# How to calculate aging tolerance of Resistor?

I wanted to calculate the worst case minimum and maximum value of Resistor 1K by considering all the tolerances(initial tolerance,temperature,environmental factors and aging).

Here is the link for the datasheet:

http://www.bourns.com/docs/Product-Datasheets/CHPREZTR.pdf

Based on the datasheet, I found

initial tolerance - 1%

temperature - 100ppm/deg C - Calculated as +0.45% and -0,4% (Based on my system operating temperature range which is between -15 deg C AND 70 deg C)

Environmental factors -10.5%

But I do not know how to calculate the aging tolerance based on the Load Life data which is given as 1% under this condition (+70 °C; 1.5 hours “ON”, 0.5 hours “OFF”; 1000 hours)

Any suggestion how to interpret the datasheet for aging tolerance?

• Depends on material used. Older carbon resistors evaporated, not sure if nowadays metal film resistors have same issue. – Marko Buršič Feb 14 '17 at 16:09
• I'm not sure that is a ageing spec.. but it only changes 1%... your tempco is going to be worse. (You can buy R's with better tempco.) – George Herold Feb 14 '17 at 16:41
• It isn't given as 1%, it's given as ≤±(1.0 % + 0.05 Ω) for the stated test. They don't show a chart for the ageing, so it it might start off decreasing then increase, or anything. I suggest you contact the manufacturer - they might have unpublished data. – Andrew Morton Feb 14 '17 at 20:03

According to the datasheet, the test is done in compliance with MIL-STD-202, method 108 (pp 37-38), condition D (1,000h).

This is an accelerated aging test at (probably) 100% rated power (while "ON") with a duty cycle of 75%. Your operating conditions will almost certainly be more benvolent than these, which in practice means that the stress of your resistor may the lower than the usual assumption.

We know from Arrhenius that each additional 10°C accelerates reactions by an aging factor $$\Q_{10}\$$, that is:

$$\frac{t_0}{t_{acc}}=Q_{10}^{\frac{T_{acc}-T_0}{10}}$$

From that, we can calculate that those 1,000h operating at 100% rated power at 70°C are roughly equivalent (i.e. induce the same aging-related drift) to 31 months (2.583 years) at 100% rated power at 25°C, assuming the usual aging factor $$\Q_{10}=2\$$.

That amounts to 1% over 2.583 years or an average 3,870 ppm/year at 25°C. You can recalculate this for any operating temperature by using the equation above. Note: this is probably a conservative calculation due to operating conditions.

However, the aging drift does not increase linearly with time, but rather with the square root of time:

$$\frac{\Delta R}{R}=K\sqrt{t}$$

Recall that the previous calculation of 3,870 ppm/year was an average for the 2.583 years of the calculation period, but the actual implicit aging constant at 25°C is K=6,225 $$\ppm/\sqrt{year}\$$, which is a better case. Note that the aging drift are stronger during the first years, and smoother (slower) afterwards:

• 2.583 years: 10,000 pmm (1,0%) as specified
• 5 years: 13,919 ppm (1,4%)
• 10 years: 19,685 ppm (2,0%)
• 20 years: 27,839 ppm (2,8%)
• 40 years: 39,370 ppm (3,9%)
• And what is your conclusion? Does the resistor drop the resistance or it gains the resistance 3.87ppm/yr? – Marko Buršič Feb 14 '17 at 19:45
• Usually the resistance increases. However, the datasheet you've linked states that it's +/-. And beware, it's 3,870 ppm/year, not 3.87! – Enric Blanco Feb 14 '17 at 20:11
• By the way, I am not the OP, so I didn't link any datasheet. I just want to tell you, that aging involves a certain chemical or mechanical process, so the resistance change can go just in one direction. As for older carbon resistors, they tend to increase the resistance due to evaporating of the film. My conclusion is that your explanation about +/- 3,870 ppm/yr is not plausible. – Marko Buršič Feb 14 '17 at 20:18
• What's not plausible from your POV? – Enric Blanco Feb 14 '17 at 20:45
• @Enric Blanco:Can you please explain how you arrived the Value 3870ppm/year.I have difficulty in understanding the terminologies on the equation that you mentioned – ANONYMOUS Feb 15 '17 at 9:39