Applicaion noe Calculaion of urn-off power losses generaed by an ulrafas diode Inroducion This applicaion noe explains how o calculae urn-off power losses generaed by an ulrafas diode, by aking ino accoun he recovery parameers and heir emperaure dependency. Such losses appear when he diode changes from he forward conducion phase o he reverse conducion phase. Furhermore, in many power supplies (DC-DC or AC-DC), in order o ensure curren coninuiy, a recificaion or freewheeling diode is ofen associaed o a MOSFET or an IGBT. In cases where he converer is working in coninuous conducion mode (CCM) wih hard swiching condiions, he urn-on losses in he MOSFET (or he IGBT) are usually he main conribuor o he efficiency drop, due o he recovery parameers of he diode. This applicaion noe provides mehods o calculae he diode urn-off power losses in wo common cases: Turn-off power losses generaed by a diode working in recifying mode (power losses in he swiching diode and power losses in he snubber resisor due o he diode) Swiching power losses generaed by he reverse recovery curren of an ulrafas diode in a swiching cell (diode + MOSFET or IGBT) The diodes discussed are all STMicroelecronics ulrafas diodes from 200 V o 1600 V. Ocober 2017 DocID030470 Rev 1 1/20 www.s.com
Conens Conens AN5028 1 Diode urn-off characerisics... 3 1.1 Reverse recovery waveform and associaed parameers... 3 1.2 Turn-off parameers and emperaure dependency... 7 2 Turn-off power losses calculaion... 9 2.1 Calculaion in recifying mode... 9 2.1.1 Turn-off power losses generaed by he diode in a simple recifying circui... 9 2.1.2 Snubber power losses due o he reverse recovery curren of he diode... 10 2.2 Calculaion in a swiching cell (hard swiching condiions)... 11 2.2.1 Turn-off power losses generaed by he diode: calculaion from ideal waveforms... 11 2.2.2 Turn-off power losses generaed by he diode: calculaion from real waveforms... 13 2.2.3 Calculaion based on energy measuremens... 16 3 Conclusion... 19 4 Revision hisory... 19 2/20 DocID030470 Rev 1
Diode urn-off characerisics 1 Diode urn-off characerisics 1.1 Reverse recovery waveform and associaed parameers The urn-off power losses in a diode appear when he diode swiches from a forward conducion phase o a reverse conducion phase, as illusraed in he figure below: Figure 1: Curren and volage waveforms of a diode during urn-off phase A = 1, he diode urns off and he curren decreases wih a slope dif/d imposed by he circui. Meanwhile, he diode volage remains equal o VF (by neglecing he parasiic inducor effec). When he curren reaches zero, he charges sored during he conducion phase begin o recombine and he diode volage is sill equal o VF during ime a unil he curren reaches a negaive value called IRM (maximum reverse curren). A ha ime, he diode volage sars o decrease while he minoriy carriers are evacuaing. The charges coninue o be evacuaed during ime b wih a slope dir/d depending on he echnology of he diode and he circui. During his ime inerval (b), he volage oscillaes around he reverse volage VR value before sabilizing. Afer b, he diode can be considered compleely urned off. DocID030470 Rev 1 3/20
Diode urn-off characerisics AN5028 The high value of dir/d combined wih some parasiic inducors are usually origins of overvolage and oscillaions in he circui, which can be criical. The reverse recovery charges, called Qrr, are defined as he inegral of he curren flowing hrough he diode during a ime inerval 2-4: 4 Q rr = I D (). d Equaion 1 2 The reverse recovery ime, called rr, is defined as he sum of imes a and b: rr = a + b Equaion 2 The recovery charges are also defined as equal o he sum of Qa (he recovery charges during a) and Qb (he recovery charges during b): Q rr = Q a + Q b Qrr and rr characerize he rapidiy of he diode and are used o disinguish he differen designaions of diodes (fas, ulrafas and hyperfas diodes). The recovery charges