AN604 Application note

Transcription

1 AN64 Applicaion noe Calculaion of conducion losses in a power recifier nroducion This applicaion noe explains how o calculae conducion losses in a power diode by aking ino accoun he forward volage dependence on emperaure and he curren waveform. The ideal curren and volage waveforms of an ulrafas diode in a power supply sysem during a swiching cycle are shown in igure 1. igure 1. deal curren and volage waveforms of a diode in a swich mode power supply () Min () V () V () V sw Tsw T max min V V R sw Swiching frequency Swiching period uy cycle uraion of diode conducion imum forward curren Minimum forward curren orward volage Reverse volage V R The conducion losses in a diode appear when he diode is in forward conducion mode due o he on-sae volage drop (V ). Mos of he ime he conducion losses are he main conribuor o he oal diode power losses and he uncion emperaure rising. This is he reason why i is imporan o accuraely esimae hem. Augus 11 oc 367 Rev 3 1/1

2 Conens AN64 Conens 1 iode forward characerisics Juncion emperaure dependence iode forward characerisics modeling: V T (T ), R (T ) Conducion losses: basic equaions Applicaion parameers: average and rms currens An applicaion example Average and rms curren calculaion V T (T ) and R (T ) calculaion Conducion losses expression Revision hisory /1 oc 367 Rev 3

3 AN64 iode forward characerisics 1 iode forward characerisics 1.1 Juncion emperaure dependence or wo differen uncion emperaures, he curren versus forward volage curves cross a a curren level poin c, depending on he diode echnology. When he curren is lower han c, he emperaure coefficien α V of he forward volage is negaive. When he curren is higher, he emperaure coefficien becomes posiive. This behavior is shown in igure. or Schoky and bipolar diodes, c is high and he working area corresponds o α V <. or SiC and GaN echnologies, c is low and he α V can be posiive or negaive. When of α V <, he forward volage and he conducion losses decrease when he uncion emperaure increases. igure. orward (,V ) characerisics of a diode T 1 T >T 1 α V > c α V α V < V 1. iode forward characerisics modeling: V T (T ), R (T ) orward characerisics ( and V ) can be modeled by a sraigh line defined by a hreshold volage V T, and a dynamic resisance R. V T and R are calculaed for forward curren levels ( 1, ) for a given uncion emperaure as shown in igure 3. Thus we can wrie: Equaion 1 V (,T ) V 1 T Equaion V (,T ) V Using Equaions 1 and, we obain V T (T ) and R (T ) expressions: Equaion 3 V ( R (T ) Equaion 4 V ( V (T ) T T 1 (T ) + R (T ) 1 (T ) + R (T ),T ) V (,T ) 1 1 1,T ) V (,T ) 1 oc 367 Rev 3 3/1

4 iode forward characerisics AN64 igure 3. V T (T ) and R (T ) parameers T Ref > T Ref1 V (,T Ref1 ) V (,T Ref ) 1 R ( T ref ) 1 R ( T ref1 ) 1 V T (T Ref ) V V ( T (T Ref1 ) 1,T Ref ) V (,T Ref1 ) V (,T Ref ) V ( 1,T Ref1 ) V V T and R are given in each ST diode daashee. n mos cases hey are calculaed a 15 C wih maximum V values for 1 (AV) and (AV), where (AV) is he average forward curren raing of he diode. or a quick calculaion hese values can be used. or more accurae esimaion, R and V T mus be calculaed using he specific applicaion condiions. See he example in Chaper 3. 4/1 oc 367 Rev 3

5 AN64 iode forward characerisics or any uncion emperaure V T (T ), R (T ) and he forward volage drop V (,T ) can be calculaed as follow: Equaion 5 V T (T ) V T Equaion 6 Equaion 7 Where α VTO and α R are hermal coefficiens calculaed from he reference emperaures: T ref1 and T ref. A common choice of T ref1 and T ref is 5 C and 15 C. These hermal coefficiens are calculaed wih he following equaions: Equaion 8 Equaion 9 (T R (T ) R (T Ref1 Ref1 V (,T ) V (,T α α VT R V R T ) + α ) + α Ref1 R VT ) + ( T ) V ( T ) T ref ref T T ref1 ( T T ) Ref1 ( T T ) Ref1 ( T T )( α + α ) ref1 ( T ) R ( T ) T ref ref T ref1 ref1 Ref1 VT R Noe: α VT < and α R > whaever he diode echnology. oc 367 Rev 3 5/1

