april 2012 doc id 022588 rev 1 1/10 AN4021 application note calculation of reverse losses in a power diode introduction this application note explains how to calculat e reverse losses in a power diode by taking into account the impact of the junction temperature (t j ) as well as the reverse voltage v r on the leakage current. the ideal current and voltage waveforms of an ultrafast diode in a power supply system during a switching cycle are illustrated in figure 1 . figure 1. ideal current and voltage wavefo rms of a diode in a switch mode power supply the reverse losses in a diode are the result of a reverse bias applied on the diode. they are due to the leakage current (i r ). this parameter (i r ) increases exponentially with the junction temperature. most of time, the reverse losses are negligible for bipolar and silicon carbide diodes. for silicon schottky structured diodes, these losses should be accurately estimated as they are the main origin of the thermal runaway risk phenomenon ( see an1542 ). t t v r v f 0 0 t sw f switching frequency t switching period duty cycle t duration of diode conduction maximum forward current minimum forward current forward voltage reverse voltage sw sw sw v d(t) i d(t) i d(t) i max i min v f i min v d(t) i r v r t sw i max www.st.com
AN4021 2/10 doc id 022588 rev 1 contents 1 diode reverse characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 junction temperature and reverse voltage dependence . . . . . . . . . . . . . . . 3 1.2 diode reverse charac teristics modeling: i r (v r ,t j ), ?c? thermal coefficient . 4 2 reverse losses: basic e quations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 an application example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4 revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
AN4021 diode reverse characteristics doc id 022588 rev 1 3/10 1 diode reverse characteristics 1.1 junction temperature and reverse voltage dependence the leakage current is an intrinsic parameter of the diode. in each st schottky and sic diode datasheet, a curve of the leakage current (typical value) versus the reverse voltage and the junction temperature is provided ( figure 2 ). most of the time, the reverse losses are calculated using maximum values in order to consider the worst operating conditions for the diode in the application. the ratio between typical and maximum values can be obtained using the values given in the section ?static electrical characteristic? of the datasheet. ( figure 3 ) figure 2. reverse leakage current versus reverse voltage applied for the stps20m100s (typical values) figure 3. typical and maximum leakage current at the voltage rating of the diode ( v rrm ) from the datasheet for the stps20m100s i r (ma) 1.e-03 1.e-02 1.e-01 1.e+00 1.e+01 1.e+02 0 102030405060708090100 t j =150c t j =125c t j =25c t j =100c t j =75c t j =50c v r (v) i r reverse leakage current symbol parameter test conditions min. typ. max. unit t = 25 c j v = 70 v r v = 100 v r 5 5 10 10 40 40 a a ma ma t = 125 c j t = 25 c j t = 125 c j
diode reverse characteristics AN4021 4/10 doc id 022588 rev 1 1.2 diode reverse characteristics modeling: i r (v r ,t j ), ?c? thermal coefficient the parameter (i r ) increases by an exponential law wit h the junction temperature. knowing a reference point i r (v r ,tj ref ) and the value of the thermal coefficient ?c?, one can easily calculate the leakage current at a given temperature t j using the following formula: equation 1 where v r is the reverse ?plateau? voltage applied across the diode. the ?c? thermal coefficient represents the le akage current dependence with the junction temperature. each diode has its own coefficient that can be calculated using two points as follows: equation 2 in each st datasheet, tj ref1 & t jref2 are respectively 25c and 125c. the ?c? coefficient is independent of the reverse voltage v r applied across the diode. ) ( re re ) , ( ) , ( f j j t t c f j r r j r r e t v i t v i - = ? ? ? ? ? ? ? ? - = ) , ( ) , ( ln 1 1 re 2 re 1 re 2 re f j r r f j r r f j f j t v i t v i t t c