Qrr, he recovery curren IRM and he recovery ime rr, are inrinsic parameers of he diode during is urn-off phase. They depend on: IF: Forward curren flowing hrough he diode before i urns off dif/d : Slope applied o he diode and imposed by he circui Tj: Operaing juncion emperaure of he diode VR: Reverse volage applied across he diode In mos ST ulrafas diode daashees, he curves of IRM, rr and Qrr versus dif/d are provided for specific values of he forward curren IF (respecively in Figure 2: "STTH8R06 IRM versus dif/d", Figure 3: "STTH8R06 rr versus dif/d" andfigure 4: "STTH8R06 Qrr versus dif/d"). In hese figures, he reverse volage VR across he diode and he juncion emperaure Tj are fixed. 4/20 DocID030470 Rev 1
Figure 2: STTH8R06 IRM versus dif/d Diode urn-off characerisics 22 20 18 I (A ) R M V R =400V T j=125 C I F=2 x I F(AV ) 16 I F=I F(AV ) 14 12 10 8 I F=0.25 x I F(AV ) I F=0.5 x I F(AV ) 6 4 2 0 di /d (A /µs) F 0 200 400 600 800 1000 Figure 3: STTH8R06 rr versus dif/d 120 110 100 90 80 70 60 50 40 30 20 10 0 (ns) rr I F=2 x I F(AV ) I F=I F(AV ) di /d (A /µs) F I F=0.5 x I F(AV ) V R =400V T j =125 C 0 200 400 600 800 1000 Figure 4: STTH8R06 Qrr versus dif/d Q rr (nc) 350 V R =400V T j =125 C 300 250 200 I F=2 x I F(AV ) I F=I F(AV ) I F=0.5 x I F(AV ) 150 100 50 0 di /d (A /µs) F 0 200 400 600 800 1000 As shown in he graphs above, he IRM, rr and Qrr parameers are highly dependen on he dif/d slope. The S facor parameer (also denoed as S) is defined as he raio beween he imes b and a: S = b a DocID030470 Rev 1 5/20
Diode urn-off characerisics AN5028 The S facor parameer is used as a meric o define how sof a diode is. Usually, a snap-off diode has S < 1, while a sof diode has S > 1. In mos ST ulrafas diode daashees, an S facor versus dif/d curve is provided, as he one shown in Figure 5: "STTH8R06 S facor versus dif/d" for he STTH8R06 diode. Figure 5: STTH8R06 S facor versus dif/d S fac or 0.70 IF 2 x IF(AV ) 0.65 V R =400V T j=125 C 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 di /d (A /µs) F 0 200 400 600 800 1000 There is a relaion beween he S facor and rr: rr = a + b wih a = I RM and di F /d b = a S => rr = I RM (1 + S) Equaion 3 di F /d The S facor parameer should be used carefully. I is heavily dependen on he circui environmen (he swich, for example). Indeed, if he swich is changed, he S facor value, measured in he same condiions, can change also. Furhermore, when speaking of he sofness facor, some people prefer o consider he slope currens raio: di F/d di R /d 6/20 DocID030470 Rev 1
Diode urn-off characerisics To provide bes workable resuls wih good accuracy, he swiching parameers above are measured in differen ways based on he recovery behavior of he diode (snap-off or sof). Figure 6: Snap-off behavior (lef) and sof behavior (righ) I D () I D () I 0 di F /d di F /d rr rr a b a b 0 1 2 0 4 -k*i RM 2 1 4 -I RM 3 -I RM 3 For diodes wih snap-off behavior, he rr parameer is measured beween 2 and 4. Wih sof diodes, 4 is aken as he ime where ID() = -k x IRM wih k usually equal o 0.25, unless specified in he daashee. In some applicaions, he choice beween snap-off and sof diodes can be crucial because his will correspond o a rade-off beween a reducion of swiching power losses and beer EMI performance. For insance, in a bridge leg configuraion (such as inverer opologies) he use of a sof diode is preferred in order o avoid dramaic cross-conducion. 1.2 Turn-off parameers and emperaure dependency Swiching parameers depend on he juncion emperaure Tj of he diode. The daashee curve exrac below shows he variaion of each parameer versus Tj. The verical axis is he raio beween he parameer a a given Tj and he parameer value a 125 C, chosen as a reference. For insance, for he Qrr curve: Q rr (T j ) Q rr (125 C) = k(k is a consan) DocID030470 Rev 1 7/20
