1/6 1 principle of operation this technical note shows how it is possible to calculate the current and voltage precision in the regulation loop of the tsm1011. the tsm1011 is a highly integrated solution for smps applications requiring cv (constant voltage) and cc (constant current) mode. the tsm1011 integrates one voltage reference and two operational amplifiers (with ored outputs - common collector). the voltage reference combined with one operational amplifier makes it an ideal voltage controller. the other operational amplifier, combined with few external resistors and the voltage reference, can be used as a current limiter. this circuit is designed for use in battery chargers with a constant voltage and a limited output current and in adapters. it can be used in every type of application requiring 0.5% and 1% voltage reference precision fixed at 2.5 volts. figure 1 : typical application using tsm1011 inssmps 1.1 voltage control the voltage control loop is controlled via a first transconductance operational amplifier, the optocoupler which is directly connected to the output and an external resistor bridge connected between the output positive line and the ground reference. the middle point is to be connected to the cv- pin of tsm1011, and, if r 2 is the upper resistor, and r 1 , the lower resistor of the bridge, the relationship between r 2 and r 1 value should be chosen as written in equation 1: equation 1 where v lim is the desired maximum output voltage. when under constant voltage control mode, the output voltage is fixed thanks to the r 1 /r 2 resistor bridge. to avoid the discharge of the load, the resistor bridge r 1 , r 2 , should be highly resistive. rsense c2 r2 r1 c1 c3 optocoupler secondary side cic 1 cvc1 ric1 rvc1 rlimit 2 3 4 8 6 5 28v vref vcc cc cc- cc+ gnd cv cv- cv+ out 2,5v r4 r5 1 r3 d1 d2 out+ out- ric2 tsm1011 7 pwm controller optocoupler primary side () 1 2 1 ref lim ref 2 1 lim r r r v v v , r , r f v + = = by giuseppe scuderi AN1623 application note tsm1011: regulation loops precision calculation november 2002
AN1623 - application note 2/6 for this type of application a total value of 100k w (or more) would be appropriate for the resistors r 1 and r 2 . note that if the low drop diode should be inserted between the load and the voltage regulation resistor bridge to avoid current flowing from the load through the resistor bridge, this loop should be taken into account in the above calculations by replacing v out by (v out + v drop ). 1.2 current control the current control loop is controlled via the second transconductance operational amplifier, the optocoupler and the sense resistor that is to be placed in series on the output negative line. v sense threshold is achieved externally by a resistor bridge tied to the v ref voltage reference. its middle point is tied to the positive input of the current control operational amplifier and its foot is to be connected to lower potential point of the sense resistor. the resistors of the bridge are matched to provide the best precision possible. equation 2 equation 3 equation 4 where i lim is the desired maximum output current, and v sense is the threshold voltage for the current control loop. note that r sense resistor should be chosen taking into account the maximum dissipation (p lim ) through it during full load operation: equation 5 for most adapter and battery charger applications, a quarter-watt, or half-watt resistor to make the current sensing function is sufficient. the current sinking outputs of the two transconductance operational amplifiers are common (to the output of the ic), this makes an oring function that ensures that whenever the current or the voltage reaches too high values, the optocoupler is activated. the relation between the controlled current and the controlled output voltage can be described with a square characteristic as shown in the following v/i output power graph figure 2 . figure 2 : output voltage versus output current 1.3 start up and circuit conditions if the tsm1011 v cc is connected to the converter output voltage, then under start-up or short-circuit conditions, the tsm1011 was not provided with a high enough supply voltage. this is due to the fact that the chip has its power supply line in common with the power supply line of the system. therefore, the current limitation can only be ensured by the primary pwm module, that should be chosen accordingly. if the primary current limitation is considered not to be precise enough for the application, then a sufficient supply for the tsm1011 has to be ensured under any condition. it would then be