Hi fellow Electronics Engineers.

In this blog we’ll discuss how manufacturers represent tolerance on their datasheets and how to interpret these parameters for your design.

Initial tolerance

The first, and most obvious stage, when calculating the overall tolerance of a resistor is  to consider the percentage that results from the manufacturer's ability to produce a resistor with accuracy. This initial tolerance (as it is often referred to) is intrinsic to the resistor technology. If you haven’t previously read The “Not So Simple Guide” to choosing resistors - Part 2, this may be a useful starting point to introduce yourself to some of the different types of resistors that are available.

Note this may come as a shock to you, but nothing in the scientific universe is perfect. Yes, I have excluded the arts, as subjectively some works of art may be perfect. However, in the scientific realm, nothing is perfect, not even you cupcake!

When selecting a resistor from your preferred distributor, you will likely see an option that corresponds to initial tolerance. However, this is not the only factor to consider when choosing the appropriate resistor for your design.

Temperature Co-efficient

Remember back in high school science class how we learned that materials change their properties when exposed to heat? Well, resistors and their resistance properties are no exception. When you change a resistor's ambient temperature, its resistance changes too. Normally, a resistor manufacturer states that the initial tolerance is given at room temperature (25°C).  However, if the temperature of the resistor increases due to environmental factors or self-heating, the resistance will also increase. This is called a positive temperature co-efficient or temp-co for short. Conversely, if you decrease the temperature of the resistor, the resistance will decrease. 

Note not all electronic components have a positive temp-co, some have a negative temp-co i.e. as they heat up the parameter in question reduces. We will cover this topic in a later blog.

The temp-co is normally shown on the resistor datasheet as PPM (Parts Per Million). It is normal in the scientific community to represent dimensionless small units in such a way; 1 ppm is just another way of saying something is 0.0001 % of a value.

When you are designing a circuit; hardware; or electronic system, there are typically  requirements for the operating temperate range it can deviate across. For instance, most consumer electronics are designed to operate in houses and  have a sympathetic operating temperature range of approx. -10°C to +40°C. Since manufacturers gives the temp-co in ppm, you’ll need to calculate the error that can be attributed to change in operating temperature. Let’s say a resistor with a temp-co of 100 ppm operating at 75°C. That is a temperature delta of 50°C, which results in a temperature related inaccuracy of (50 x 0.01%) 0.5%.

Ageing Co-efficient

‘There is nothing permanent except change’ – Heraclitus

Time not only affects our bodies, but it also affects everything in the known universe, including our resistors. That’s right! A resistor we select on day one will have a different resistance value 10 years later.  We call this phenomenon the ageing co-efficient, or age-co for short.

With reference to The “Not So Simple Guide” to choosing resistors - Part 2  we looked at different resistor technologies.   Start with thick-film resistors, they're a good and low-cost option for most users, especially in digital applications like pull-up resistors. I can’t think of any reasons why you’d want to look any further. But if you're working in analog and need the gain of an op-amp to remain stable for a long time, like 20 years, then thick-film resistors might not be the best choice. For instance, a typical thick-film resistor, operating at an average temperature of 70°C, will have an extra 1% after just 1000 hours (we normally say 10,000 hours = 1 year). The next problem is  the industry can’t agree on a mathematical model that allows us to extrapolate this trend.  So we rely on statistical look-up tables for long term predictions, and I have personally seen data that suggests a 1% thick-film resistor after 25 years can increase up to 15%.

To understand why thick-film resistors undergo significant changes over time , we must consider the manufacturing process.   Thick-film resistors are made by pasting a conductive material onto a ceramic substrate (similar material to a coffee mug), which is cost-efficient but relatively low-controlled.

If you require long-term stability, may I suggest considering a different technology such as thin-film resistors. They start manufacturing in a similar way to thick-film resistors, with a ceramic substrate, but the rest of the process is quite different. A dense, uniform metallic alloy layer is deposited onto the ceramic base under a vacuum, resulting in a resistive material thickness of approximately 250 Angstroms (1 Angstrom is 1.0E-10 m). This significantly improves all the sources of error that we have discussed in this blog. The initial tolerance for a thin-film resistor is more likely to be 0.1% instead of 1%, temp-co is commonly 25 ppm, and for age-co after 1,000 hours at 70°C, it is 0.05%. However, the downside is the cost. Thin-film resistors  will set you back 10 – 20 pence each, whereas a thick film costs less than 5 pence.

The icing on the cake regarding thin-film, is that industry has established a model using the Arrhenius equation developed by Dutch chemist Svante Arrhenius, that allows us to predict long-term ageing trends for thin-film resistors.

Note this is only an approximate model as in reality the ageing effect is really a random process. Often, we describe this phenomenon as the ‘random walk’. However, this method is normally acceptable for most engineering calculations.

The equation clearly shows that the long-term stability of a resistor is heavily influenced by the average operating temperature. In this example a temperature delta of 30°C results in an age drift factor of 2.

There are several other resistor technologies available that offer higher accuracy at a higher cost.  For instance, a bulk metal foil resistor can have an initial accuracy of 0.005%, a temp-co of 1 PPM/°C and a life-stability of 0.015% (70°C, 10 khrs). However, these specialised resistors can be expensive costing approx. £40 each (as of 2023).

Environmental effects and overload

By now, it shouldn’t be much of a surprise that your resistor’s tolerance will be impacted if it’s exposed to  any of the following environmental factors (this list is non-exhaustive):  thermal-shock, vibration, mechanical-shock, voltage overload pulses (including electrostatic discharge), and power overload pulses.

Once again, it's important to note that different resistor technologies behave differently when exposed to these stimuli. Therefore, it's crucial to consider the technology of the resistor and its behavior in the environment before committing to it.

To worst-case, or not to worst-case, that is the question.

As we have discovered, or reminded ourselves, there are many sources of inaccuracy in a simple resistor. One might think that the correct way to proceed now is to sum up all the sources of error and accept the total. Summing all the error sources we have discussed in this blog would give us the following formula: -