tfilm (01/20/83)
This topic is prompted by questions I have raised in designing thin film resistors. It is related to the generic definition and use of TCR in computing resistance variation over a *limited* temperature range. By definition: TCR=(R1-R0)/((T1-T0)*R0) (a) where T0 and R0 are reference temperature and resistance values. T0 is usually taken to be either room temperature or 0 deg C; TCR is usually recorded in units of ppm/deg C. One may rearrange (a) to calculate the resistance R1, at any temperature T1, within the temperature range of interest. R1=R0*(1+(TCR)*(T1-T0)) In most of the literature where I have seen TCR used (I can't seem to find any currently good examples) I believe it is used without reference to T0 or R0: R2=R1*(1+(TCR*(T2-T1)) R2/R1=1+TCR*(T2-T1) (b) I believe this is based on the assumtion that TCR is relatively (not precisely) linear over the temperature range of interest. Using (a): R2/R1=(1+TCR*(T2-T0))/(1+TCR*(T1-T0)) (c) Assuming a worst case temperature deviation about T0 of <+/->100 deg C: T2-T0=100 deg C, T0-T1=100 deg C and: TCR=150E-06 We have from (a): R2/R1=1.015/.985 R2/R1=1.031 (d) Simplifying (a) with the approximate equality (=apx=) for e<<1: 1/(1<+/->e)=apx=1<-/+>e (e) gives: R2/R1=apx=1+TCR*(T2-T1) For the 200 deg C temperature range: R2/R1=apx=1.030 (f) The error in making this assumption is calculated with (d) and (f): err=(1.031-1.030)/1.031 err=.001=.1% Getting back to my initial question, is there any mathmatical/analytical documentation specifically addressing the use of TCR in this manner which would support what I believe is an *approximately* correct usage? I appreciate any and all useful suggestions/references. MEL ihuxp!tfilm