Diode urn-off characerisics Figure 7: Turn-off parameers versus juncion emperaure Tj AN5028 For example, o calculae he Qrr a 75 C, we firs use he Qrr versus dif/d curve (Figure 4: "STTH8R06 Qrr versus dif/d") in order o evaluae he Qrr a 125 C for a given dif/d. Then we proceed as follows: Q rr (75 C) Q rr (125 C) = 0.53 (in Figure 7: "Turn-off parameers versus juncion emperaure Tj") Q rr (75 C) = Q rr (125 C) 0.53 wih Q rr (125 C) = 150nC (in Figure 4: "STTH8R06 Qrr versus dif/d") di F /d = 200A/µs Tj = 125 C VR = 400 V IF = IF(AV) Q rr (75 C) = 150nC 0.53 = 79.5 nc 8/20 DocID030470 Rev 1
Turn-off power losses calculaion 2 Turn-off power losses calculaion The power losses calculaion can be helpful for designers o: Esimae he oal power losses generaed inside a diode, in order o evaluae is juncion emperaure. Esimae he oal power losses generaed by differen diodes (in snubber circuis, power ransisors, ec.) in order o selec one ha provides he highes efficiency for a converer. The general urn-off power losses expression is he average of dissipaed power in he diode during is urn-off phase: P SWoff = 1 T sw 4 v D ()i D ()d Equaion 4 1 The volage waveform during he urn-off phase and he associaed dv/d are applicaion dependen. The swiches used in he circui also influence he measuremen of diode performance. Consequenly, he volage waveform during he swiching phase can be differen from one swich o anoher. Tha s why ST recommends measuring he volage and curren flowing hrough he diode during he urn-off phase, and using he energy measuremen o accuraely calculae he urn-off power losses. Throughou his secion, formulas are given o esimae power losses, wih he suppor of he daashee parameers, wihou performing any measuremens. They depend on he configuraion of he circui (recifying diode, freewheeling diode, snubber diode, ec.). 2.1 Calculaion in recifying mode In recifying mode, he dif/d value is fixed by he leakage inducor of he ransformer, called Ll. 2.1.1 Turn-off power losses generaed by he diode in a simple recifying circui In he figure below, an example of a forward converer is considered wih is equivalen circui a he urn-off phase. Figure 8: Forward opology converer and is equivalen circui a diode urn-off phase D 3 D 1 L i L + I ou L l C R Snubber + - V in i T N p T N d N s V s D 2 C - V ou R L Equivalen circui a diode urn-off phase V s D 1 D 2 C R I0 DocID030470 Rev 1 9/20
Turn-off power losses calculaion AN5028 The ideal curren and volage waveforms during D1 urn-off phase is given in he graph below: Figure 9: Ideal curren and volage waveforms of a recifying diode during is urn-off phase From Equaion4 and ideal waveforms above Figure 9: "Ideal curren and volage waveforms of a recifying diode during is urn-off phase", he diode urn-off power losses in simple recifying mode is given by: P SWoff = F sw ( V 2 RI RMS ) = F swv R Q b 6dI F /d 3 Equaion 5 2.1.2 Snubber power losses due o he reverse recovery curren of he diode A snubber circui is used o absorb he overvolage ha occurs during each swiching phase. I is usually composed of a capacior and a resisor conneced in series. The previous Figure 8: "Forward opology converer and is equivalen circui a diode urn-off phase" shows a diode wih is snubber circui (resisor and capacior cell). When he diode urns off, an energy equal o: 1 L 2 2 li RM is sored in he leakage inducor Ll. The oal dissipaed energy in he snubber (in he resisor) is given by: E snubber = 1 L 2 2 2 li RM + CV S Equaion 6 The second par of he formula CV S 2 no being generaed by he diode, he power losses caused by he diode are given by: P Snubberdueodiode = 1 L 2 li 2 RM F sw Equaion 7 I is very imporan o ake he snubber losses ino accoun, especially in high power applicaions where a high snubber value can be used. 10/20 DocID030470 Rev 1
