application note 1/5 AN661/1194 by t. castagnet calculation of the losses in a chopper topology figure 1. basic diagram of a general dc motor control 1. introduction in chopper applications, the components which dissipate power are: ? the input rectifier bridge; ? the free wheeling diode; and ? the power switch. this paper analyses the losses in the chopper in the fast rectifier (using a stta806di as an example) and the igbt (using a stgp10n50). the input capacitor has a small value in order to reduce inrush current at start-up, and to reduce input low frequency harmonic currents. the input voltage is 100 hz full-wave rectified ( see figure 5). the transistor is controlled through a low gate resistance (20 w ) in order to increase turn-off speed. turn-on is controlled by the transistor emitter inductance. 2. calculation of the losses in one switching cycle 2.1 the fast rectifier for free wheeling operation, we can neglect the turn-on and off state losses: e ton = 0 ; e off = 0 ; the dissipated energy of the device mainly consists of the conduction energy, e on, and the turn-off losses energy, e toff : e on = t sw . ( v to . i fav + r d . i frms 2 ) with i fav = d . i p ; i frms = i p . ?d on high inductive load (square waveforms) d = diode duty cycle (1 - transistor duty cycle) e toff = ( s . v r . i rm 2 ) / ( 6 . di f /dt ) with di f /dt = di c /dt (controlled by transistor drive) igbt diode m rfi filter driver
application note 2/5 2.2 the igbt transistor in motor control applications the switching frequency f sw of the igbt transistor is generally less than 20khz; therefore we neglect its gate energy e g .the off state energy e off is also negligible. the dissipated energy is the conduction energy, e on , the turn on energy, e ton , and the turn off energy, e toff : e on = t sw . (e o . i cav + r t . i crms 2 ) with i cav = d . i p , i crms = i p . ?d on high inductive load (square waveforms) e ton = v ce . [(i rm + i c ) 2 /2 + s .i rm .(2.i c + 3.i rm )/6 ] / (di c /dt) ? 1.1 . v ce . (i rm + i c ) 2 / ( 2 . di c /dt ) where diode parameters i rm and s depend mainly from di c /dt & t jd e toff ? v ce . i t . t t / 2 + i c . v ce 2 / ( 2 . dv ce /dt ) the information given by this formula can often be found in the device datasheet. the value for a particular application is obtained using the figures 2., 3. and 4. : e toff is almost proportional to v ce and i c . 0 50 100 150 200 250 300 350 400 450 500 0 20 40 60 80 100 120 v ce ( v ) e t(off) ( % ) 0 5 10 15 20 25 30 35 0 50 100 150 200 250 300 i c ( a ) e t(off) ( % ) figure 2. turn-off energy e toff versus applied voltage v ce . r g =47 w w w w w , i c = 10a, t j = 100 o c figure 3. turn-off energy e toff versus collector current i c . r g =47 w w w w w , v ce =400v, t j =100 o c stgp10n50 stgp10n50 figure 4. turn-off energy e toff versus junction temperature t j . r g =47 w w w w w , i c =10a, v ce =400v, v ge = 15v stgp10n50 0 25 50 75 100 125 150 50 60 70 80 90 100 110 120 t j ( o c ) e t(off) ( % ) 3. calculation of losses in one mains half cycle (10ms) 3.1 an approach to the calculation of the losses in chopper applications, devices turn on and off the motor current i mot , while the voltage across them is the direct line voltage u d : these two values define the chopper losses. in one mains half cycle, the dissipated energy can be calculated by adding the losses of all switching cycles during this time. modelling i mot and u d simplifies the evaluation. for switching losses, it can be assumed we suggest that the motor current i mot is almost constant (i c = i av ), and that the direct voltage u d is full wave rectified (u d = 2 x ? 2 x u a / p ). e sw = s j [ e sw (v ce j , i c j )] = s j e sw (u d j , i av ) with 1 j n ? t / t sw , and n 3 50 e sw = 2 . e sw (u a . ? 2 , i av ) / p (a) when e sw is proportional to v ce ( a ) e sw = e sw (u a . ? 2, i av ) / 2 when e sw is proportional to v ce 2 3.2 calculation of conduction losses of the igbt conduction losses energy of all switching cycles on one half cycle are added : e on = s j ( e on ) = t sw . [ e o . d . s j i cp (j) + r t . d . s j i cp (j) 2 ] e on = t . d . [ e o . i av + r t . i rms 2 ]
