Converting V-I Curve to B(t) Curve for Magnetic Core: Quick Guide

[tim9000]

Hey, I'm only asking this here because its a bit of a time-critical question (no pun inteded). But if one takes a V Vs I curve (like to measure BH without the equipment to measure flux directly), that is to say, measures the change of increase in voltage and increase in current (where current is the dependent variable) for a set supply frequency, of a coil around a magnetic core. Can one convert the data that is a V I Curve into a into a B(t) curve for the core?
(Provided one knows the dimensions, number of turns, etc.)
Cheers

 

[Hesch]

Can one convert the data that is a V I Curve into a into a B(t) curve for the core?

If you want to determine a B(t) curve, you must also have V(t) and I(t) curves, which could be sinusoidal, stepfunctions or whatever. You cannot determine B by means of DC-voltage and DC-current.

B(t) ≈ Ψ(t) / A , where A is the cross section area and Ψ is the flux.

V(t) = dΨ_n(t) / dt , Ψ_n = Flux * turns.

 

[tim9000]

If you want to determine a B(t) curve, you must also have V(t) and I(t) curves, which could be sinusoidal, stepfunctions or whatever. You cannot determine B by means of DC-voltage and DC-current.

B(t) ≈ Ψ(t) / A , where A is the cross section area and Ψ is the flux.

V(t) = dΨ_n(t) / dt , Ψ_n = Flux * turns.

Ah, yes I'm familiar with those relationships.
[I do know the core dimensions and number of turns]
So the current and voltage would have been sine waves, I know the supply frequency and I have rms values, so I can calculate the peaks of the sineusoids.
So from here I can get B(I) but how do I get B(t)?

Thanks heaps

 

[Hesch]

B(t) is synchronous ( has same phase ) as I(t).

So if the I(t) is a sine-function, V(t) will be a cosine-function, ( ignoring the resistance in the coil ).

 

[tim9000]

B(t) is synchronous ( has same phase ) as I(t).

So if the I(t) is a sine-function, V(t) will be a cosine-function, ( ignoring the resistance in the coil ).

Umm, yeah, so I've got a B H curve (assuming H = NumberOfTurns*current)
and I imagine that it runs along-up the BH curve into saturation and back down again (to zero then through the negative of the curve) 50 times a second (as the supply was 50Hz). So I suppose I could take the furthest point of saturation and say it took one peak of the sine wave to get there (like half of the sin wave), which is 1 / (2*50) seconds?
Then I divide that length into a set of like 10 divisions, so steps of like 0.001 s.
Remember that I had a set of voltages and currents, would I then use only the largest current value, find it's PeakCurrent, then to find the corresponding B value is (Because graphically I don't think would be verry accurate) say:
I(t) = PeakCurrent*Sin(0.001 * t * 2 * PI * 50)
Then since I only have a finite number of voltage values get the gradient between the two points where the value of the voltage would lie between and use that to INTERPOLATE what the voltage would approximately of been, then use that to get the B(0.001t) ?
Cheers

 

[Hesch]

I've got a B H curve (assuming H = NumberOfTurns*current)

This is not a correct assumption. You could say:

H = N * I * ( some constant )

This constant depends on the shape of coil and core. For example as for the H-field surrounding a straight wire:

H = N * I / 2πr

Then since I only have a finite number of voltage values get the gradient between the two points where the value of the voltage would lie between and use that to extrapolate what the voltage would approximately of been, then use that to get the B(0.001t) ?

I have not understood if you are supplying the coil by voltage or current? Anyway if the core becomes saturated, the voltage or the current will not be sinusoidal. There is a lot of different methods to interpolate, extrapolate, and so on. I think the better method is to measure by means of some stepfunctions:

Say you set a resistor in series with the coil. Now you supply this circuit by 5Vdc. Then you step the dc-voltage to 5V +1V = 6V ( next time stepping from 6V to 7V ). By means of an oscilloscope, that measures the current, you can determine dΨ_n/dt.

It's just a suggestion, which I think will be more accurate/controlled. For example you can determine time-constant of the circuit.

 

[tim9000]

This is not a correct assumption.

yeah woops, I always forget about the length of the magnetic path as the denominator.

I have not understood if you are supplying the coil by voltage or current? Anyway if the core becomes saturated, the voltage or the current will not be sinusoidal. There is a lot of different methods to interpolate, extrapolate, and so on. I think the better method is to measure by means of some stepfunctions:

Say you set a resistor in series with the coil. Now you supply this circuit by 5Vdc. Then you step the dc-voltage to 5V +1V = 6V ( next time stepping from 6V to 7V ). By means of an oscilloscope, that measures the current, you can determine dΨn/dt.

It's just a suggestion, which I think will be more accurate/controlled. For example you can determine time-constant of the circuit.

Unfortunately I only have data to work with and can't do anymore testing.
It's current that is the dependent variable, and the magnitude of the sineusoidal voltage that gets controlled/modified.
Yes the current won't be sineusoidal due to saturation, so maybe forget about that, but at a specific Volt-seconds it will have a value and after 1 / (2*50) seconds it will be at the peak of the spike and the magnetic flux density will be as far right as it goes won't it?
Can I still use this information to my advantage?

EDIT:
actually it'd be a quater of the cycle until it peaks: 1 / (4*50) seconds
so what I was getting at is couldn't I just say I have B and H and say well the rms magnitude of H divided by 1 / (4*50) = 0.005 seconds
so it's units are A/m.s
and then if I want to take say 20 intervals, on the first interval the value of H would be H*0.00025 / 0.005 [A/m.s]
then I could just interpolate the corresponding value of B
Plot them and get a B(t) curve?

 

[tim9000]

I've pondered on this further and I suppose I'm saying that when it gets to the final saturation value, when the excitation voltage was highest, the current has spiked and we've arrived at that value of B. It doesn't matter how we got there, how nonlinear the journey was, but we do know it took a quater of the voltage cycle to get there?
So you just divide up the amount of time it takes to get to a quater of the voltage cycle by how many data points you have on your curve, so the first time interval is zero and the last one is a quater of the voltage cycle, and the times should match the values of B?
What do you think, this was at 50 Hz so I just divided a quater cycle time up by the number of data points:

Or is this wrong because it implies it takes the same amount of time to get from point to data point?

I was thinking each B value would have a corrsponding Volt-seconds value, and that each Volt-seconds value I could work out the time from that??

 

[tim9000]

Forgetting the aforemntioned B(t) method, I thought I could instead use a V.s/AN = V/wAN curve, but instead of the applied V, I could just choose an arbitrary voltage for all the points of B then
I was thinking I could generate the B(t) curve, for example 50V DC by Time at point = B_{at point} / [840*A*2*PI*50]
or a 1V DC curve by Time at point = B_{at point} / [840*2*PI*50]

Just to double check, V.s = V/(2*pi*freq) right??
Why not just V/Hz?
Because time period = 1/f
so V/f would be [V.s]