Hello there,
In short, a simulation will never match real world measurements unless a more accurate inductor model is used in the simulation, and even then it's hard to pin down perfectly.
An air core inductor would be better for use for study here, at least to start.
Here is some more information about this...
This is a simple problem when the inductor is linear, for example with an additional series resistor R1 and calling the inductors internal series resistance Rs, the voltages across R1 and the physical inductor are equal when the following equality is satisfied:
w^2*L^2+Rs^2=R1^2
and solving for w^2 we get:
w^2=(R1^2-Rs^2)/L^2
and obviously with both w and L always positive that means we have:
w=sqrt(R1^2-Rs^2)/L
so:
2*pi*f=sqrt(R1^2-Rs^2)/L
f=sqrt(R1^2-Rs^2)/(2*pi*L)
That's the frequency where both the voltages become equal, and the inductor voltage is measured physically right across the inductor (so the inductor series resistance adds a little to the inductor voltage), and as long as the voltage from the source is measured right at the top of the first resistance R1 it does not matter what R1 is as long as we know the value.
There is a catch of course, and that is that most inductors that are more than a few uH are going to have a core that is not air, but something that was chosen to have a high enough permeability to get more inductance from the same number of turns and that not only makes it smaller it also increases the efficiency. This brings in a HUGE problem in the analytical nature of the problem unfortunately, because now the inductor is non linear and the degree of non linearity is very hard to specify most of the time because of the variables involved and the core model we choose to use.
For a linear core model the above is valid, but for any other core type it is not valid because for one the excitation current is no longer a sine wave even with a pure sine wave input. It would look more like a wide needle like wave, where we get higher peaks with lower currents to ether side. That's because as the current changes, the permeability changes, and as the permeability changes the inductance itself changes. The above would change then at the very least to:
f=sqrt(R1^2-Rs^2)/(2*pi*L(i))
where now we see that L is a function of current, and we assume that we know the function that yields some sort of averaged L value over the entire time period for that average current level.
It's even more complicated than that because L is also a function of time:
f=sqrt(R1^2-Rs^2)/(2*pi*L(i,t))
and so now we have a much bigger problem in trying to determine the averaged value of L for example.
In reality though, using even the simpler anisotropic BH curve we see the inductance start out low for low currents, then increase to some max for intermediate currents, then decrease again for high currents. Even if we choose to stay on the lower end of the curve we will see the inductance start from some low value and increase to some higher value, and during that portion of the curve it can change a lot.
If we use the real BH curve assuming we could know that exactly for the given temperature, we would see the inductance increase as the current increased and then start to decrease again for increasing current, and then when the current starts to decrease the inductance would increase again but more slowly.
Obviously if we dont know the inductance we cant know the waveshape, although the current usually looks like a very non sinusoidal wave.
This last problem brings in the problem of what the voltage might look like, because if the current is very non sinusoidal then the voltage could be too. If the voltage is non sinusoidal then we cant use a meter to measure the voltage we have to use a scope.
In a simulation the current and voltage will look sinusoidal because the inductor is most likely a linear inductor, but if you would like to see what it looks like for a non linear inductor then you need to choose a model which models some of the characteristics of the core material as well.
If you want to stick with a linear model in the simulation then it would be better to use an air core coil so you get at least some results that might be close, as long as the other effects dont start to take a toll, like for example the AC resistance of the wire itself goes up with frequency so the equivalent series resistance Rs could go up significantly in the real world inductor as frequency goes up. This AC resistance would not be the same as the inductive reactance but would act more like an increase in Rs as frequency went up. For the approximate averaged analysis you can see this complicates things too:
f=sqrt(R1^2-Rs(f)^2)/(2*pi*L(i,t))
where as you can see Rs is now a function of frequency f.
To add still yet another difficulty, if there is an y DC offset present in the drive waveform then we have to contend with that too, meaning the equation gets more complex again:
f=sqrt(R1^2-Rs(f)^2)/(2*pi*L(iac,Idc,t))
where the inductor is now a function of both the instantaneous AC current and the DC current as well as time.