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 www.dynexsemi.com 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 www.dynexsemi.com 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 www.dynexsemi.com 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 www.dynexsemi.com 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. 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