What is the pdf of resistor values (tolerances)

• Rib5
In summary, resistors usually have a gaussian distribution around their tolerance. +/-5% means that 90% of the resistors will be within those bounds.
Rib5
Hi guys,

I was reading about monte carlo analysis in the introduction from a textbook, and they gave an example of a voltage divider. They assumed resistor values had an equal probability of having values between the two tolerances. I know this is a simplistic assumption and I was wondering what kind of distribution resistors really follow.

I am guessing that it is most likely a gaussian distribution, but just wanted to know if that is specified somewhere. What does +-5% really mean? Is it that 90% of the resistors will be within those bounds? or does it have to do with standard deviation?

It is a guarantee that ALL resistors are within 5% of of spec'd value. For example, a 100 ohm resistor with a tolerance spec of +-5% could be anywhere between 95 and 105 ohms. It is NOT a guarantee that a circuit will work that calls for a 97 ohm resistor when replacing it with a 100 ohm +-5% resistor.

I find it hard to believe that no matter how many resistors you bought that you would NEVER get a value outside of the tolerances?

Rib5 said:
I am guessing that it is most likely a gaussian distribution,
Is it that 90% of the resistors will be within those bounds? or does it have to do with standard deviation?
Two sigma is 95% and that's what I take it to mean. The pdf might not be bell-shaped because some resistors were removed and labelled 2%.
There are rules for finding tolerances for uncorrelated errors. If I lay my hands on it I'll post it. It saves you from doing a monte carlo.

whome9 said:
... because some resistors were removed and labelled 2%.
Yep. The good ones (1%) are weeded out first then the 2%, etc. So with the 5%, 100ohm resistors you will probably not find one that is exactly 100ohm.

dlgoff said:
Yep. The good ones (1%) are weeded out first then the 2%, etc. So with the 5%, 100ohm resistors you will probably not find one that is exactly 100ohm.
The only thing I don't like about this is that the higher precision resistors are supposed to be more stable, yet they come from the same batch. Their initial values may be close, but they won't hold over time.

Rib5 said:
I find it hard to believe that no matter how many resistors you bought that you would NEVER get a value outside of the tolerances?

So what do you think is acceptable? One resistor out of every 1000 is 5.1% off? One out of every 10,000 is 7% off? One out of every 1,000,000,000 is 40% off? Where do you draw the line?

Rib5 said:
I find it hard to believe that no matter how many resistors you bought that you would NEVER get a value outside of the tolerances?
At the 2 sigma level with a bell-shaped curve you would get an outside value 1 time out of 20. 3 sigma, 1 time in 100.

Averagesupernova said:
So what do you think is acceptable? One resistor out of every 1000 is 5.1% off? One out of every 10,000 is 7% off? One out of every 1,000,000,000 is 40% off? Where do you draw the line?

I'm don't care what the tolerance is. My question was about the distribution of values around those tolerances, this way you can predict what values you might get.

Rib5 said:
I find it hard to believe that no matter how many resistors you bought that you would NEVER get a value outside of the tolerances?

That's what 100% testing gets you. Resistors are 100% tested before being packaged for shipment. That's true for most types of components.

Rib5 said:
I'm don't care what the tolerance is. My question was about the distribution of values around those tolerances, this way you can predict what values you might get.

I'm guessing it would be a truncated Gaussian (because of the 100% manufacturing test that I just mentioned). However, it could have some binomial character to it, if the resistor type lends itself to sorting at test. The only way to be sure would be to contact the manufacturer and see if they would/could tell you.

BTW, even for Monte Carlo purposes, you don't generally need to include a distribution attribute for the variation of values. As long as all components are varied across their tolerance, and as long as you get in enough runs to cover all the combinations of tolerances, you should be able to bracket the operation of the circuit.

berkeman said:
That's true for most types of components.
Even in a corporatocracy like the US?
100% testing is costly, and with sampling the manuf. can play the odds. Almost no one will sue over an out-of-tolerance resistor.

Ah ok, thanks guys. I didn't realize that they actually tested all the components! This makes a lot more sense to me now.

whome9 said:
Even in a corporatocracy like the US?
100% testing is costly, and with sampling the manuf. can play the odds. Almost no one will sue over an out-of-tolerance resistor.

Yep. If the datasheet lists the tolerance, it is tested in manufacturing. The tempco is not 100% tested, obviously, and would generally be given as a typical value. Generally if the datasheet lists a min or a max for a simple component (or tolerance), it will be tested. Sometimes the datasheet will explicitly say that some value is not 100% tested, but that is the exception.

For a voltage divider you could use formulas for uncorrelated errors. If I can find my hard copy I'll post them.

Another way is to approximate the normal distribution with 6, 10 or 20 points and then have your spreadsheet combine them according to the voltage divider formula.
20 points gives you 400 combinations, but some repeat.
You may not need the shape of the distribution but you can find the 5% endpoints.
Multiplying and dividing normal distributions gives you non-normal distributions.

1. What is the pdf of resistor values?

The pdf (probability density function) of resistor values is a mathematical representation of the likelihood of a resistor having a certain value. It is used to describe the distribution of resistor values and their corresponding tolerances.

2. How is the pdf of resistor values determined?

The pdf of resistor values is determined by taking into account the manufacturing process and the materials used to create resistors. It also considers the inherent variability in the values due to factors such as temperature and voltage.

3. Why is it important to understand the pdf of resistor values?

Understanding the pdf of resistor values is important for selecting resistors with the appropriate tolerance for a given application. It also helps in predicting the overall performance and reliability of a circuit.

4. What are the main factors that affect the pdf of resistor values?

The main factors that affect the pdf of resistor values include the manufacturing process, the type of materials used, and environmental factors such as temperature and voltage. The quality control measures implemented by the manufacturer also play a role in determining the pdf of resistor values.

5. How can the pdf of resistor values be used in circuit design?

The pdf of resistor values can be used in circuit design to select resistors with the appropriate tolerance for a given application. It can also be used to determine the expected variability in resistor values and help in making design decisions to ensure the reliability and performance of a circuit.

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