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