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november 2013 docid025557 rev 1 1/39 AN4402 application note multichannel drivers driving inductive loads with l99mc6 and l9733 introduction the l99mc6 and the l9733 are respectively hexa and octal multi-channel drivers capable of driving various types of loads: resistive, inductive, capacitive loads and leds. they integrate an spi interface for a high level of configurability, offering detailed device diagnostics and protection features such as overtemperature, overcurrent detection, in order to support robust automotive designs. the output stages of these flexible devices consist of n-channel mosfets. they both have an internal charge pump which allows all the outputs of the l9733 and three outputs of the l99mc6 (outputs 1, 2, 3) to control loads either in high-side or in low-side configuration without additional components. the l99mc6 outputs 4, 5 and 6 are fixed low-side drivers. figure 1. block diagrams on the l99mc6 and l9733 ("1($'5 6 ## 3#+ #3. $/ $) #ontrol logic 30) ).07- $2. 3#2 $2. 3#2 $2. 3#2 $2. $2. $2. 6$$ #,+ #3 $/ $) 07-). 07-). 30) #ontrol logic 07-). 6$/ 2%3 6"!44 $2. 3#2 $2. 3#2 $2. 3#2 $2. $2. $2. 3#2 3#2 3#2 $2. 3#2 $2. 3#2 -.$ - www.st.com
contents AN4402 2/39 docid025557 rev 1 contents 1 description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 active clamp of the l99mc6 and l9733 . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 low-side configured outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 high-side configured outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 case 1: v bat v cl_ls - v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 case 2: v bat v cl_ls - v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 demagnetization energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1 low-side configured output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 3.2 calculation of the demagnetization energy . . . . . . . . . . . . . . . . . . . . . . . .11 3.2.1 summary of the demagnetization energy ? low-side . . . . . . . . . . . . . . . 15 3.2.2 calculation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 high-side configured outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3.1 demagnetization energy with vbat < vcl_ls ? vcl_hs . . . . . . . . . . 17 3.3.2 demagnetization energy with vbat > vcl_ls ? vcl_hs . . . . . . . . . . 19 3.4 clamping energy at high battery voltage . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4.1 qualitative analysis when the gate-drain clamp is active . . . . . . . . . . . 21 3.4.2 example of a low-side configured output of the l99mc6 . . . . . . . . . . . 23 3.4.3 example of a high-side configured output of the l99mc6 . . . . . . . . . . . 24 3.4.4 conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 energy capability and load compatibility . . . . . . . . . . . . . . . . . . . . . . . 27 4.1 guideline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2 example of l99mc6 driving a relay with a low-side driver . . . . . . . . . . . . 28 appendix a documents reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 appendix b glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 appendix c summary of the demagnetization energy . . . . . . . . . . . . . . . . . . . . 35 revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
docid025557 rev 1 3/39 AN4402 list of tables 3 list of tables table 1. specification of clamping voltages - l99mc6 and l9733 . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 table 2. e demag_ls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 table 3. example of application parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 table 4. energy parameters vs r p values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 table 5. analogies between the equations for a low-side and a high-side . . . . . . . . . . . . . . . . . . . . 17 table 6. e demag1_hs with v bat < v cl_ls ? v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 table 7. e demag2_hs with v bat > v cl_ls ? v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 table 8. low-side output - conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 table 9. overestimation of e demag caused by the simplification: r l = 0 ? . . . . . . . . . . . . . . . . . . . 23 table 10. high-side output - conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 table 11. energy values vs battery voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 table 12. application conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 table 13. e demag_max and corresponding t demag for a single pulse, t jstart = 150c, r l = 0 ? , v bat = 13.5 v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 table 14. e demag_max and corresponding t demag for a repetitive pulse with t jstart = 100 c, r l = 0 ? , v bat = 13.5 v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 table 15. glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 table 16. demagnetization time and demagnetization energy for a low-side configured output . . . . 35 table 17. demagnetization time and demagnetization energy for a high-side configured output . . . 36 table 18. document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
list of figures AN4402 4/39 docid025557 rev 1 list of figures figure 1. block diagrams on the l99mc6 and l9733 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 figure 2. low-side and high-side configured output driving inductive loads . . . . . . . . . . . . . . . . . . . . 6 figure 3. low-side of a l99mc6 during the turn-off phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 figure 4. l99mc6 high-side during the turn-off, v bat < v cl_ls - v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 figure 5. l99mc6 high-side during the turn-off, v bat > v cl_ls - v cl_hs . . . . . . . . . . . . . . . . . . . . . . 9 figure 6. relay with spike protection resistor in parallel to the coil . . . . . . . . . . . . . . . . . . . . . . . . . . 10 figure 7. equivalent electrical diagram during the turn-off phase of an inductive load with parallel resistor, driven by a low-side configured output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 figure 8. equivalent electrical diagram of the turn-off phase of an inductive load driven by a low-side configured output, without parallel resistor to the load . . . . . . . . . . . . . . . . . . . . . 14 figure 9. e demag_ls vs r p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 figure 10. equivalent circuit during the demagnetization of a high-side with parallel resistor, v bat < v cl_ls - v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 figure 11. equivalent circuit during the demagnetization of a high-side with parallel resistor, v bat > v cl_ls - v cl_hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 figure 12. contribution of the factor 1 / (1 - (v cl_ls /v bat )) to the increase e demag with v bat . . . . . 22 figure 13. e demag_ls vs v bat ? example of a low-side output of the l99mc6 . . . . . . . . . . . . . . . . . 23 figure 14. example - relative e demag_ls to e demag@vbat=13v versus v bat /13v (no parallel resistor) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 figure 15. e demag_hs vs v bat ? example of a high-side output of the l99mc6 . . . . . . . . . . . . . . . . 25 figure 16. datasheet l99mc6 - inductive energy capability of configurable channels, configured as low-side switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 figure 17. e demag_max vs t demag for a single pulse t jstart = 150c . . . . . . . . . . . . . . . . . . . . . . . 30 figure 18. e demag_max vs t demag for repetitive pulse t jstart = 100c . . . . . . . . . . . . . . . . . . . . . . 31
docid025557 rev 1 5/39 AN4402 description 38 1 description this document describes the protection features implemented in the l99mc6 and l9733 to control inductive loads. it provides calculations of the energy dissipated in the output mosfets of these devices during the switch-off phase of this type of loads in different configurations: ? the outputs are configured either as low-side or high-side drivers ? with and without parallel resistor to the inductive load although the examples are applied to the l99mc6, general results are also applicable to devices integrating the same type of active clamping protections. finally, the developers will find a guideline to verify if the outputs of these devices are compatible with their load specifications and application conditions.
