Need EE Help for Work PLEEEASE?

[kevinthenerd]

Imagine a circuit with five resistors. They all start out at the same value at room temperature, but when current is applied, the resistivity changes due to the change in temperature. I'm asuming it's a linear relationship:

(delta R)/(R0) = (alpha)*(delta T)
R0 = initial resistance
R = resistance
T = temperature

The circuit looks like this:
PNG that I threw together in Paint

I have a hunch that this circuit would be useful for determining the true current flowing through the circuit, correcting for the change in temperature due to resistor heating. You'd know the difference in voltages registered between the resistors that have now changed due to heating, and this would give you an indication of how the resistivity has changed as a result. I'm getting a little stuck, however.

I originally assumed that R2 would output four times the power as each of R1 (by I^2*R), but I realized that this is not quite precise because the ratio of voltage to current changes as R1 and R2 change. Given this assumption, however, I got pretty far...

I assumed that the Newtonian convection heat transfer coefficient was the same for all of the resistors and that the area is the same for all of the resistors, and this gave me, assuming 4*Q1 = Q2...

(T2 - T ambient) = 4*(T1 - T ambient)

I eventually got an expression for each R based on V1, V2, and R0 alone. Considering the power is related to V^2/R, the error in this can't be too bad. (The unknown here is the resistance... the voltage is pretty well known considering I'm measuring it directly.)

I'd like to do better than this. I'm stuck at this stage:

V1 / R1 = V2 / R2
V1 / V2 = (1 + alpha*delta_T1)/(1 + alpha*delta_T2)

Maybe I'm being brain dead with the math. I don't know.

 

[kevinthenerd]

If you know of any other way to account for resistor heating to measure current with a voltage-measuring device, let me know. (Measuring voltage instead of current would be great here considering I'll be measuring high levels of DC current, and I happen to have voltage measuring DAQ systems already handy.) I acquired (with permission, of course) a short piece of wire made of Constantan from another lab... let me know if it would just be better to measure the voltage accross that given its low thermal coefficient of resistivity.

 

[kevinthenerd]

bump?

 

[kevinthenerd]

help?

 

[Jassi]

I don't know if you noticed or not but you have a wheatstone bridge configuration with the R1s. Do you have a Circuits 1 text book handy? That should be able to guide you through the solution to the problem.

If you already knew, my bad...

 

[smack Down]

I would say screw the model and test your device with a few know inputs and see if you can detect the change at the output. Then just make a look up table if you range is small.

 

[kevinthenerd]

Originally posted by: Jassi
I don't know if you noticed or not but you have a wheatstone bridge configuration with the R1s. Do you have a Circuits 1 text book handy? That should be able to guide you through the solution to the problem.

If you already knew, my bad...

Yes, I took the "Intro to EE" class that mechanicals have to take. It's nearly irrelevant here because all four resistances are changing simultaneously. If only one was changing predictably, I could take the voltage accross the middle, but as it stands, I have no way to do temperature correction.

If anyone has a radically new approach, I'd appreciate it. I'm trying to determine the current in a circuit, and given the high current levels I'll be looking at, simply measuring the voltage accross a resistor may not be the best idea because of temperature effects.

In the final circuit, I'm going to have a nichrome wire sitting in a beaker with enough juice going through it to boil water. (It glows brightly in service and eventually breaks at the end of the experiment.) I'll be measuring the voltage accross this wire and hopefully be measuring the current going through the wire in order to determine its change in resistivity to predict its change in temperature, but measuring the voltage accross another resistor that's changing (to get the current) defeats the purpose of precisely measuring the current anyway.

 

[kevinthenerd]

Originally posted by: smack Down
I would say screw the model and test your device with a few know inputs and see if you can detect the change at the output. Then just make a look up table if you range is small.

One idea I had that almost runs along these lines is to make a massive array where each resistor would be getting such a tiny portion of the power that temperature effects would be totally negligible.

I should just use the research budget and order a high current, tight-tolerance resistor, but I've yet to find the combination of the both of the two yet. I need to keep looking I guess.

