# Measuring voltage with a voltage divider and drift due to temperature coeffecient of the resistors

#### MikeA

Joined Jan 20, 2013
354
Say I have a temperature compensated ADC and a simple voltage divider 100K over 1K using some 1206 resistors that results in the output being 99x less.

If I'm measuring 100V DC, the resistors will heat up a different amount if I'm measuring 10V DC. I did some math on a napkin, and it appears the 99x factor should remain the same if both resistors in the divider have the same temperature coefficient.

Is that correct?

#### ronsimpson

Joined Oct 7, 2019
2,795
Yes. Keep the resistors close together. or at least not on offside ends of the board. The resistors should be from the same type and from the same company.

#### MikeA

Joined Jan 20, 2013
354
Now that I thought about it more, I don't think my napkin math is correct at all, as the the 100K resistor will have a muuuuuch higher drift due to having 100x time more heat dissipated through that resistor.

In my example of 100V DC and 100K over 1K, the 100K resistor will be dissipating 100mW, and the 1K will be dissipating only 1mW.

Is this logical?

#### MikeA

Joined Jan 20, 2013
354
The resistors should be from the same type and from the same company.
Reasonable.

Yes. Keep the resistors close together. or at least not on offside ends of the board.
But why specifically?

#### BobTPH

Joined Jun 5, 2013
8,092
Actually, they will not heat equally, so no, the ratio does not stay the same.

The power dissipated is I^2 R, the I is the same, so the 100K dissipates 100 times the power.

#### crutschow

Joined Mar 14, 2008
33,346
Note that the stated temperature coefficient is usually ±, so both resistors may not drift in the same direction.

There are low temperature coefficient resistors you can buy, which are often have 0.1% or better resistance values also.

#### MikeA

Joined Jan 20, 2013
354
Note that the stated temperature coefficient is usually ±, so both resistors may not drift in the same direction.
Woa! I thought that ± means it can drift in both directions, depending if the temperature is above or below some reference point.

But that it would drift in only one and predictable direction if the temperature is rising, and it would drift in only one and predictable direction if the temperature is dropping.

So that's not true? Copper will always increase resistance when it gets hotter. It will never go the opposite way randomly. Why would a resistor made of a known material go either way?

#### BobTPH

Joined Jun 5, 2013
8,092
Do you think both resistors will be at the same temperature?

#### MikeA

Joined Jan 20, 2013
354
Do you think both resistors will be at the same temperature?
No. The top one (100K) will be much hotter.

#### BobTPH

Joined Jun 5, 2013
8,092
Then how did you determine that the ratio stays the same?

#### MikeA

Joined Jan 20, 2013
354
Then how did you determine that the ratio stays the same?
I have reversed that idea in post #3.

#### WBahn

Joined Mar 31, 2012
29,496
Now that I thought about it more, I don't think my napkin math is correct at all, as the the 100K resistor will have a muuuuuch higher drift due to having 100x time more heat dissipated through that resistor.

In my example of 100V DC and 100K over 1K, the 100K resistor will be dissipating 100mW, and the 1K will be dissipating only 1mW.

Is this logical?
You want to keep the resistors as close together as you can so as to thermally couple them to keep them as close to the same temperature as possible. That way heat will be transferred from the hot resistor to the cooler resistor. Since it's a voltage divider, you can have one end of each resistor very close to the other and even sharing the same pad. Having them parallel to each other will also maximum the thermal coupling. There are also encapsulations you could use to further couple them.

Another technique would be to build the 100 kΩ resistor out of multiple smaller resistances in series that are wrapped around the 1 kΩ resistor on the board. That not only reduces the power dissipated by each high-value resistor, and hence the temperature rise, but also places the small resistor in an oven formed by the other resistors. This has some potential downsides in terms of parasitics, which may or may not be a concern for your application.

If differential temperature changes are really a concern, be sure to start out with very low tempco resistors to begin with as well as using resistors with a tolerance rating appropriate to the goals.