active clamp of the l99mc6 and l9733 AN4402 6/39 docid025557 rev 1 2 active clamp of the l99mc6 and l9733 by nature, an inductive load such as a relay coil develops a voltage across its terminals in order to resist the current variations passing through it. according to lenz's law, the voltage across the inductor is proportional to its inductance and to the rate of change of the current: v l = l di l / dt. this voltage can reach very high values when the current is abruptly turned off. opening mechanically a circuit with an energized inductor without any protection will result in a high voltage surge across the load of possibly several hundreds of volts, which can cause an electrical arc. during the turn-off phase of a mosfet driving an inductive load the voltage across the drain and the source of the mosfet (v ds ) will increase until the mosfet breakdown voltage is reached. it is the so-called avalanche effect. operating in avalanche can have a negative impact on the lifetime of standard mosfets. the output stages of the l99mc6 and of the l9733 consist of protected n-channel mosfets which can be driven either in low-side or high-side configuration. in order to avoid avalanche conditions during the switch-off of an inductive load, the l99mc6 and the l9733 integrate a so-called active clamp, which limits v ds below the mosfets' breakdown ( figure 2 ). indeed, during the turn-off of inductive loads, the output mosfet is driven in linear (and high dissipation) mode. this results in a higher control capability of this type of loads without additional devices. figure 2. low-side and high-side conf igured output driving inductive loads +ljk6lgh&rqiljxudwlrq 2/ ' 92/' /rjlf 92/6 6 9 %$7 5 / , / / 9'5,9( 9 6 /rz6lgh&rqiljxudwlrq 2/ ' 92/' 9'5,9( /rjlf 9 %$7 / 5 / , / 9 '6 9 ' *dwh'udlq dfwlyhfodps *dwh'udlq dfwlyhfodps *dwh6rxufh dfwlyhfodps 9 %$7 6rxufhyrowdjh9 6 *1' 9 &/b+6 9 6 , 287 7lph , / /rdgfxuuhqw, / w '(0$*b/6 w '(0$*b+6 7lph *1' 9 &/b/6 9 %$7 /rdgfxuuhqw, / 'udlqyrowdjh9 ' 9 ' , 287 , / ("1($'5
docid025557 rev 1 7/39 AN4402 active clamp of the l99mc6 and l9733 38 2.1 low-side configured outputs right after the turn-off of a low-side switch, the inductor current decreases, and v l goes negative with the sign convention ( figure 3 ). consequently, the mosfet drain-source voltage v ds increases until v ds reaches v zener_ls + v f + v gs_th = v cl_ls . at this moment the mosfet is turned back on in linear mode. the control loop consisting of a zener between the mosfet gate and drain ( figure 3 ) is called the gate-drain clamp in the rest of the document. this circuits maintains v ds (=v d , since the source is connected to gnd in this case) to v cl_ls until the energy stored in the inductor is completely dissipated (waveform on figure 2 ). v cl_ls has been chosen below the mosfet breakdown in order to avoid the avalanche conditions. this protection reduces the stress applied to the mosfet. figure 3. low-side of a l99mc6 during the turn-off phase 2.2 high-side configured outputs for a high-side configured output, either the gate-drain clamp or the gate-source clamp is activated ( figure 7 and figure 8 ), depending on the conditions. we can distinguish two cases: ? case 1: v bat < v cl_ls - v cl_hs ? case 2: v bat > v cl_ls - v cl_hs 2/ ' 92/' 9'5,9( /rjlf 9 %$7 9 / *dwh'udlqdfwlyhfodps 9 '6 9 &/b/6 / l / 5 / 9 =(1(5b/6 9 ) 9 *6b7+ 9 &/b/6 9 =(1(5b/6 9 ) 9 *6b7+ ("1($'5
active clamp of the l99mc6 and l9733 AN4402 8/39 docid025557 rev 1 2.2.1 case 1: v bat v cl_ls - v cl_hs during turn-off, the evolution of the voltage across the inductor causes v s to go negative ( figure 2 ) and the gate-source clamp ( figure 3 ) is activated when v s = -v cl_hs . note: in this document v cl_hs is considered positive. v s is maintained at -v cl_hs . therefore v ds = v bat + v cl_hs < v cl_ls and the gate-drain clamp is not activated. figure 4. l99mc6 high-side during the turn-off, v bat < v cl_ls - v cl_hs case 1 corresponds to a demagnetization of the inductive load at typically v bat 16 v for the l99mc6 and at v bat 36 v for the l9733. it is applicable to the nominal battery voltage for automotive applications (13.5 v). note: the gate-source clamp only maintains v s to -v cl_hs . i l is still supplied by the battery and not by the gate-source clamp. 2/ ' 92/' 9&& /rjlf 'xulqjwkhwxuqriiskdvh 9 / /gl / gwvlqfhl / ghfd\v 9 &/b+6 9 =(1(5b+6 9 ) 9 *6b7+ 9 6 lvpdlqwdlqhgdw9 &/b+6 *dwh'udlqdfwlyhfodps 92/6 6 *dwh6rxufhdfwlyhfodps 9 %$7 5 / l / 9 *6b7+ 9 ) 9 =(1(5b+6 9 6 9 &/b+6 9 / /gl / gw 9 %$7 9 &/b/6 9 &/b+6 ("1($'5 table 1. specification of clamping voltages - l99mc6 and l9733 l99mc6 l9733 typ. v cl_ls 35 v datasheet parameter: v drn_cl1-6 55 v datasheet parameter: drn1-8cl typ v cl_hs 19 v datasheet parameter: v src_cl1-3 19 v datasheet parameter: src_1-8cl v bat limit for case1 / case2 16 v 36 v
docid025557 rev 1 9/39 AN4402 active clamp of the l99mc6 and l9733 38 2.2.2 case 2: v bat v cl_ls - v cl_hs at the turn-off, the evolution of the voltage across the inductor causes an increase of v ds until v ds = v cl_ls . then, the gate-drain clamp is activated (see figure 5 ), like for a low-side switch. v ds is maintained at v cl_ls = v zener_hs + v f + v gs_th . since v s = v bat - v cl_ls > - v cl_hs , this prevents the activation of the gate-source clamp. figure 5. l99mc6 high-side during the turn-off, v bat > v cl_ls - v cl_hs case 2 corresponds to a demagnetization of the inductive load for v bat 16 v for the l99mc6 and for v bat 36 v for the l9733. 2/ ' 92/' 9&& /rjlf 'xulqjwkhwxuqriiskdvh 9 / /gl / gwvlqfhl / ghfd\v 9 &/b/6 9 =(1(5b/6 9 ) 9 *6b7+ *dwh'udlqdfwlyhfodps 92/6 6 +ljkvlghdfwlyhfodps 9 %$7 5 / l / 9 *6b7+ 9 ) 9 =(1(5b+6 9 / /gl / gw 9 %$7 !9 &/b/6 9 &/b+6 9 '6 9 &/b/6 ("1($'5