Turn-off power losses calculaion 2.2 Calculaion in a swiching cell (hard swiching condiions) The circui given in Figure 10: "Freewheeling diode in a basic swiching cell" is he ypical cell of a freewheeling diode funcion found in buck, boos and inverer opologies. I is usually used o characerize diode swiching parameers like IRM, rr, Qrr, ec. In his configuraion, he dif/d parameer is fixed by he speed of he swich (MOSFET Q, in he case below). Figure 10: Freewheeling diode in a basic swiching cell V ou L D V D ID V bus + - IQ V Q Ve Q The reverse recovery curren of he diode is he cause of he urn-off power losses in he diode. I is also he origin of addiional power losses in he associaed MOSFET during is urn-on phase. 2.2.1 Turn-off power losses generaed by he diode: calculaion from ideal waveforms During he MOSFET urn-on phase, he gae volage reaches a level ha causes an increase of he MOSFET curren and a decrease of he diode curren. We call 0 he ime during which he diode curren decreases unil he zero value is reached (beween 1 and 2). Then comes he ime required for he diode curren o decrease o he maximum reverse curren IRM, called a (beween 2 and 3). Meanwhile, he MOSFET curren coninues rising unil i achieves he value I0 = IRM. b is defined as he ime beween he curren IRM (3) and he ime ha he diode curren goes back o zero (4). Whereas he ime during which he MOSFET volage decreases from Vou o zero is called b'. DocID030470 Rev 1 11/20
Turn-off power losses calculaion AN5028 Figure 11: Ideal curren and volage waveforms of a swiching cell during MOSFET urn-on and diode urn-off phase 1 2 3 4 I 0 +I RM V ou V Q () I 0 I Q () EON(Q) 0 a b =b I 0 I D () EOFF(D) V D () Q rr -IRM V R =V ou From he phenomenon described above, he recovery curren of he diode inroduces some addiional swiching losses in he MOSFET. The approximaions of his model are: di F d = di Q d is consan b = b (This is a specific case: he reverse volage across he diode reaches Vou and in he meanime he recombinaion of minoriy charges sored in he diode is compleed.) dv Q = dv D is consan d d Parasiic inducance Ll is negleced The following power losses are calculaed considering he ideal waveforms and he power definiion given in Figure 11: "Ideal curren and volage waveforms of a swiching cell during MOSFET urn-on and diode urn-off phase". MOSFET urn-on power losses beween 1 and 3 are ( wih P SWOFF(diode)[ 1 3 ] = 0) : P = F SWON(MOSFET)oal[ swv ou ( 1 I 1 3] 2 0 0 ) + F sw V ou ( I 0I RM di F + Q a ) Equaion 8 d Losses independen of he diode / Losses due o he diode MOSFET urn-on power losses and diode urn-off power losses beween 3 and 4 are: P SWON(MOSFET)oal[ + P SWOFF(diode)[ = F sw V ou ( 1 I 3 4] 3 4] 2 0 b ) + F sw V ou ( 1 I 3 RM b 1 I 3 RM b ) +F sw V ou Q b Equaion 9 Losses independen of he diode / Losses due o he diode 12/20 DocID030470 Rev 1
Turn-off power losses calculaion By adding Equaion 8 and Equaion 9 and by aking ino accoun only he power losses due o he diode, we obain: P SWON(MOSFET+diode)dueodiode = F sw V ou ( I 0I RM di F d + Q rr ) Equaion 10 These equaions can be easily used (wih parameers indicaed in each ST daashee) by considering he swiching losses induced by he diode urn-off during MOSFET urn-on (for example o compare differen producs). To calculae he urn-off power losses in he diode, Equaion 5 of paragraph 2.1.1 can be used. Based on Equaion 10, we can conclude ha for wo diodes wih idenical Qrr, he lower he IRM of he diode is, he lower is swiching power losses will be. Unlike he above calculaions, in he nex secion he calculaions are done wih real waveforms, wihou approximaions, o ge more accurae resuls: The non-lineariy of di/d and dv/d is aken ino accoun b b 2.2.2 Turn-off power losses generaed by he diode: calculaion from real waveforms The following waveforms have been observed across a diode and he associaed MOSFET in a basic swiching cell circui. During he volage measuremen, he probe can inroduce some parasiic inducance. The sum of all his inducance is called LP. In real waveforms, he effecs of parasiic inducance Lp can be observed in he graph wih a volage fall corresponding o LpdlQ/d (in Figure 12: "Real curren and volage waveforms of a swiching cell during MOSFET urn-on and diode urn-off phases"). Figure 12: Real curren and volage waveforms of a swiching cell during MOSFET urn-on and diode urn-off phases DocID030470 Rev 1 13/20