necessary to add some circuitry to supply the chip with a separate power line. the schematic in figure 1 shows how to realize a low-cost power supply for the tsm1011 (with no additional winding). please pay attention to the fact that in the particular case presented here, this low-cost power supply can reach voltages as high as twice the voltage of the regulated line. the absolute maximum rating of the tsm1011 supply voltages is 28 volts. it is possible to insert r limit resistors in order to limit tsm1011 i cc current in high voltage condition.the current sunk by internal zener diode can be calculated by following formula: equation 6 () ref 5 4 sense lim v , r , r , r f i = sense lim sense v i r = ? ? ? ? ? = ref 4 5 sense lim v r r r 1 i lim sense lim i v p = iout vout ilim vlim < 5% < 10% voltage regulation current regulation () it lim z cc vz r v v i - =
AN1623 - application note 3/6 2 precision calculation in order to calculate the precision of i lim and v lim in the regulation loop, it is possible to write one relationship that point some parameters out for current and voltage output variation. as shown in figure 3 and figure 4 it is possible to make a model of the current and voltage control transconductance operational amplifiers using a voltage source for input offset and an impedence z 1 with v 1 voltage drop. typical precision requirements for battery charging are less than 10% for i lim and less then 5% for v lim see figure 2 . now, let's go on to the voltage and current loop precision calculation. 2.1 current loop precision calculation 2.1.1 theoretical calculation let's show some different steps in order to calculate the current precision loop according to the figure 3 it is simple to verify that: equation 7 for the virtual ground at the input of the current amplifier: equation 8 equation 9 equation 10 substituting equation 9 in equation 7 equation 11 where equation 12 equation 13 substituting equation 12 in equation 13 equation 14 d i lim tot is the sum of the following: equation 15 where equation 16 equation 17 equation 18 equation 19 equation 20 equation 21 substituting equation 16 and equation 21 in equation 15 and considering the absolute value of these terms: equation 22 equation 22 is important in order to calculate d i lim tot and shows the many parameters that characterize current variation. it can be observed that v io =4mv, v ref =2.5v and v 1 <5mv, so the term v io +v 1 can be neglected with respect to v ref . () 4 5 5 sense ref 5 r r r r v v v + + = 0 v v v v ve ve 1 sense 5 r io = - - + - = - - + 1 io 5 r sense v v v v - - = m out 1 g i v = 5 1 io sense 5 4 sense ref r v v v r r v v + + = + + ()() 4 1 io 5 4 ref 5 sense r v v r r v r v + + - = lim sense sense i r v = () ? ? + ? ? ? ? ? + - = 1 io 4 5 ref 4 5 sense lim v v r r 1 v r r r 1 i iout lim rsense lim 4 r lim 5 r lim vio lim vref lim tot lim i i i i i i i d + d + d + d + d + d = d 4 sense 5 ref lim vref lim r r r v i i = d d = 4 sense 4 5 io lim vio lim r r r r v i i + - = d d = () 4 sense 1 io ref 5 lim 5 r lim r r v v v r i i + - = d d = () [] 1 io ref 2 4 sense 5 4 lim 4 r lim v v v r r r r i i + - - = d d = ()() [] 1 io 5 4 ref 5 4 2 sense sense lim rsense lim v v r r v r r r 1 r i i + + - - = d d = ? ? ? ? ? + - = d d = 4 5 m sense out lim iout lim r r 1 g r 1 i i i () () [] ()() out 4 5 m sense sense 4 1 io 5 4 ref 4 5 2 sense 4 1 io ref 2 4 sense 5 5 4 1 io ref sense io sense 4 5 4 ref sense 4 5 tot lim i r r 1 g r 1 r r v v r r v r r r 1 r v v v r r r r r v v v r 1 v r r r r v r r r i d ? ? ? ? ? + + + d ? ? ? ? ? + + - + + d + - + + d ? ? + - + + d ? ? ? ? ? + + d ? ? ? ? ? = d
AN1623 - application note 4/6 figure 3 : simplified model for current precision calculation 2.1.2 practical example in order to simplify the comprehension of d i lim tot formula, let's take a practical example that uses absolute and relative tolerances typical for tsm011 applications. consider for example: see footnote1) see footnote 1 let's assume that i out will vary between 0 and 5ma, therefore: i lim = 3a g m = 3.5ma/mv - r 4 = 174k w r 5 = 10k w - r sense = 0.047 w rewriting equation 22 equation 23 it is possible to obtain a good current variation r4 r5 v r5 r ic2 gnd v e- v e+ r3 i out v ref r sense v sense v 1 v io g m v 1 i lim 1 5 3 2 6 7 out tsm1011 footnote 1 using tsm1011a version % 5 . 0 v v ref ref = d % 1 r r 5 5 = d % 1 r r 4 4 = d % 1 r r sense sense = d mv 2 v io = d ma 5 . 2 i out = d out 4 5 m sense sense sense sense 4 ref 5 4 4 4 sense ref 5 5 5 4 sense 5 ref io sense 4 5 4 ref ref sense 4 ref 5 tot lim i r r 1 g r 1 r r r r v r r r r r v r r r r r r v v r r r r v v r r v r i d ? ? ? ? ? + + d ? ? ? ? ? + + d ? ? ? ? ? + + d ? ? ? ? ? + + d ? ? ? ? ? + + + d ? ? ? ? ? = d % 3 . 5 i i lim tot lim = d