demagnetization energy AN4402 10/39 docid025557 rev 1 3 demagnetization energy in this section, we propose to calculate the energy dissipated in the output mosfets of the l99mc6 and l9733 during the switch-off of an inductive load. we will distinguish the following conditions: ? the output is configured either as high-side or low-side driver ? with or without resistor placed in parallel (note r p ) to the inductive load r p is often placed in parallel to the relay coil in automotive applications in order to attenuate the voltage surge caused by the coil when the circuit is opened ( figure 6 ). figure 6. relay with spike protection resistor in parallel to the coil in order to determine e demag , we will take a deeper look at the evolution of the current flowing through the inductive load (noted i l ) and r p (noted i p ), between the mosfet turn- off and i l reaching zero. we consider: ? the time origin as the moment when the mosfet is switched off ? the current through the inductor at t = 0 as i l0 = i l (t = 0) ? the demagnetization time, noted t demag , as the time required for i l to reach zero ? the energy dissipated in the mosfet during the switch-off phase is noted e demag 5hod\frqwdfw 5hod\frlo/5 / 6xujhsurwhfwlrquhvlvwru 5 3 ("1($'5
docid025557 rev 1 11/39 AN4402 demagnetization energy 38 3.1 low-side configured output figure 7 represents the equivalent electrical diagram during the turn-off phase of a low-side configured output which drives an inductive load with parallel resistor. figure 7. equivalent electrical diagram duri ng the turn-off phase of an inductive load with parallel resistor, driven by a low-side configured output. v l is negative during the turn-off phase according to the used sign convention, since di l /dt < 0. 3.2 calculation of the demagnetization energy right after the turn-off, assuming that the active clamp is activated (i cl > 0): equation 1 equation 2 with taking the time origin as the moment when the output is turned off, this differential equation ( equation 2 ) accepts the following general solutions (for t 0): 9 &/b/6 l 3 l / / 5 / 5 3 9 / /gl / gw 9 %$7 9 5/ 5 / l / 9 53 5 3 l 3 l &/ ("1($'5 v bat r l i l l di l dt ------- - v cl_ls ++ = di l dt ------- - i l --- - + v bat v cl_ls ? r l --------------------------------------- - = l r l ------ - =
demagnetization energy AN4402 12/39 docid025557 rev 1 equation 3 where a is a constant which is determined by the boundary condition: equation 4 substituting a with its expression in equation 3 gives: equation 5 considering that: equation 6 equation 7 combining equation 5 , equation 6 and equation 7 : equation 8 r l // r p is the equivalent resistance of r l in parallel with r p : equation 9 equation 8 is valid if i cl (t) 0 otherwise the active clamp is not triggered. in particular at t = 0, i cl (t = 0) 0 is equivalent to: i l t () ae t -- ? v bat v cl_ls ? r l --------------------------------------- - + = i l t0 = () a v bat v cl_ls ? r l --------------------------------------- - + i l0 v bat r l -------------- === i l t () v cl_ls r l ------------------- e t -- ? v cl_ls v bat ? r l --------------------------------------- - for t 0 () ? = r p i p v bat v cl_ls ? = i cl t () i p t () i l t () + = i cl t () v cl_ls r l ------------------- e t -- ? v cl_ls v bat ? r l // r p --------------------------------------- - ? = r l // r p 1 1 r l ------ - 1 r p ------ - + --------------------- r l r p r l r p + -------------------- - ==
docid025557 rev 1 13/39 AN4402 demagnetization energy 38 equation 10 if r p does not satisfy this condition, the energy stored in the inductance would be dissipated only in r l and r p and no additional energy is dissipated in the output mosfet. in general, r p is high-ohmic enough to satisfy this condition. a low-ohmic value of r p would result in significant power losses during the activation of the relay. moreover, this would lead to a much longer demagnetization time and possibly decreases the reliability of some loads such as relays. equation 8 is valid until t = t demag_ls , where t demag_ls is defined by i cl (t demag_ls ) = 0: equation 11 the energy which is dissipated in the low-side driver during the turn-off phase is equal to the integration of the dissipated power v cl_ls i cl (t) from t = 0 to t = t demag . using the expression of i cl (t) given by equation 8 , we obtain: equation 12 finally, the demagnetization energy dissipated in the low-side driver with a parallel resistor to the inductor is: equation 13 if no parallel resistor to the inductive load is present, it is possible to derive the demagnetization time and energy directly from figure 8 . another possibility is to determine t demag_ls and e demag_ls in this condition from equation 11 and equation 13 , when r p tends to + (and r l // r p tends to r l ). r p v cl_ls v bat ? v bat --------------------------------------- - r l > ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- - r l // r p r l ------------------- - ?? ?? ?? = e demag_ls v cl_ls t = 0 tt demag_ls = ? v cl_ls r l ------------------- e t -- ? v cl_ls v bat ? r l // r p --------------------------------------- - ? ?? ?? ?? dt = e demag_ls v cl_ls r l ------ - v cl_ls r l // r p ------------------- - v cl_ls v bat ? () ? 1 r p r l r p + -------------------- - v cl_ls v cl_ls v bat ? --------------------------------------- - ? ?? ?? ?? ln + ?? ?? ?? ? ? ? ? ? ? =