#### crutschow

Joined Mar 14, 2008
33,346
So that's not true? Copper will always increase resistance when it gets hotter. It will never go the opposite way randomly. Why would a resistor made of a known material go either way?
Because the resistor material is a combination of alloys that are designed to have a zero coefficient of drift but, of course it's never perfect, so can be either slightly under or slightly over the desired zero.
As you note, the coefficient of resistance change is usually in one direction, so whether the temperature is increasing or dropping, or above or below a reference point makes no difference.

#### MikeA

Joined Jan 20, 2013
354
Because the resistor material is a combination of alloys that are designed to have a zero coefficient of drift but, of course it's never perfect, so can be either slightly under or slightly over the desired zero.
I'm still having trouble wrapping my mind about how a known material can have an unpredictable temp coefficient.

Say I have a 100ppm/C 100K resistor.

If it heats up by 100C, it could shift 1000 ohms either up or down in an unpredictable way?

#### WBahn

Joined Mar 31, 2012
29,496
I'm still having trouble wrapping my mind about how a known material can have an unpredictable temp coefficient.

Say I have a 100ppm/C 100K resistor.

If it heats up by 100C, it could shift 1000 ohms either up or down in an unpredictable way?
Depends on what the specs are for that resistor.

There is a minimum temp coefficient and a max temp coefficient. If the tempco is specified as +/- 100 ppm/°C, then it could go up by as much as 100 ppm/°C or down by as much as 100 ppm/°C. Since this is not acceptable in some applications, some resistors are spec'ed something like 0 / +100 ppm/°C, meaning that it will not go down, but it could go up by as much as 100 ppm/°C.

Ideally, resistors would have a tempco of exactly zero. So the materials that resistors are made from are a blend of materials (such as a certain metal alloy for metal-film resistors) that have been formulated to balance out tendencies to go up and tendencies to go down. But it is impossible to get it exactly right, so some resistors will go up and some will go down. If it's important that the tempo be unidirectional, then the blend is biased enough to ensure that it always goes in one direction, but the tradeoff is that, on average, they will change more than the resistors that can go either way because of this bias.

#### crutschow

Joined Mar 14, 2008
33,346
I'm still having trouble wrapping my mind about how a known material can have an unpredictable temp coefficient.
Because that "known material" is not exactly the same from batch to batch due to slight differences in each batch of alloys used to make the resistor material.
The material is never a perfect mixture of alloys.

A single material, such as copper, has a more predictable (and higher) temperature coefficient, since there's less variation between two pieces of similar copper material.

Last edited:

Joined May 28, 2009
514
Say I have a temperature compensated ADC and a simple voltage divider 100K over 1K using some 1206 resistors that results in the output being 99x less.

If I'm measuring 100V DC, the resistors will heat up a different amount if I'm measuring 10V DC. I did some math on a napkin, and it appears the 99x factor should remain the same if both resistors in the divider have the same temperature coefficient.

Is that correct?
If you need a stable voltage, you can always use a zener diode.

#### crutschow

Joined Mar 14, 2008
33,346
If you need a stable voltage, you can always use a zener diode.
Expect for some Zeners designed for temperature stability, most of them have a high temperature coefficient of voltage change.
For the best stability you can use a precision IC voltage reference.

#### MikeA

Joined Jan 20, 2013
354
some resistors are spec'ed something like 0 / +100 ppm/°C, meaning that it will not go down, but it could go up by as much as 100 ppm/°C.
Ahh. Your earlier suggesting of thermally coupling resistors makes makes much more sense, now that I know this type of resistor that can go only go up exists. If resistors could go the opposite way, randomly, coupling them doesn't like a good idea.
But I get the concept now. Before I would not have guessed that there is an alloy so close to 0 that it could go ether way.

#### schmitt trigger

Joined Jul 12, 2010
772
Another technique would be to build the 100 kΩ resistor out of multiple smaller resistances in series that are wrapped around the 1 kΩ resistor on the board. That not only reduces the power dissipated by each high-value resistor, and hence the temperature rise, but also places the small resistor in an oven formed by the other resistors.
This is the same technique that I have used, with very successful results.
In addition to the lower self-heating, it spreads the high voltage across several components, for additional safety. For this reason, I always use it when dividing down line-level voltages.