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august 2011 doc id 3607 rev 3 1/12 AN604 application note calculation of conduction losses in a power rectifier introduction this application note explains how to calculate conduction losses in a power diode by taking into account the forward voltage dependence on temperature and the current waveform. the ideal current and voltage waveforms of an ultrafast diode in a power supply system during a switching cycle are shown in figure 1. figure 1. ideal current and voltage wavefo rms of a diode in a switch mode power supply the conduction losses in a diode appear when the diode is in forward conduction mode due to the on-state voltage drop (v f ). most of the time the conduction losses are the main contributor to the total diode power losses and the junction temperature rising. this is the reason why it is important to accurately estimate them. i d (t) v d (t) v d ( t ) i max i min t t i d ( t ) v r v f 0 0 t sw t sw f switching frequency t switching period duty cycle t duration of diode conduction i maximum forward current i minimum forward current v forward voltage v reverse voltage sw sw sw max min f r www.st.com
contents AN604 2/12 doc id 3607 rev 3 contents 1 diode forward characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 junction temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 diode forward charac teristics modeling: v t0 (t j ), r d (t j ) . . . . . . . . . . . . . . . 3 2 conduction losses: basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 application parameters: average and rms currents . . . . . . . . . . . . . . . . . . 6 3 an application example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1 average and rms current calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 v t0 (t j ) and r d (t j ) calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 conduction losses expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
AN604 diode forward characteristics doc id 3607 rev 3 3/12 1 diode forward characteristics 1.1 junction temperature dependence for two different junction temperatures, the current versus forward voltage curves cross at a current level point i c , depending on the diode technology. when the current is lower than i c , the temperature coefficient vf of the forward voltage is negative. when the current is higher, the temperature coefficient becomes positive. this behavior is shown in figure 2. for schottky and bipolar diodes, i c is high and the working area corresponds to vf < 0. for sic and gan technologies, i c is low and the vf can be positive or negative. when of vf < 0, the forward voltage and the conduction losses decrease when the junction temperature increases. figure 2. forward (i f ,v f ) characteristics of a diode 1.2 diode forward characteristics modeling: v t0 (t j ), r d (t j ) forward characteristics (i f and v f ) can be modeled by a straight line defined by a threshold voltage v t0 , and a dynamic resistance r d . v t0 and r d are calculated for 2 forward current levels (i f1 , i f2 ) for a given junction temperature as shown in figure 3. thus we can write: equation 1 equation 2 using equations 1 and 2 , we obtain v t0 (t j ) and r d (t j ) expressions: equation 3 equation 4 vf > 0 v f i f vf < 0 t j2 >t j1 t j1 vf = 0 i c 0 1 f j d j t0 j 1 f f i ) (t r ) (t v ) t , (i v ? + = 2 f j d j t0 j 2 f f i ) (t r ) (t v ) t , (i v ? + = 1 f 2 f j 1 f f j 2 f f j d i i ) t , (i v ) t , (i v ) (t r ? ? = 1 f 2 f 1 f j 2 f f 2 f j 1 f f j t0 i i i ) t , (i v i ) t , (i v ) (t v ? ? ? ? =
diode forward characteristics AN604 4/12 doc id 3607 rev 3 figure 3. v t0 (t j ) and r d (t j ) parameters v t0 and r d are given in each st diode datasheet. in most cases they are calculated at 125 c with maximum v f values for i f1 = i f(av) and i f2 = 2 i f(av) , where i f(av) is the average forward current rating of the diode. for a quick calculation these values can be used. for more accurate estimation, r d and v t0 must be calculated using the specific application conditions. see the example in chapter 3 . i f v f 0 i f2 i f1 v f ( i f1 , t jref2 ) v f (i f2 , t jref2 ) v f (i f1 , t jref1 ) v f (i f2 ,t jref1 ) v t0 (t jref2 ) v t0 (t jref1 ) t jref2 > t jref1 v f (i f ,t jref2 ) v f (i f ,t jref1 ) ) ( jref2 d t r 1 ) ( jref1 d t r 1
AN604 diode forward characteristics doc id 3607 rev 3 5/12 for any junction temperature v t0 (t j ), r d (t j ) and the forward voltage drop v f (i f ,t j ) can be calculated as follow: equation 5 equation 6 equation 7 where vto and rd are thermal coefficients calculated from the 2 reference temperatures: t jref1 and t jref2 . a common choice of t jref1 and t jref2 is 25 c and 125 c. these thermal coefficients are calculated with the following equations: equation 8 equation 9 note: vt0 < 0 and rd > 0 whatever the diode technology. () jref1 j t0 v jref1 t0 j t0 t t ) (t v ) (t v ? ? + = () jref1 j d r jref1 d j d t t ) (t r ) (t r ? ? + = () () f d r t0 v jref1 j jref1 f f j f f i t t ) t , (i v ) t , (i v ? + ? ? + = () () jref1 jref2 jref1 t0 jref2 t0 t0 v t t t v t v ? ? = () () jref1 jref2 jref1 d jref2 d d r t t t r t r ? ? =