demagnetization energy AN4402 14/39 docid025557 rev 1 figure 8. equivalent electrical diagram of the turn-off phase of an inductive load driven by a low-side configured output, without parallel resistor to the load v l is negative during the turn-off phase according to the used sign convention, since di l /dt < 0. equation 14 equation 15 the theoretical case where r l = 0 ? is considered by using v bat = r l i l0 for r l > 0: equation 16 using the maclaurin development of order 2 of for x in the vicinity of 0 with , we obtain: 9 &/b/6 l / / 5 / 9 / /gl / gw 9 %$7 9 5/ 5l / l &/ ("1($'5 lim r p + e demag_ls l r l ------ - v cl_ls i l0 v cl_ls v bat ? r l --------------------------------------- - v cl_ls v cl_ls v bat ? --------------------------------------- - ?? ?? ?? ln ? ?? ?? ?? = lim r p + t demag_ls l r l ------ - v cl_ls v cl_ls v bat ? --------------------------------------- - ?? ?? ?? ln = v cl_ls v cl_ls v bat ? --------------------------------------- - ?? ?? ?? ln v cl_ls v bat r l i l0 + ? v cl_ls v bat ? ------------------------------------------------------------- - ?? ?? ?? ln 1 r l i l0 v cl_ls v bat ? --------------------------------------- - + ?? ?? ?? ln = ? ? ? = 1x + () ln x x 2 2 ----- - ? 0x 2 () + = x r l i l0 v cl_ls v bat ? --------------------------------------- - =
docid025557 rev 1 15/39 AN4402 demagnetization energy 38 equation 17 equation 18 3.2.1 summary of the demagnetization energy ? low-side 3.2.2 calculation example an output of the l99mc6 is configured as low-side driver and it controls an inductive load in the following conditions: e demag_ls r p + r l 0 lim 1 2 -- - li l0 2 v cl_ls v cl_ls v bat ? --------------------------------------- - ?? ?? ?? = t demag_ls r p + r l 0 lim li l0 v cl_ls v bat ? --------------------------------------- - = table 2. e demag_ls conditions demagnetization energy in a low-side driver: e demag_ls with parallel resistor to the inductive load r l > 0 ? equation 19 with , valid if without parallel resistor to the inductance r l > 0 ? equation 20 with without parallel resistor to the inductance r l = 0 ? equation 21 with v cl_ls r l ------ - v cl_ls r l // r p ------------------- - v cl_ls v bat ? () ? 1 r p r l r p + -------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ? ?? ?? ?? ln + ?? ?? ?? ? ? ? ? ? ? l r l ------ - = r p v cl_ls v bat ? v bat --------------------------------------- r l > ------ - v cl_ls i l0 v cl_ls v bat ? r l --------------------------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ln ? ?? ?? ?? ------------- - = 1 2 -- - li l0 2 v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ------------- - =
demagnetization energy AN4402 16/39 docid025557 rev 1 we verify that the condition on r p ( equation 10 ) is satisfied: r p must be higher than 79 ? . using the formulas of table 2 , we have: figure 9. e demag_ls vs r p r p dissipates a part of the energy stored in the inductor. as r p decreases, i p increases and the amount of energy transferred from the inductor to r p increases as well. table 3. example of application parameters parameter value v bat 13v l512mh r l 46 r p 200 ? - 10k ? and no r p (r p + ) v cl_ls 35v (typical value of the l99mc6) table 4. energy parameters vs r p values r p [ ? ]t demag_ls [ms] e demag_ls [mj] e demag_ls decrease due to r p [mj] 200 2.9 8.3 15.3 300 3.6 12.4 11.2 400 4.0 14.8 8.8 600 4.3 17.5 6.1 1k 4.7 19.8 3.8 10k 5.1 23.2 0.4 no r p ( r p + ) 5.2 23.6 ? ("1($'5 ? ? ? ?? ? ? e ? d'z>^?u:? z w ? : ?
docid025557 rev 1 17/39 AN4402 demagnetization energy 38 moreover, the demagnetization time decreases when r p decreases, therefore the battery supplies less energy during the demagnetization phase. is negative since r l // r p < r l. this term further decreases when r p decreases. this explains the decrease of e demag , when r p decreases. the drawback of a low value of r p is the fact that the power losses in r p , when the inductive load is on, are higher as the r p value is lower. 3.3 high-side configured outputs 3.3.1 demagnetization energy with v bat < v cl_ls ? v cl_hs by similarity between the circuits displayed in figure 7 and figure 10 , we have the following equivalence between low-side and high-side configured outputs when v bat < v cl_ls ? v cl_hs : low-side: v cl_ls ? high-side: v bat + v cl_hs replacing v cl_ls by v cl_hs + v bat in equation 19 , equation 20 and equation 21 provides the expression of the energy dissipated in the high-side driver during the switch-off phase. t demag_ls l r l ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- - r l // r p r l ------------------- - ?? ?? ?? l r l ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- - ?? ?? ?? r l // r p r l ------------------- - ?? ?? ?? ln + ?? ?? ?? == r l // r p r l ------------------- - ?? ?? ?? ln table 5. analogies between the equations for a low-side and a high-side low-side high-side, v bat < v cl_ls ? v cl_hs v ds v cl_ls v bat + v cl_hs voltage drop across the load v bat - v cl_ls - v cl_hs i l (t) with and with and di l dt ------- - i l --- - + v bat v cl_ls ? r l --------------------------------------- = l r l ------ - = i l t0 = () i l0 v bat r l ------------- - == di l dt ------- - i l --- - + v cl_hs r l ------------------- ? = l r l ------ - = i l t0 = () i l0 v bat r l ------------- - ==