3/5 application note because n 3 50 and s j i cp (j) . t sw ? i av . t s j i cp (j) 2 . t sw ? i rms 2 . t the conduction losses in one half mains cycle are: p on = d . [ e o . i av + r t . i rms 2 ] ( b ) 3.3 calculation of the switching losses of the igbt the switching losses are evaluated as shown with formula ( a ) : e ton ? 1.1 . t . f sw . u a . ? 2 .( i av + i rm ) 2 / ( p . di c /dt) e toff ? t . 2 . f sw . e toff ( u a . ? 2 , i av ) / p p sw ? ( e ton + e toff ) / t ( c ) 3.4 calculation of the diode conduction losses the dissipation in conduction can be calculated in the same way as with the igbt : p on = (1 - d ) . [ v to . i av + r d . i rms 2 ] ( d ) 3.5 calculation of the diode switching losses di c /dt is is assumed to be constant, and therefore the diode parameters s and i rm become independent of v r : p sw ? e toff / t p sw ? u a . ? 2 . f sw . s . i rm 2 / ( 3 . p . di c /dt ) (e) the result is overrated because di c /dt depends on u a and s depends on i mot , but these are much lower than other chopper losses . 4. thermal rating for a reasonable safety margin, the aim should be to limit the operating junction temperature of the diode and the igbt to around 125 o c. generally the diode and the igbt are considered to be far enough apart on the heat sink for their cooling to be independent of each other. the thermal resistances of the igbt and the rectifier are calculated separately. the whole heat sink is the result of paralleling the heatsinks required for the two devices. for each power device thermal cooling is defined as: (p sw + p on ) = (r th + r th(ct) + r th(jc) ) . (t j - t amb ) (f) the heat sink thermal resistance is calculated as: r th(ht) = r th(d) . r th(t) / ( r th(d) + r th_t ) (g) when the devices are too close for this assumption to be made, mutual thermal impedances should be taken into account. 5. conclusion this note gives some pointers to the design of the cooling system of a chopper converter. the thermal calculation should be confirmed by practical tests to fully validate the cooling rating. when the power of the system is less than 500w and the switching frequency is round 16khz, the losses will be mainly generated by the turn off of the igbt. figure 5. waveforms of applied mains voltage u d and the motor current i mot (worst case) in a washing machine application) v r i p i m i mot u d t
application note 4/5 appendix 1. terminology e ton = turn on energy ) e on = conduction energy ) for the diode and e toff = turn off energy ) the igbt e off = off state energy ) e g = gate energy t jd = junction temperature of the diode s = softness factor of the diode i rm = reverse recovery of the diode v to = on state threshold voltage of the diode (@ t j max ) r d = dynamic on state resistance of the diode (@ t j max ) i fav = average forward diode current i frms = r.m.s forward diode current di f /dt = rate of removal of diode current at turn off v r = reapplied diode voltage ( direct voltage ) d = diode duty cycle d = transistor duty cycle t sw = switching period f sw = switching frequency i crms = r.m.s. collector current ) i cav = average collector current ) of the igbt i cp = peak collector current ) di c /dt = turn on rate of rise of collector current of the igbt v ce = turn off reapplied voltage of the transistor t jt = junction temperature of the transistor e o = on state threshold voltage of the igbt ( @ t j max ) r t = dynamic resistance of the igbt (@ t j(max) ) i t = tail current of the igbt t t = tail current duration u a = mains voltage i rms = r.m.s. motor current i av = average motor current i p = peak motor current t = half period of the mains (10 ms) p on = total conduction losses power ) for p sw = total switching losses power ) diode r th_x = device heat sink thermal ) (x=f) resistance ) or r th_jc = junction case thermal ) igbt resistance ) (x=t) p t = total losses power ) r th_ht = total heat sink thermal resistance r th_ct = case contact thermal resistance appendix 2. calculation of the average and rms values of common waveforms sine wave: i av = 2 . i p . d p i rms =i p . ? d 2 square wave: i av = i p . d i rms =i p . ?d triangular wave: i av =i p . d 2 i rms = i p . ? d 3 trapezoid: i av = d . i a + i b 2 i rms = ? d . i a 2 + i a .i b + i b 2 3 i p i p i p t on d = t on / t t 0 i b i a
5/5 application note information furnished is believed to be accurate and reliable. however, stmicroelectronics assumes no responsibility for the co nsequences of use of such information nor for any infringement of patents or other rights of third parties which may result from i ts use. no license is granted by implication or otherwise under any patent or patent rights of stmicroelectronics. specification mentioned in this publication are subject to change without notice. this publication supersedes and replaces all information previously supplied. stmicroelectron ics products are not authorized for use as critical components in life support devices or systems without express written approval of stmic roelectronics. the st logo is a trademark of stmicroelectronics ? 1999 stmicroelectronics - printed in italy - all rights reserved stmicroelectronics group of companies australia - brazil - china - finland - france - germany - hong kong - india - italy - japan - malaysia - malta - morocco - singapore - spain - sweden - switzerland - united kingdom - u.s.a. http://www.st.com
|