AN1623 - application note 5/6 2.2 voltage loop precision calculation 2.2.1 theoretical calculation let's show some different steps in order to calculate the voltage precision loop. according to figure 4 it is simple to verify that: equation 24 where equation 25 d v lim tot is the sum of: equation 26 where equation 27 equation 28 equation 29 equation 30 equation 31 substituting equation 27 and equation 31 in equation 26 and considering the absolute value of terms: equation 32 equation 32 is more important in order to calculate d v lim tot and shows many parameters that characterize voltage variation. it can be observed that v io =4mv, v ref =2.5v and v 1 <5mv, so the term v io +v 1 can be neglected with respect to v ref . 2.2.2 practical example in order to better understand the formula, let's take a practical example that uses absolute and relative tolerances typical for tsm011 applications. let's consider for example: see footnote 1 assume that i out will vary between 0 and 5 ma, therefore: v lim = 18v g m = 3.5ma/mv r 1 = 30k w - r 2 = 186k w rewriting equation 32 equation 33 it is possible to obtain a good current variation () 1 io ref 1 2 lim v v v r r 1 v - - ? ? ? ? ? + = m out 1 g i v = iout lim 1 r lim 2 r lim vio lim vref lim tot lim i i v v v v d + d + d + d + d = d 1 2 ref lim vref lim r r 1 v v v + = d d = ? ? ? ? ? + - = d d = 1 2 io lim vio lim r r 1 v v v ? ? ? ? ? + - = d d = 1 2 m io lim iout lim r r 1 g 1 i v v () 1 io ref 1 2 lim 2 r lim v v v r 1 r v v - - = d d = () 1 io ref 2 1 2 1 lim 1 r lim v v v r r r v v - - - = d d = () () 1 1 io ref 2 1 2 2 1 io ref 1 out 1 2 m io 1 2 ref 1 2 tot lim r v v v r r r v v v r 1 i r r 1 g 1 v r r 1 v r r 1 v d - - + + d - - + + d ? ? ? ? ? + + + d ? ? ? ? ? + + + d ? ? ? ? ? + = % 5 . 0 v v ref ref = d % 1 r r 1 1 = d % 1 r r 2 2 = d mv 2 v io = d ma 5 . 2 i out = d 1 1 ref 1 2 2 2 ref 1 2 out 1 2 m io 1 2 ref ref 1 2 ref tot lim r r v r r r r v r r i r r 1 g 1 v r r 1 v v r r 1 v v d + d + + d ? ? ? ? ? + + + d ? ? ? ? ? + + + d ? ? ? ? ? + = 2.3% v v lim tot lim = d
AN1623 - application note 6/6 figure 4 : simplify model for voltage precision calculation 3 conclusion this application note relative to the tsm1011 shows how very simple it is to calculate a current and voltage variation in order to discern how many parameters characterize the precision of regulation loop. in accordance with market needs, current and voltage precision in the tsm1011 is extremely accurate. this allows a broaden application range for our products as compared with those of competitors. at this moment the current and voltage variation precision requested by market is: the tsm1011 ("a" version) shows excellent performance in typical adapter and battery charger applications. the results achieved in the above two practical examples for current and voltage precision are: these results confirm the optimum performances and give clear explanation of the external parameters that affect accuracy and precision for the tsm1011 attached to this application note is an excel file showing the general schematic of the tsm1011 and which allows the possibility of varying values i lim and v lim according to the parameter variations that characterize the application. it is possible, moreover, to change the resistor accuracy in order to avoid high-cost components when the application requires a lower precision. 6 vcc v lim 1 5 tsm1011 4 r3 i out v ref 7 28v r2 r1 gnd v 1 v e- v e+ v io g m v 1 out % 1 i i lim tot lim 0 = d 5% v v lim tot lim = d % 5 . 5 i i lim tot lim = d % 3 . 2 v v lim tot lim = d information furnished is believed to be accurate and reliable. however, stmicroelectronics assumes no responsibility for the consequences of use of such information nor for any infringement of patents or other rights of third parties which may result f rom its use. no license is granted by implication or otherwise under any patent or patent rights of stmicroelectronics. specificati ons mentioned in this publication are subject to change without notice. this publication supersedes and replaces all information previously supplied. stmicroelectronics products are not authorized for use as critical components in life support devices or systems without express written approval of stmicroelectronics. the st logo is a registered trademark of stmicroelectronics ? 2002 stmicroelectronics - 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 http://www.st.com
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