demagnetization energy AN4402 18/39 docid025557 rev 1 table 6. e demag1_hs with v bat < v cl_ls ? v cl_hs conditions e demag1_hs : v bat < v cl_ls ? v cl_hs r l > 0 ? with parallel resistor to the inductor equation 22 with , valid if r l > 0 ? no parallel resistor to the inductor: r p = + equation 23 with r l = 0 ? r p = + equation 24 with v cl_hs v bat + () r l ------ - v cl_hs v bat + () r l // r p -------------------- v cl_hs () ? 1 r p r l r p + -------------------- v cl_hs v bat + v cl_hs ---------------------------------------- ? ?? ?? ?? ln + ?? ?? ?? ? ? ? ? ? ? l r l ------ - = r p v cl_hs v bat ------------------- r l > ------ - v cl_hs v bat + () i l0 v cl_hs r l ------------------- v cl_hs v bat + v cl_hs ---------------------------------------- ?? ?? ?? ln ? ?? ?? ?? ------------- - = 1 2 -- - li l0 2 v cl_hs v bat + v cl_hs ---------------------------------------- ?? ?? ?? ------------- - =
docid025557 rev 1 19/39 AN4402 demagnetization energy 38 figure 10. equivalent circuit during the de magnetization of a high-side with parallel resistor, v bat < v cl_ls - v cl_hs v l is negative during the turn-off phase according to the used sign convention, since di l /dt < 0. 3.3.2 demagnetization energy with v bat > v cl_ls ? v cl_hs as discussed in the section 2.2.2 , the gate-drain clamp is activated. from an electrical point of view figure 7 and figure 10 are equivalent, regardless whether the switch is in high-side or low-side configuration (provided that v bat < v cl_ls ? v cl_hs ). 9 6 9 &/b+6 l 3 l / / 5 / 5 3 9 / /gl / gw 9 %$7 9 5/ 5 / l / 9 53 5 3 l 3 l &/ ' 6 9 '6 9 %$7 9 &/b+6 9 &/b/6 9 %$7 9 &/b/6 9 &/b+6 ("1($'5
demagnetization energy AN4402 20/39 docid025557 rev 1 figure 11. equivalent circuit during the dema gnetization of a high-side with parallel resistor, v bat > v cl_ls - v cl_hs therefore, the results for the low-side configured outputs are directly applicable to the high- side configured outputs when v bat < v cl_ls ? v cl_hs . l 3 l / / 5 / 5 3 9 / /gl / gw 9 %$7 9 5/ 5 / l / 9 53 5 3 l 3 l &/ ' 6 9 '6 9 &/b/6 9 %$7 !9 &/b/6 9 &/b+6 9 6 9 %$7 9 &/b/6 !9 &/b+6 ("1($'5 table 7. e demag2_hs with v bat > v cl_ls ? v cl_hs conditions e demag2_hs : v bat > v cl_ls ? v cl_hs r l > 0 ? with parallel resistor to the inductor equation 25 with , valid if v cl_ls r l ------ - v cl_ls r l // r p ------------------- - v cl_ls v bat ? () ? 1 r p r l r p + -------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ? ?? ?? ?? ln + ?? ?? ?? ? ? ? ? ? ? l r l ------ - = r p v cl_ls v bat ? v bat --------------------------------------- r l >
docid025557 rev 1 21/39 AN4402 demagnetization energy 38 3.4 clamping energy at high battery voltage 3.4.1 qualitative analysis when the gate-drain clamp is active the gate-drain clamp is activated as we will see, the theoretical condition with r l = 0 ? doesn?t provide accurate results, especially when v bat is close or equal to v cl_ls . however, we can draw two qualitative observations from the simplified expression of e demag ( equation 17 ). equation 17 : e demag is higher than the energy stored in the inductor since v bat < v cl_ls , we see from the simplified expression of e demag ( equation 17 ), that the dissipated energy in the output mosfet is higher than the energy stored in the inductor (). this is due to the fact that the battery provides additional energy to the output mosfet during the turn-off phase. e demag increases faster than a square function of v bat i l0 is proportional to the battery voltage (), and the term is proportional to the square of i l0 and therefore to the square of v bat . r l > 0 ? no parallel resistor to the inductor: r p = + equation 26 with r l = 0 ? r p = + equation 27 with table 7. e demag2_hs with v bat > v cl_ls ? v cl_hs (continued) conditions e demag2_hs : v bat > v cl_ls ? v cl_hs l r l ------ - v cl_ls i l0 v cl_ls v bat ? r l --------------------------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ln ? ?? ?? ?? i l0 v bat r l ------------- - = 1 2 -- - li l0 2 v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? i l0 v bat r l ------------- - = e demag_ls r p + r l 0 lim e demag2_ls r p + r l 0 lim 1 2 -- - li l0 2 v cl_ls v cl_ls v bat ? --------------------------------------- - ?? ?? ?? == 1 2 -- - li l0 2 i l0 v bat r l ------------- - = 1 2 -- - li l0 2
demagnetization energy AN4402 22/39 docid025557 rev 1 moreover the factor increases rapidly as v bat gets closer to the clamping voltage. the impact of this term is sometimes overlooked, although it is responsible for a drastic increase of the clamp energy at high v bat . assuming that the inductance is constant, independently from the current level i l0 (no saturation of the inductance), the demagnetization energy increases faster than a square function of v bat , especially when the battery voltage is close to the clamping voltage. figure 12. contribution of the factor 1 / (1 - (v cl_ls /v bat )) to the increase e demag with v bat the gate-source clamp is activated from equation 24 , we observe that the dissipated energy in a high-side configured output, when the gate-source clamp is activated exceeds the energy stored in the inductor. it is also due to the additional energy which is supplied by the battery during the turn-off phase. equation 24 : moreover, the demagnetization energy in this case increases faster than a square function of v bat due to the additional term: . v cl_ls v cl_ls v bat ? --------------------------------------- - 1 1 v cl_ls v bat ------------------- ? ---------------------------- - = ("1($'5 ? ? e ? 9 9 ?9 ?9 e9 ?9 9 9 ?9 l~rs >^z> ls d s >^z> ls d e demag1_hs r p + r l 0 lim 1 2 -- - li l0 2 v cl_hs v bat + v cl_hs ---------------------------------------- ?? ?? ?? = 1 v bat v cl_hs ------------------- +