 

[kevinthenerd]

Here's one part of that massive array I had in mind. It's very easy to see how it becomes fractal-like in nature.
Simple circuit

 

[Born2bwire]

Originally posted by: Jassi
I don't know if you noticed or not but you have a wheatstone bridge configuration with the R1s. Do you have a Circuits 1 text book handy? That should be able to guide you through the solution to the problem.

If you already knew, my bad...

You should be able to detect very sensitive changes in the resistance due to the fact that it's a wheatstone bridge. If you ever use a force-strain sensor, it will generally be a wheatstone bridge whose resistances change with deformation of the sensor. But if your goal is to accurately determine the resistances of the circuit, you aren't going to really be able to do that unless you can characterize the temperature-resistance relationship since you have five unknowns and only two measurements. But really, have you tried to see what happens to your resistors as a result of these currents? What kind of temperatures result from your high currents? You can also easily see if the resistance is changing by just doing a current sweep through the resistor and seeing if the voltage is changing linearly. That is probably what I would do to get an accurate model for the resistance. And then just use temperature probes to check your resistors. What kind of currents are you dealing with anyway?

 

[kevinthenerd]

Originally posted by: Born2bwire

Originally posted by: Jassi
I don't know if you noticed or not but you have a wheatstone bridge configuration with the R1s. Do you have a Circuits 1 text book handy? That should be able to guide you through the solution to the problem.

If you already knew, my bad...

You should be able to detect very sensitive changes in the resistance due to the fact that it's a wheatstone bridge. If you ever use a force-strain sensor, it will generally be a wheatstone bridge whose resistances change with deformation of the sensor. But if your goal is to accurately determine the resistances of the circuit, you aren't going to really be able to do that unless you can characterize the temperature-resistance relationship since you have five unknowns and only two measurements. But really, have you tried to see what happens to your resistors as a result of these currents? What kind of temperatures result from your high currents? You can also easily see if the resistance is changing by just doing a current sweep through the resistor and seeing if the voltage is changing linearly. That is probably what I would do to get an accurate model for the resistance. And then just use temperature probes to check your resistors. What kind of currents are you dealing with anyway?

Somewhere around 30 amps? I don't remember exactly.

I've done strain gauge measurements, and I used a wheatstone to do them.

What do you mean "current sweep"? I don't know of meters that don't cost a fortune that can measure this kind of current. I don't think data up to 500 mA is going to be quite legitimate for data in the region I'll be working. It may not even be linear; who knows?

You don't have five unknowns. I'm assuming that the group of four resistors are all the same temperature. All five resistors are assumed to be the same value initially (no current). With power applied in steady state, you initally have three unknowns: the current and the two resistances. You know the two voltages, and you should be able to relate the two resistances as a function of the current, giving you two unknowns after that's all said and done: one of the resistances and the current. You can find the current with one of the voltages and its known resistance, and you're done.

I really don't know how to go about relating the two resistances with the current in a function that makes sense. That's where I'm stuck. Even if you end up with a lot of variables when you're done (like the convection heat transfer coefficient and the thermal coefficient of resistivity) it'd still be nice to know the theoretical model so I know where to go next.

 

[kevinthenerd]

Something I didn't mention is that the nichrome wire is outside of this diagram. I'm simply trying to come up with a temperature-compensated current measurement with these five resistors. I don't have to keep this configuration; I haven't even obtained the resistors yet. This is just something I came up with, but I'm a little stuck getting it to work theoretically.

 

[Jeff7]

:shocked:

Someone using PNG for what it was intended to do!!! Amazing!🙂

<-- Sorry, PNG Fanboy



(Save PNG's with Irfanview's PNGOut utility. It takes awhile but compresses the hell out of anything. It shrunk your PNG there down to 4,911 bytes in 64.781 seconds.)

 

[Born2bwire]

Originally posted by: kevinthenerd

Originally posted by: Born2bwire

Originally posted by: Jassi
I don't know if you noticed or not but you have a wheatstone bridge configuration with the R1s. Do you have a Circuits 1 text book handy? That should be able to guide you through the solution to the problem.

If you already knew, my bad...