Turn-off power losses calculaion AN5028 As previously menioned, any approximaion is done on dv/d, di/d and b and b in he following equaions. Moreover, we assume ha he dv/d is independen of he swiching behavior of he diode. From real waveforms in Figure 12: "Real curren and volage waveforms of a swiching cell during MOSFET urn-on and diode urn-off phases" and wihou aking ino accoun he parasiic inducance conribuion, we can calculae ha: MOSFET urn-on power losses beween 1 and 3 are( wih P SWOFF(diode)[ 1 3] = 0): P = F 2 swon(mosfet)[ swv ou I Q (). d + F 1 3] 1 sw V 3 ou I Q (). d 2 wih I 0 = I Q + I D = F sw V 2 ou [ I Q (). d + 3 I 1 0. d 3 I 2 D (). d P swon(mosfet)[ 1 3] 2 2 ] P = F swon(mosfet)[ swv ou ( I Q (). d) + F sw V ou I 0 a + F sw V ou Q a Equaion 11 1 3] 1 Losses independen of he diode / Losses due o he diode MOSFET urn-on power losses and diode urn-off power losses beween 3 and 4 are: P + P swon(mosfet)[ sw = F OFF(DIODE)[ sw I Q ()V DS ()d + F 3 4] 3 4] 3 sw I D ()V D ()d wih I 0 = I Q + I D and V ou = V DS V D, he above equaion becomes: P + P swon(mosfet)[ sw = F OFF(DIODE)[ sw (I 0 I D ())V DS ()d + F 3 4] 3 4] 3 sw I D ()(V DS () V ou )d = F 4 sw I 0 V DS ()d F 3 sw V 4 ou I D ()d 3 4 P + P swon(mosfet)[ sw = F 4 OFF(DIODE)[ swi 0 V DS ()d + F sw V ou Q b Equaion 12 3 4] 3 4] 3 4 Losses independen of he diode / Losses due o he diode The power losses in he diode, and he MOSFET generaed by he diode, can be deduced from equaion (11) and (12): P sw(mosfet+diode)[dueodiode] = F sw V ou (I 0 a + Q rr ) Equaion 13 Equaion (13) is close o equaion (10) wih he advanage ha he non-lineariy of he dif/d is aken ino accoun. However, a is no specified in he daashee, and should be measured in he applicaion. One of he ineresing aspecs of his formula (where MOSFET swiching-on power losses and diode swiching-off power losses are added) is ha he calculaion does no involve he dv/d. 4 3 4 3 14/20 DocID030470 Rev 1
Turn-off power losses calculaion To summarize he general case of a swiching cell a he MOSFET urn-on and a he diode urn-off, 5 areas can be considered: Figure 13: Ideal curren and volage waveforms of a swiching cell during MOSFET urn-on phase and diode urn-off phase Power losses in he diode and in he MOSFET due o he Qrr is given by: P Area1+Area2 = F sw V ou Q rr (due o diode) Power losses which are independen of he diode, because hey are induced by links o he dv/d (fixed in firs approximaion by he swich): P Area3 = F sw I 0 4 3 V DS ()d (independan of he diode) Power losses generaed by he diode during he ime a ( funcion of IRM): P Area4 = F sw V ou I 0 a (due o diode) Power losses which are independen of he diode correspond o he power losses ha he MOSFET would have wih an ideal diode (SiC Schoky diode for example): P Area5 = F sw V ou 2 1 I Q (). d (independan of he diode) A simple way o calculae swiching power losses wihou using approximaions is o use energy measuremens wih he scope. DocID030470 Rev 1 15/20
Turn-off power losses calculaion 2.2.3 Calculaion based on energy measuremens AN5028 In his secion, energy measuremens are used o evaluae he power losses in a swiching cell during he main swich urn-on. In he firs sep, an example of energy measuremens from he scope a he swich urn-on phase is represened. Measuremens are done by considering an ST ulrafas diode (STTH15AC06) and a MOSFET in a swiching cell in hard swiching condiions (as in Figure 10: "Freewheeling diode in a basic swiching cell"). In he second sep, he power losses generaed by he ulrafas diode during he MOSFET urn-on phase is deduced by replacing he silicon diode wih a SiC Schoky