docid025557 rev 1 23/39 AN4402 demagnetization energy 38 3.4.2 example of a low-side configured output of the l99mc6 figure 13 shows that under the considered conditions ( table 8 ), the simplification r l = 0 ? leads to a significant overestimation of the dissipated energy in the low-side driver. the overestimation is even greater as v bat increases ( tab le 9 ). figure 13. e demag_ls vs v bat ? example of a low-side output of the l99mc6 figure 14 displays the relative evolution of e demag with v bat . the reference is for table 8. low-side output - conditions parameter value l 512 mh r l 46 r p 400 v cl_ls 35 v (typical value of the l99mc6) table 9. overestimation of e demag caused by the simplification: r l = 0 ? v bat e demag [mj] r l > 0 , r p = 400 e demag [mj] r l = 0 ( w/o r p ) overestimation of e demag [mj] with r l = 0 6v 0.9 5.2 4.3 10v 6.6 17 11.4 16v 26.9 57.1 30.2 24v 83.6 221 137 x x x? x? xe x? x x x? ? e ? ? e ? ? ? ????? / > ?? d' ?u:? s d ?s? upe}zwuz>a upe}zw up]?zzw /> ("1($'5
demagnetization energy AN4402 24/39 docid025557 rev 1 v bat = 13 v and r p is not considered. we observe that the e demag_ls increases faster than a square function of v bat , as previously anticipated . for example, doubling v bat from 13 v to 26 v increases e demag_ls by a factor 5. a slight additional increase of v bat to 28.6 v (2.2 x 13 v) increases e demag_ls by a factor 6.35. figure 14. example - relative e demag_ls to e demag@vbat=13v versus v bat /13v (no parallel resistor) 3.4.3 example of a high-side configured output of the l99mc6 ? ? e ? ? ? x x? xe x x? ?x ?x? ?xe d'?sd l d'??s v~s d l?s? s d l?s up?sdlup??s ~sdl?s? sda?s sda??xs x?? ("1($'5 table 10. high-side output - conditions parameter value l 512mh r l 46 r p 400 v cl_hs 16v (typical value of the l99mc6) v cl_ls 35v (typical value of the l99mc6)
docid025557 rev 1 25/39 AN4402 demagnetization energy 38 figure 15 shows that under the considered conditions, the simplification r l = 0 ? leads to a significant overestimation of the dissipated energy in the high-side driver. the overestimation is even greater as v bat increases. considering that the demagnetization energy is the same for a low-side driver and for a high-side driver of the l99mc6 for v bat 16v, the conclusions for high battery voltages are also applicable. figure 15. e demag_hs vs v bat ? example of a high-side output of the l99mc6 table 11. energy values vs battery voltages vbat e demag [mj] r l >0 , r p = 400 e demag [mj] r l =0 ( w/o r p ) overestimation of e demag [mj] with r l =0 6v 1.9 5.7 3.8 10v 8.2 18.5 10.3 16v 29.9 57.1 30.2 24v 83.6 221 137 x x x? x? xe x? x x x? ? e ? ? e ? ? ?????? / > ?? d'z,^ ?u:? s d ?s? upzz>a upzv}zw upzzw /> ("1($'5
demagnetization energy AN4402 26/39 docid025557 rev 1 3.4.4 conclusions from this example, we see that calculating e demag with r l = 0 can lead to a huge overestimation of the dissipated energy in the low-side and high-side drivers, especially at high v bat . therefore, it is more accurate to take into account the impact of load resistance r l (and the parallel resistor r p , if any) on the demagnetization energy. e demag increases with v bat at a faster rate than the quadratic function of v bat . therefore, the developer must be careful about the device compatibility to the considered load, if the outputs drive inductive loads at high battery voltages.
docid025557 rev 1 27/39 AN4402 energy capability and load compatibility 38 4 energy capability and load compatibility although the avalanche condition is prevented by the active clamp, the inductive energy capability of the l99mc6 and l9733 is limited. as the mosfet operates in linear mode with a high v ds , a high power is dissipated during the turn-off phase. the sudden increase of the junction temperature causes a stress to the device. the maximum device capability must not be exceeded in order to avoid permanent damages. this aspect must be taken into account during the development phase. it is possible to identify two main mechanisms that can lead to the device failure: ? the temperature during the demagnetization rises quickly (depending on the inductance) and the uneven energy distribution on the power surface can cause the presence of a hot spot causing the device failure with a single pulse . ? like in normal operation, the lifetime of the device is affected by the fast thermal variation as described by the coffin-manson law. a repetitive demagnetization energy causing a temperature variation above 60k will cause a shorter life time. these considerations lead to two simple design rules: ? the energy dissipated in the application conditions during the corresponding demagnetization time must be lower than the device capability for the same t demag . ? in case of a repetitive pulse, the average temperature variation of the device should not exceed 60k at turn-off. to fulfill these rules, the designer must calculate the energy dissipated in the output mosfet at turn-off and the corresponding t demag and then compare it with the device capability as shown in the example section 4.2 . 4.1 guideline step1: calculation of t demag and e demag this step consists in calculating the demagnetization time and energy dissipated in the output under the defined load and application conditions. the relevant formulas are collected in table 16 and table 17 . step2: maximum energy capability of the device at the relevant t demag the designer must determine the device output capability in terms of demagnetization energy from the datasheet relevant curve with the same demagnetization time. note that the curve providing the current capability for inductive loads of the l99mc6 is valid for the specific conditions: v bat = 13.5v and r l = 0 ( figure 16 ).