You should be able to detect very sensitive changes in the resistance due to the fact that it's a wheatstone bridge. If you ever use a force-strain sensor, it will generally be a wheatstone bridge whose resistances change with deformation of the sensor. But if your goal is to accurately determine the resistances of the circuit, you aren't going to really be able to do that unless you can characterize the temperature-resistance relationship since you have five unknowns and only two measurements. But really, have you tried to see what happens to your resistors as a result of these currents? What kind of temperatures result from your high currents? You can also easily see if the resistance is changing by just doing a current sweep through the resistor and seeing if the voltage is changing linearly. That is probably what I would do to get an accurate model for the resistance. And then just use temperature probes to check your resistors. What kind of currents are you dealing with anyway?

Somewhere around 30 amps? I don't remember exactly.

I've done strain gauge measurements, and I used a wheatstone to do them.

What do you mean "current sweep"? I don't know of meters that don't cost a fortune that can measure this kind of current. I don't think data up to 500 mA is going to be quite legitimate for data in the region I'll be working. It may not even be linear; who knows?

You don't have five unknowns. I'm assuming that the group of four resistors are all the same temperature. All five resistors are assumed to be the same value initially (no current). With power applied in steady state, you initally have three unknowns: the current and the two resistances. You know the two voltages, and you should be able to relate the two resistances as a function of the current, giving you two unknowns after that's all said and done: one of the resistances and the current. You can find the current with one of the voltages and its known resistance, and you're done.

I really don't know how to go about relating the two resistances with the current in a function that makes sense. That's where I'm stuck. Even if you end up with a lot of variables when you're done (like the convection heat transfer coefficient and the thermal coefficient of resistivity) it'd still be nice to know the theoretical model so I know where to go next.

You measure the current indirectly by measuring the voltage across the resistor. Just sweep the current through a resistor from 0 to 30 A and watch the voltage drop across the resistor. As long as you maintain a linear relationship, you should be fine with the exception of a possible DC offset. If the relationship is nonlinear, then add a temperature probe to your resistor and track the transient and steady-state relationships. What kind of power dissipations are you looking at?

I don't know offhand if you could accurately assume that all the resistors of your bridge are going to be at the same temperature. Unless you go about working out that they all have the same power dissipation, but as soon as the resistances start to vary, then the currents will vary and then you may not be able to assume that you still retain the same power dissipation on each resistor.

But all of this is rather moot since you do not have the resistors. When you choose your resistors, you should be able to obtain temperature characteristics from the data sheet to tell you the amount of change in the resistance given temperature. And then when you have them on hand, you should be able to make measurements of each individual resistor to confirm and/or characterize your temperature/resistance relationship.

 

[kevinthenerd]

Originally posted by: Jeff7
:shocked:

Someone using PNG for what it was intended to do!!! Amazing!🙂

<-- Sorry, PNG Fanboy



(Save PNG's with Irfanview's PNGOut utility. It takes awhile but compresses the hell out of anything. It shrunk your PNG there down to 4,911 bytes in 64.781 seconds.)

The first PNG was compressed with Paint, and the second was compressed with Gimp. Did you notice a significant difference between the efficiency of the two?

 

[kevinthenerd]

We've dealt many times in the past with a company that specializes in measurement equipment (National Instruments, makers of Labview). I'm just gonna call a sales representative and see what they have to say about my problem. Thanks.

 

[Jeff7]

Originally posted by: kevinthenerd

Originally posted by: Jeff7
:shocked:

Someone using PNG for what it was intended to do!!! Amazing!🙂

<-- Sorry, PNG Fanboy



(Save PNG's with Irfanview's PNGOut utility. It takes awhile but compresses the hell out of anything. It shrunk your PNG there down to 4,911 bytes in 64.781 seconds.)

The first PNG was compressed with Paint, and the second was compressed with Gimp. Did you notice a significant difference between the efficiency of the two?

I've actually found GIMP's PNG compression engine to be quite similar to Pbrush's in performance, surprisingly. Irfanview's default PNG compressor is generally better than either, but the PNGOut plugin is really one of the best out there.