conduction losses: basic equations AN604 6/12 doc id 3607 rev 3 2 conduction losses: basic equations conduction losses are the average dissipated power in the diode during the forward conduction phase given in equation 10 : equation 10 equation 10 can also be written as follows: equation 11 where i f(av) is the forward average current and i f(rms) is the forward root mean square current flowing through the diode. note: in case of a square waveform, a short form ula can be used to calculate conduction losses: equation 12 2.1 application parameters : average and rms currents the average and rms currents are different for each application condition. they can be calculated using equations 12 (average current) and 13 (rms current). equation 13 equation 14 figure 4 presents simplified expression of average and rms currents of commonly observed waveforms in a power rectifier. in most cases, these waveforms can be used for a rough estimation. () dt (t) i t , i v t 1 ) (t p sw t 0 f j f f sw j cond ? ? = 2 f(rms) j d f(av) j t0 j cond i ) (t r i ) (t v ) (t p ? + ? = i ) t , (i v ) (t p f(av) j f f j cond ? ? = () ? = sw t 0 f sw av f dt t i t 1 i ) ( () ? = sw t 0 2 f sw rms f dt t i t 1 i ) (
AN604 conduction losses: basic equations doc id 3607 rev 3 7/12 figure 4. average and rms currents of commonly observed waveforms square waveform t i d (t) 0 t sw ? t sw i max trapezoidal waveform t sw ? t sw t i d (t) 0 i max i min = = max rms f max av f i i i i ) ( ) ( + + = + = 3 i i i i i 2 i i i min max 2 min 2 max rms f min max av f ) ( ) ( t i d (t) 0 i max t sw ? t sw 2 i i i 2 i max rms f max av f = = ) ( ) ( half period sinusoidal waveform t i d ( t) 0 i max t sw t sw triangular waveform 3 i i 2 i i max rms f max av f = = ) ( ) (
an application example AN604 8/12 doc id 3607 rev 3 3 an application example let us consider the example of a 90 w notebook adapter. this is a flyback converter ( figure 5 ) working in continuous mode. the output voltage v out is 19 v and the maximum output current is 4.7 a. the rectifier diode is an st power schottky stps30m100s. figure 6 shows the ideal waveforms of the diode: i min = 4 a, i max = 11.8 a and = 0.6. let us calculate the maximum conduction losses in the diode for this application. figure 5. flyback converter figure 6. ideal current and voltage waveforms of the diode in the flyback converter. v out stps30m100s v in i load control snubber ac line v d (t) i max i min t t i d (t) v r v f 0 0 t sw t sw
AN604 an application example doc id 3607 rev 3 9/12 3.1 average and rms current calculation the first step is the calculation of the average and rms currents. the forward average current is the output current: i f(av) = i load = 4.7 a. as illustrated in figure 6 , the forward current has a trapezoidal shape. the formula to calculate the rms current of trapezoidal waveform is given in figure 4. i f(rms) is then: equation 15 3.2 v t0 (t j ) and r d (t j ) calculation the second step is the calculation of v t0 (t j ) and r d (t j ) in the application condition range. figure 7. stps30m100s forward voltage drop versus forward current t jref1 = 25 c and t jref2 = 125 c. to calculate maximum conduction losses, read maximum values of v f at i min and i max in figure 7. this figure is available in the stps30m100s datasheet. these values are summarized in table 1. ()() 6.4 a 0.6 3 4 11.8 4 11.8 i 2 2 f(rms) = ? ? + + = table 1. v f(max) values at i min and i max i f (a) v f(max) (i f , 25 c) (v) v f(max) (i f , 125 c) (v) i min = 4 0.52 0.43 i max = 11.8 0.63 0.55 i min = 4a i max = 11.8a 0.43v 0.55v 0.63v 0.52v (typical values) t = 125 c j (maximum values) t = 125 c j (maximum values) t = 25 c j i fm
an application example AN604 10/12 doc id 3607 rev 3 from equations ( 3 ), ( 4 ), ( 8 ) and ( 9 ) calculate v t0 (t jref1 ), v t0 (t jref2 ), r d (t jref1 ), r d (t jref2 ), vt0 and rd . calculated values of these parameters are summarized in table 2. from equations 5 and 6 we can write v t0 (t j ) and r d (t j ) as follow: equation 16 equation 17 3.3 conduction losses expression from equations 7 , 15 and 16 the expression for maximum conduction losses is then: equation 18 finally, let us plot the value of conduction losses in the diode as a function of the junction temperature ( figure 8 ). figure 8. maximum conduction loss es versus junction temperature table 2. v t0 , r d , vt0 , and rd parameters t jref (c) v t0 (v) r d (m ) vt0 (vc -1 ) rd ( c -1 ) t jref1 = 25 0.464 14.123 -951.35810 -6 12.83910 -6 t jref2 = 125 0.368 15.406 j -6 j t0 t 10 951.358 - 0.487 ) (t v ? = j -6 -3 j d t 10 12.839 10 13.802 ) (t r ? + = j -3 j cond(max) t 10 3.987 2.866 ) (t p ? + = 2.0w 2.2w 2.4w 2.6w 2.8w 3.0w p(t) cond(max) j 25c 35c 45c 55c 65c 75c 85c 95 c 105c 115c 125c t j
AN604 revision history doc id 3607 rev 3 11/12 4 revision history table 3. document revision history date revision changes aug-1993 1 initial release 03-may-2004 2 stylesheet update. no content change 24-aug-2011 3 completely revised for currently available products.
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