energy capability and load compatibility AN4402 28/39 docid025557 rev 1 the l99mc6 provides data under the following conditions: ? single pulse, with t jstart = 150c: it is applicable for switch-off conditions, which occur rarely ? repetitive pulse with t jstart =125c: it is applicable for switch-off conditions, with a high occurrence rate. it is applicable with time between two occurrences is long enough to allow the junction temperature to decrease to 125c ? repetitive pulse with t jstart =100c: it is applicable for switch-off conditions, with a high occurrence rate. it is applicable if the time between two occurrences is long enough to allow the junction temperature to decrease to 100c even if e demag dissipated in the application conditions is below the maximal energy allowed by the device with the same inductance (at r l = 0 and r l = 13.5 v), it does not automatically mean that the load compatibility is given. indeed, it is possible that a lower e demag in the application conditions is dissipated in a shorter time (t demag ), resulting in a higher power dissipation and therefore a higher junction temperature increase. the developer must verify that the energy which has been calculated in the step1 is below the maximum energy capability of the device with the corresponding demagnetization time . step3: confirmation by measurements it is recommended to perform bench tests in the real application conditions. this phase is key because it allows verifying that the load data (inductance and resistance), which are used for the calculations in step1 and step2, are representative of the real application. it avoids either an underdimensioning of the system and therefore unexpected failures, or overdimensioning with the involved extra-costs for external protection devices. some sources of mismatch between calculations and measurement can be: ? a mismatch between the calculation r l and the real r l . indeed, r l is in general specified only at room temperature. since the winding is made of copper, its resistance is subject to variations due to temperature. ? measuring the inductance with a lcr meter by applying a small ac signal does not take into account the impact of the dc voltage bias of the inductance in the real application ? the decrease of the inductance at high currents (saturation of the inductor) might not be taken into account ? self-heating effects of the load on r l and l are not considered 4.2 example of l99mc6 driving a relay with a low-side driver table 12. application conditions parameter value type of output configurable output (out1,2 or 3), configured as low-side switch l512 mh r l 46 r p 400 v cl_ls 35v (typical value of the l99mc6)
docid025557 rev 1 29/39 AN4402 energy capability and load compatibility 38 step 1: calculation of t demag and e demag the demagnetization energy and the demagnetization time under the conditions listed in table 12 are given by equation 19 and equation 11 : e demag_ls = 83.6 mj and t demag_ls = 11.7 ms with v bat,max = 24 v e demag_ls = 16.6 mj and t demag_ls = 4.2 ms with v bat,typ = 13.5 v the validity condition of equation 19 is satisfied since r p > 21 (for v bat = 24 v) and r p > 74 (for v bat = 13.5 v). step 2: maximum energy capability of the l99mc6 at the relevant t demag considering the type of output, the relevant diagram of the datasheet is: ?configurable switch lsd ? maximum turn-off current versus inductance? ( figure 16 ) . note: if the considered output is one of the fixed low-side switches (outputs 4, 5, 6) or one of the outputs configured as high-side driver, the relevant diagrams are respectively ?fixed lsd switch ? maximum turn-off current versus inductance? and ?configurable switch hsd? maximum turn-off current versus inductance?. figure 16. datasheet l99mc6 - inductive energy capability of configurable channels, configured as low-side switch v bat,max (jump start) 24v ? i l0 @ v bat,max = 0.522a, low probability of occurrence v bat,typ 13.5v ? i l0 @ v bat,typ = 0.293a, nominal conditions table 12. application conditions (continued) parameter value /p+ ,$ $ % & $ 6lqjohsxovh7 m ?& % 5hshwlwlyhsxovh7 m ?& & 5hshwlwlyhsxovh7 m ?& ("1($'5 3 - 0 7 #"5 7 -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt -n) * - n" & %&."(@."9 n+ 5 %&."( nt
energy capability and load compatibility AN4402 30/39 docid025557 rev 1 figure 16 displays the maximum allowed current of outputs 1, 2 or 3 (configurable outputs) in low-side configuration, driving an inductive load. different conditions (single or repetitive pulses) and start temperature (junction temperature right before the switch-off phase of the mosfet) are considered. the test conditions for these curves are v bat = 13.5 v and r l = 0 ? . these conditions are different from the application conditions and are therefore not directly applicable to our specific case. one way to verify the load compatibility consists in building the curve e demag,max versus the corresponding t demag from the relevant i-l plot of figure 16 , where e demag,max is the maximum energy which the device can sustain. condition 1: the jump start conditions (v bat,max = 24 v) have a very low probability of occurrence. the single pulse is applicable. from figure 17 , we see that the energy capability of the device for a single pulse at 11.7ms is higher than the energy dissipated in the application conditions. figure 17. e demag_max vs t demag for a single pulse t jstart = 150c condition 2 (v bat,typ = 13.5 v) corresponds to the nominal conditions with t j = 100 c: the repetitive pulse condition is applicable. building the curve e demag,max versus the corresponding t demag for repetitive pulses at t jstart = 100 c from figure 16 , we obtain table 14 and figure 18 . table 13. e demag_max and corresponding t demag for a single pulse, t jstart = 150c, r l = 0 ? , v bat = 13.5 v l [mh] i l0 [a] t demag [ms] r l = 0 ? v bat = 13.5 v e demag_max [mj] r l = 0 ? v bat = 13.5 v 400 0.542 9.9 93 500 0.536 12.2 114 600 0.530 14.4 134 700 0.525 16.7 153 ? ? e ? ? ??e? ? d' ?u?? d'zdy u^]vpo?o?d :^dzd a? ?u:? / p+, / p$ 9 %$7 95/ : ( '(0$*b0$; p- 7 '(0$* pv / p+, / p$ 9 %$7 95/ : ( '(0$*b0$; p- 7 '(0$* pv / p+, / p$ 9 %$7 95/ : ( '(0$*b0$; p- 7 '(0$* pv / p+, / p$ 9 %$7 95/ : ( '(0$*b0$; p- 7 '(0$* pv 'hylfhpd[lpxpdoorzhg hqhuj\a p-zlwk w '(0$* pv $ssolfdwlrqfrqglwlrqv 9 %$7 9/ p+ 5 / : 5 / : w '(0$* pv ( '(0$* p- ("1($'5
docid025557 rev 1 31/39 AN4402 energy capability and load compatibility 38 figure 18. e demag_max vs t demag for repetitive pulse t jstart = 100c however, the data provided by the datasheet for repetitive pulse conditions at t jstart = 100 c have demagnetization times which are longer than 4.2 ms (calculated in step1) . another possibility to calculate e demag_max for a given t demag consists in using the empiric property: is constant. for example, using the first row of table 14 , we have: table 14. e demag_max and corresponding t demag for a repetitive pulse with t jstart = 100 c , r l = 0 ? , v bat = 13.5 v l [mh] i l0 [a] t demag [ms] r l =0 v bat =13.5v e demag_max [mj] r l =0 v bat =13.5v 400 0.434 7.9 60 500 0.430 9.8 74 600 0.425 11.6 86 700 0.421 13.4 99 ? e ? ? e ? ? ? ? ? e d'zdy ?u:?u???]?]?o?d :^dzd a ? d' ?u?? $ssolfdwlrqfrqglwlrqv 9 %$7 9/ p+ 5 / : 5 / : w '(0$* pv ( '(0$* p- ("1($'5 e demag_max t demag ----------------------------------- - e demag_max2 e demag_max1 t demag2 t demag1 ------------------------ 60 4.2 7.9 ------- - ? 43.7mj ===
energy capability and load compatibility AN4402 32/39 docid025557 rev 1 since the energies calculated in the step 1 are below the device maximum capability for the same demagnetization time, the low-side output of the l99mc6 is compatible with the load and the switch-off conditions previously defined.