diode ha exhibis negligible urn-off power losses. Finally, his resul is compared o calculae power losses by using Equaion 10. The firs sep consiss of measuring he volage and he curren flowing hrough he MOSFET during is urn-on phase o esimae he oal energy in he MOSFET due o he diode urn-off. Figure 14: MOSFET urn-on oal energy measuremen wih an ulrafas diode 219µJ Depending on he curren probe used, a ime inerval may be observed beween he curren and he volage curves. I is imporan o measure his ime inerval and offse i in order o obain he curren and he volage in phase. Oherwise he energy measured would be no accurae enough. In mos oscilloscopes, he ime delay correcion funcion is called deskew. This ime can be easily measured on a resisive circui by comparing sar ime beween he volage and he curren curves. In our measuremen example, a correcion of 12 ns has been applied on he curren probe o accommodae he curren and he volage waveforms. In he second sep, he ulrafas diode is replaced wih a silicon carbide Schoky diode (SiC diode), wih no reverse recovery charges, in order o measure he swiching energy exclusively generaed by he MOSFET (corresponding o area 5 of Figure 13: "Ideal curren and volage waveforms of a swiching cell during MOSFET urn-on phase and diode urn-off phase") 16/20 DocID030470 Rev 1
Turn-off power losses calculaion Figure 15: MOSFET urn-on energy measuremen wih SiC diode 55µJ By subracing he energy measured in Figure 15: "MOSFET urn-on energy measuremen wih SiC diode" from he energy measured in Figure 14: "MOSFET urn-on oal energy measuremen wih an ulrafas diode", we ge he energy exclusively dependen of he swiching parameers of he ulrafas diode a he MOSFET urn-on: Eon MOSFET(dueodiode) = Eon MOSFEToal (wihulrafasdiode) Eon MOSFEToal (wihsicdiode) = 219µJ 55µJ = 164µJ DocID030470 Rev 1 17/20
Turn-off power losses calculaion AN5028 To ge he oal energy in he swiching cell due o he diode urn-off, we need o include he diode urn-off energy measuremen. The Figure 16: "Ulrafas diode urn-off energy measuremen" shows ha his energy is equal o 163 µj. Figure 16: Ulrafas diode urn-off energy measuremen I 0 di F /d I RM V ou 163 µj E SW(MOSFET+diode)dueohediode = Eon MOSFET(dueodiode) + Eoff diode = 164µJ + 163µJ = 327µJ Finally, his energy is compared o he resul from he Equaion 10 by using only he swiching parameers of he diode measured in Figure 16: "Ulrafas diode urn-off energy measuremen": Table 1: Resul Qrr IRM dlf/d I0 VOUT 582 nc 15.5 A 455 A/µs 9.6 A 400 V E SW(IGBT+diode)dueodiode = V ou ( I 0I RM di F d + Q rr ) = 363µJ For insance, in a 30 khz frequency applicaion, he power losses difference beween he heoreical calculaion and he measuremens is around 1 W (~10%). Even if he power losses due o he diode calculaed using Equaion 10 are a bi more pessimisic han he energy measuremen mehod resul, he difference is very small. This means ha he calculaion wih Equaion 10 can be used o quickly compare, wih good degree of confidence, ulrafas diodes wih differen swich-off behaviors. 18/20 DocID030470 Rev 1
Conclusion 3 Conclusion The urn-off power losses combined wih he conducion power losses (in applicaion noe www.s.com/an604) are he main power losses ha should be aken ino consideraion when using ulrafas diodes. Throughou his applicaion noe, differen equaions for power losses calculaion, hrough differen elecronic power circui configuraions, are given. They enable designers o easily esimae power losses wih relaively good accuracy. Knowing hose power losses, designers can selec a suiable diode for a given applicaion and esimae he diode juncion emperaure. However, as previously menioned, he energy measuremens mehod remains he bes way o accuraely evaluae power losses. 4 Revision hisory Table 2: Documen revision hisory Dae Revision Changes 03-Oc-2017 1 Firs release. DocID030470 Rev 1 19/20
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