1 introduction when an adjustable shunt voltage reference like tl431 is used in programmable mode, we may encounter some errors due to the programmation. this application note will give to the reader a method to determine the relative error on the output voltage. the schematic used to program a shunt voltage reference is presented on figure 1 . the voltage reference provide some relative errors: this is what we call the inner precision . as we have to use an external resistor bridge configuration, we obviously have some additional errors as all resistor elements are not perfects. the application note will present the calculation in order to reach a final formula which can be used easily to calculate the relative error of the global schematic. the following elements are taken into account: l the inner precision of the voltage reference. l the precision of resistors. fig. 1: typical application schematic of a shunt voltage reference tl431 r2 r1 r vcc v vref tl431 r vcc v vref v = ( 1 + r1 / r2 ) x vref + r1 x iref iref v = vref application note AN1761 tl431 accuracy of shunt voltage references in programmable mode by jr?me dagostino revision a 1/3 september 2003
2/3 AN1761 2 calculations of the accuracy based on the schematic used to program the voltage reference, we can write: where v stands for cathode voltage, vref is for the voltage present on the ref pin and iref is the input reference pin current. iref is a very low current in the range of a few a we will neglect if the term r1 . iref is low enough regarding the other terms of the equation. most of the time, this simplification can be done. thus, if we write the total equation of the partial derivative, we obtain: with so, the total equation gives and if we try to make terms like dx / x appear, we obtain: and by operating some simplifications, we finally have: then, if we consider small variations of all parameters around their values, we have the final expression which can be used to calculate the relative error: as an application, let us consider a tl431a ( 1% precision) programmed at 5v with r1=r2 at 2% precision. using the above formula, we can calculate the 5v output precision: v 1 r 1 r 2 ------ - + ? ?? vref r 1 iref + = dv vref ? ? v vref d r 1 ? ? v r 1 d r 2 ? ? v r 2 d ++ = vref ? ? v 1 r 1 r 2 ------ - + = r 1 ? ? vvref r 2 ----------- = r 2 ? ? vr 1 C vref r 2 () 2 --------------------------- = v d 1 r 1 r 2 ------ - + ? ?? vref d vref r 2 ----------- r 1 d r 1 vref r 2 2 ----------------------- - r 2 d C + = v d 1 r 1 r 2 ------ - + ? ?? vref dvref vref -------------- ? ?? r 1 r 2 ------ - ? ?? vref r 1 d r 1 --------- - ? ?? r 1 r 2 ------ - ? ?? vref dr 2 r 2 --------- - ? ?? C + = dv v ------ - dvref vref -------------- r 1 r 1 r 2 + -------------------- dr 1 r 1 --------- - dr 2 r 2 --------- - C ? ?? + = d v v ------- d vref vref --------------- r 1 r 1 r 2 + -------------------- d r 1 r 1 ---------- - d r 2 r 2 ---------- - + ? ?? + = d v v ------- 1 1 2 -- -22 + () +3% ==
calculations of the accuracy AN1761 3/3 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 all other names are the property of their respective owners. ? 2003 stmicroelectronics - all rights reserved stmicroelectronics group of companies australia - belgium - brazil - canada - china - czech repubic - finland - france - germany hong kong - india - israel - italy - japan - malaysia - malta - morocco - singapore - spain sweden - switzerland - united kingdom - united states http://www.st.com
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