AN4021 reverse losses: basic equations doc id 022588 rev 1 5/10 2 reverse losses: basic equations reverse losses expression is the average dissipated power in the diode during the reverse biasing phase: equation 3 in case of a typica l square waveform as illustrated on figure 1 , the reverse losses are equal to: equation 4 substitution of equation 1 into equation 4 yields equation 5 in some literature, it is possible to find the following expression: equation 6 with: equation 7 dt t v i t v t t p sw t j r r r sw j rev = 0 ) , ( ) ( 1 ) ( ) , ( ) 1 ( ) ( j r r r j rev t v i v t p - =d ) ( re re ) , ( ) 1 ( ) ( f j j t t c f j r r r j rev e t v i v t p - - =d ) ( re ) ( f j j t t c ref j rev e p t p - = () f j r r r ref t v i v p re , ) 1 ( - =d
an application example AN4021 6/10 doc id 022588 rev 1 3 an application example let us consider the example of a 45 w notebook adapter, using a flyback converter ( figure 4 ) working in continuous mode. the input voltage v in is 375 v and the output voltage v out is 14.5 v. the rectifier diode is a st power schottky stps20m100s (20 a, 100 v). figure 5 shows the ideal waveforms of the diode. the duty-cycle of the transistor is: = 0.2 and the transformer ratio is: m = 0.148. let us calculate the maximum reverse losses in the diode for this application. figure 4. flyback converter figure 5. ideal current and voltage waveforms of the diode in the flyback converter v out stps20m100s v in i load control snubber ac line m t t 0 spike i (t) d v f i r i (t) d v (t) d v (t) d -v r - (m v + v ) in out t sw t sw 0
AN4021 an application example doc id 022588 rev 1 7/10 step 1: reverse voltage applied across the diode when the transistor on the primary side of the transformer is on, the rectification diode is blocked with a reverse voltage equal to: equation 8 step 2: i r (v r ,t jref ) and thermal coefficient ?c?: the second step is to read the reference point value using the figure 2 given in each datasheet for the corresponding v r . the reference temperature (t jref ) considered is at a junction temperature of 125 c. in this example: i r(typ) (v r = 70 v, t jref = 125 c) = 5 ma (typical value) in order to consider the worst case for the power losses, we use the maximum values for the leakage current using the ratio given by the figure 3 . equation 9 i r(max) (v r = 70 v, t jref = 125 c) = 5 x 4 = 20 ma using equation 2 and figure 2 , the coefficient ?c? can be calculated: equation 10 step 3: reverse losses expression: from equation 5 , the maximum reverse losses expression is then: equation 11 finally, one can plot the evolution of revers e losses in the diode versus the junction temperature ( figure 6 ). v vout v m v in r 70 5 . 14 375 148 . 0= + = + = 4 10 40 ) 125 , 100 ( ) 125 , 100 ( ) ( (max) = = = c v i c v i ratio typ r r 1 6 3 1 re 2 re 1 re 2 re 069 . 0 ) 10 5 10 5 ln( 25 125 1 ) ) , ( ) , ( ln( 1 - - - = - = - =c t v i t v i t t c f j r r f j r r f j f j ) ( re (max) re ) , ( ) 1 ( ) ( f j j t t c f j r r r j rev e t v i v t p - - =d ) 125 ( 069 . 0 3 (max) 10 20 70 ) 2 . 0 1 ( ) ( - - - = j t j rev e t p (max) 12 . 1 ) ( = j rev e t p ) 125 ( 069 . 0- j t with t jref = 125 c
an application example AN4021 8/10 doc id 022588 rev 1 figure 6. maximum reverse losses versus the junction temperature as shown on figure 6 , the reverse losses increase exponentially with the temperature. for st bipolar diodes, the doping being platinum, the leakage current is very low resulting in negligible reverse losses. for schottky diode, there is a trade-off between the forward voltage drop and the reverse leakage current. in order to improve the efficiency of a switch mode power supply, a schottky diode with a low forward voltage to the detriment of higher leakage current would be preferred. in this case, the heat sink size will be larger in order to keep the ju nction temperature of the diode low enough and avoid a thermal runaway phenomenon. (refer to the an1542). 0,0 0,4 0,8 1,2 1,6 2,0 2,4 2,8 3,2 3,6 4,0 4,4 4,8 5,2 5,6 6,0 6,4 25 35 45 55 65 75 85 95 105 115 125 135 145 155 p rev(max) (w) t (c) j
AN4021 revision history doc id 022588 rev 1 9/10 4 revision history table 1. document revision history date revision changes 26-apr-2012 1 initial release.
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