docid025557 rev 1 33/39 AN4402 documents reference 38 appendix a documents reference 1. configurable 6-channel device (l99mc6, docid16523) 2. octal self configuring low/high side driver (l9733, docid11319) 3. vipower m0-5 and m0-5enhanced high-side drivers (um1556, docid023520) 4. transistor protection by transil? (an587, docid3599)
glossary AN4402 34/39 docid025557 rev 1 appendix b glossary table 15. glossary abbreviation description v bat battery voltage v ds mosfet drain-source voltage v s mosfet source voltage v zener_ls zener voltage of the gate-drain clamp v zener_hs zener voltage of the gate-source clamp v cl_ls clamping voltage when the gate-drain clamp is active v cl_hs clamping voltage when the gate-source clamp is active sign convention : v cl_hs > 0 v f typical diode forward voltage v gs_th mosfet gate-source threshold voltage l inductance v l voltage across the inductor r l inductor dc resistance v rl voltage across r l r p resistor in parallel to the inductive load v rp voltage across r p i p current through r p i l current through the inductor i l0 inductor current right before the turn-off phase: i l0 = i l (t=0) e demag_ls demagnetization energy of a low-side: dissipated energy in the low-side e demag1_hs demagnetization energy of a high-side when v bat v cl_ls - v cl_hs e demag2_hs demagnetization energy of a high-side when v bat v cl_ls - v cl_hs t demag_ls demagnetization time of a low-side t demag1_hs demagnetization time of a high-side when v bat v cl_ls - v cl_hs t demag2_hs demagnetization time of a high-side when v bat v cl_ls - v cl_hs
AN4402 summary of the demagnetization energy docid025557 rev 1 35/39 appendix c summary of the demagnetization energy table 16. demagnetization time and demagnetizati on energy for a low-side configured output load conditions t demag_ls demagnetization time e demag_ls demagnetization energy in the low-side configured output with parallel resistor to the inductor r l > 0 with , valid if without parallel resistor to the inductor r l > 0 with without parallel resistor to the inductor r l = 0 with l r l ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- r l // r p r l ------------------- - ?? ?? ?? r l ------ - v cl_ls r l // r p ------------------- - v cl_ls v bat ? () ? ?? ?? 1 r p r l r p + -------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ? ?? ?? ?? ln + ?? ? ?? l r l ------ - = r p v cl_ls v bat ? v bat --------------------------------------- r l > ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ------ - v cl_ls i l0 v cl_ls v bat ? r l --------------------------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ln ? ?? ?? ?? ------------- - = li l0 v cl_ls v bat ? --------------------------------------- 1 2 -- - li l0 2 v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ------------- - =
summary of the demagnetization energy AN4402 36/39 docid025557 rev 1 table 17. demagnetization time and demagnetizati on energy for a high-side configured output v bat range load conditions t demag_hs demagnetization time e demag_hs demagnetization energy in the high-side configured output v bat v cl_ls - v cl_hs with parallel resistor to the inductor r l > 0 with with , valid if without parallel resistor to the inductor r l > 0 with without parallel resistor to the inductor r l = 0 with l r l ------ - ln v cl_hs v bat + v cl_hs ---------------------------------------- r l // r p r l -------------------- ?? ?? ?? + -------------------- = v cl_hs v bat + () r l ------ - v cl_hs v bat + () r l // r p -------------------- v cl_hs () ? 1 r p r l r p + -------------------- v cl_hs v bat + v cl_hs ---------------------------------------- ? ?? ?? ?? ln + ?? ?? ?? ? ? ? ? ? ? l r l ------ - = r p v cl_hs v bat ------------------- r l > ------ - ln v cl_hs v bat + v cl_hs ---------------------------------------- ?? ?? ?? ------ - v cl_hs v bat + () i l0 v cl_hs r l ------------------- v cl_hs v bat + v cl_hs ---------------------------------------- ?? ?? ?? ln ? ?? ?? ?? ------------- - = li l0 v cl_hs ------------------- 1 2 -- - li l0 2 v cl_hs v bat + v cl_hs ---------------------------------------- ?? ?? ?? ------------- - =
AN4402 summary of the demagnetization energy docid025557 rev 1 37/39 v bat v cl_ls - v cl_hs with parallel resistor to the inductor r l > 0 with with , valid if without parallel resistor to the inductor r l > 0 with without parallel resistor to the inductor r l = 0 with table 17. demagnetization time and demagnetization energy for a high-side configured output (continued) v bat range load conditions t demag_hs demagnetization time e demag_hs demagnetization energy in the high-side configured output l r l ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- r l // r p r l ------------------- - ?? ?? ?? r l //r p r p r l r p r l + -------------------- = v cl_ls r l ------ - v cl_ls r l // r p ------------------- - v cl_ls v bat ? () ? 1 r p r l r p + -------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ? ?? ?? ?? ln + ?? ?? ?? ? ? ? ? ? ? l r l ------ - = r p v cl_ls v bat ? v bat --------------------------------------- r l > l r l ------ - ln v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? l r l ------ - v cl_ls i l0 v cl_ls v bat ? r l --------------------------------------- v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? ln ? ?? ?? ?? i l0 v bat r l ------------- - = li l0 v cl_ls v bat ? --------------------------------------- 1 2 -- - li l0 2 v cl_ls v cl_ls v bat ? --------------------------------------- ?? ?? ?? i l0 v bat r l ------------- - =
revision history AN4402 38/39 docid025557 rev 1 revision history table 18. document revision history date revision changes 22-nov-2013 1 initial release.
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