COMPONENT TOLERANCES AND
|Trial||R1 + ΔR1||R2 + ΔR2||
A bit of work here, but interesting to see the effects! What happened when R1 was increased or decreased? Also note, increasing or decreasing resistors of the same tolerance produces the same magnitude of error. What combination gave the worst case error? And further, we notices that the magnitude of the worst case error ΔVo (Trials 6 and 7) appears to be sum of the magnitudes of the individual resistor errors (Trials 1 or 2 and 3 or 4).
ΔVo_tot = 0.012 = 0.006 + 0.006
Also interesting - what happened when both R1 and R2 go up or down? There's no effect on the output voltage. Why? In these cases the resistor ratio essentially stayed the same.
Does the divider meet the spec of 1 ± 0.010 V given all of the resistor combinations that might be installed on the factory floor? Unfortunately, no. But there's better resistors available.
HANDS-ON DESIGN What is the max error for resistors with 0.5% or 0.1% tolerances? Run a few SPICE simulations to fins out. What happens to the individual and sum of errors when you mix tolerances, say 5% for R1 and 1% for R2?
Our experiment above answered an important question: how sensitive is the output voltage to changes in R1 or R2? From trials 1 and 3 you could calculate the sensitivity in V per Ω as the ratio of the voltage change to the resistance change.
What are these sensitivities good for? Now you can approximate the voltage change ΔVo given any resistance change ΔR'.
Well, not quite any resistance change. But, the approximation is a good one for resistance changes that are relatively small, several percent or so. Accurate enough for most circuit applications.
Are there other ways to calculate DC sensitivities? In Part II, you'll get a chance to use some calculus (Method 2) to find some answers. Finally, we'll request SPICE (Method 3) to do the job for us.
The above table could have been generated for temperature coefficients where ΔR represents the total resistance change over some temperature ΔT. For example, if you specified a resistor with a tempco of ±100 ppm/°C, the ΔR over a ΔT = 10 °C change would be
ΔR1 = R1 ∙ TEMPCO ∙ ΔT
= 1500 Ω ∙ ±100/106 °C-1 ∙ 10 °C
= ±1.5 Ω
ΔR2 = R2 ∙ TEMPCO ∙ ΔT
= 1000 Ω ∙ ±100/106 °C-1 ∙ 10 °C
= ±1.0 Ω
Keeping our focus on the resistors, we assumed that the +2.500 VDC input voltage was without error. Of course in the real world it will have its own tolerance. By varying V1 to find its effect on Vo, you can include it in your overall error budget.
Also, this topic explores sensitivities of DC voltage levels. AC and transient sensitivities are other topics all together.
See Part II for a chance to use some calculus and SPICE to find the same sensitivities.
Download the file or copy this netlist into a text file with the *.cir extension.
R_DIVIDER.CIR - FIND COMPONENT SENSITIVITY * V1 1 0 DC 2.5V R1 1 2 1500 R2 2 0 1000 * * ANALYSIS .TRAN 1MS 10MS *.SENS V(2) * * VIEW RESULTS .PROBE .END
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