6 Conducion losses: basic equaions AN64 Conducion losses: basic equaions Conducion losses are he average dissipaed power in he diode during he forward conducion phase given in Equaion 1: Equaion 1 P CON Tsw 1 (T ) V T sw Equaion 1 can also be wrien as follows: Equaion 11 P (T ) V (T ) CON T (,T ) () d (av) + R (T ) (rms) Noe: Where (AV) is he forward average curren and (RMS) is he forward roo mean square curren flowing hrough he diode. n case of a square waveform, a shor formula can be used o calculae conducion losses: Equaion 1 P (T ) V (,T ) CON (AV).1 Applicaion parameers: average and rms currens The average and rms currens are differen for each applicaion condiion. They can be calculaed using Equaions 1 (average curren) and 13 (rms curren). Equaion 13 ( AV ) 1 T sw Equaion 14 ( RMS) 1 T sw () d () d igure 4 presens simplified expression of average and rms currens of commonly observed waveforms in a power recifier. n mos cases, hese waveforms can be used for a rough esimaion. 6/1 oc 367 Rev 3

7 AN64 Conducion losses: basic equaions igure 4. Average and rms currens of commonly observed waveforms Square waveform Trapezoidal waveform () () Min ( AV) ( RMS) ( AV) ( RMS) + Min + Min+ Min 3 Half period sinusoidal waveform () Triangular waveform () ( AV) ( RMS) π ( AV) ( RMS) 3 oc 367 Rev 3 7/1

8 An applicaion example AN64 3 An applicaion example Le us consider he example of a 9 W noebook adaper. This is a flyback converer (igure 5) working in coninuous mode. The oupu volage V ou is 19 V and he maximum oupu curren is 4.7 A. The recifier diode is an ST power Schoky STPS3M1S. igure 6 shows he ideal waveforms of he diode: Min 4 A, 11.8 A and.6. Le us calculae he maximum conducion losses in he diode for his applicaion. igure 5. lyback converer V in STPS3M1S load AC Line Snubber V ou Conrol igure 6. deal curren and volage waveforms of he diode in he flyback converer. () Min V () V V R 8/1 oc 367 Rev 3

9 AN64 An applicaion example 3.1 Average and rms curren calculaion The firs sep is he calculaion of he average and rms currens. The forward average curren is he oupu curren: (AV) load 4.7 A. As illusraed in igure 6, he forward curren has a rapezoidal shape. The formula o calculae he rms curren of rapezoidal waveform is given in igure 4. (RMS) is hen: Equaion 15 ( 11.8) + ( 4) (RMS) A 3 3. V T (T ) and R (T ) calculaion The second sep is he calculaion of V T (T ) and R (T ) in he applicaion condiion range. igure 7. STPS3M1S forward volage drop versus forward curren M T 15 C (imum values) 11.8A T 15 C (Typical values) Min 4A T 5 C (imum values).5v.63v.43v.55v T ref1 5 C and T ref 15 C. To calculae maximum conducion losses, read maximum values of V a Min and in igure 7. This figure is available in he STPS3M1S daashee. These values are summarized in Table 1. Table 1. V () values a Min and (A) V () (, 5 C) (V) V () (, 15 C) (V) Min oc 367 Rev 3 9/1

10 An applicaion example AN64 rom Equaions (3), (4), (8) and (9) calculae V T (T ref1 ), V T (T ref ), R (T ref1 ), R (T ref ), α VT and α R. Calculaed values of hese parameers are summarized in Table. Table. V T, R, α VT, and α R parameers T ref ( C) V T (V) R (mω) α VT (V C -1 ) α R (Ω C -1 ) T ref T ref rom Equaions 5 and 6 we can wrie V T (T ) and R (T ) as follow: Equaion 16-6 V (T ) T T Equaion 17 R (T ) T 3.3 Conducion losses expression rom Equaions 7, 15 and 16 he expression for maximum conducion losses is hen: Equaion 18 P (T ) CON() -3 T inally, le us plo he value of conducion losses in he diode as a funcion of he uncion emperaure (igure 8). igure 8. imum conducion losses versus uncion emperaure 3.W P CON() (T).8W.6W.4W.W T.W 5 C 35 C 45 C 55 C 65 C 75 C 85 C 95 C 15 C 115 C 15 C 1/1 oc 367 Rev 3

11 AN64 Revision hisory 4 Revision hisory Table 3. ocumen revision hisory ae Revision Changes Aug niial release 3-May-4 Syleshee updae. No conen change 4-Aug-11 3 Compleely revised for currenly available producs. oc 367 Rev 3 11/1

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