# Inductor datasheets not showing impedance vs frequency plots

I regularly come across datasheets for inductors that do not mention the impedance vs frequency plot.

I am starting to think that maybe the DC impedance does not change (much) up to a certain point in the given graphs, that is why it is not shown.

For example MSS1583-154KED inductor shows these two plots only:

And lets take for example the 100uH case, for the DC resistance it says 0R090 typical, 0R103 maximum. And I think up to ~11Mhz, this resistance wont change much, like it might get to 0R150 Ohms.

I have seen plots/inductors where my point here is wrong, but I am trying to find a middle ground for the inductors that dont have their impedance plot shown.

• Hm, that should say inductance, since it's not changing much, from the left side, in the right figure. But this equally well says impedance doesn't change much from linear (i.e. for pure L, Z = jwL, and L is constant). Commented Sep 19, 2023 at 21:36

If you know ESR and inductance vs frequency you can calculate the impedance as

$$Z(f) = {\rm ESR} + j2\pi f L(f)$$

The way they will have measured the $$\L(f)\$$ characteristic is to measure the impedance and determine the inductance by inverting this formula.

If you're concerned about the frequency dependence of ESR, some vendors do provide this information. For example, Murata's SimSurfing tool provides this chart (after a bit of tweaking) for a 22 uH / 2 A inductor (they don't seem to have one in the size you're looking for):

If you can find a SPICE model for your inductor on the Coilcraft site (I couldn't, although they do have them for many other series), you could extract the ESR vs frequency information from using it in a simulation.

• This works until winding capacitance becomes a significant factor. Commented Sep 19, 2023 at 14:36
• @MathKeepsMeBusy At which point the L(f) starts to diverge from a flat line, just as shown in the charts in the question post. Commented Sep 19, 2023 at 15:02
• Note that ESR is a function of f as well! Commented Sep 19, 2023 at 21:31
• Cool, I verified that function with 10uH SER2918H-103KL inductor from its datasheet where it mentions impedance as well: gr.mouser.com/datasheet/2/597/ser2900-270685.pdf Looks about right, Thank you! Commented Sep 20, 2023 at 9:17

If you want detailed data, you need to measure it yourself. Just for kicks, I measured and compared a single winding of a Coilcraft MSD1260-473 (47 uH coupled inductor).

The first two graphs are measured series inductance & resistance versus frequency using a HP 4194A impedance analyzer. The right-hand graph is expanded to show the resonance portion. The spec sheet says that the resonance is typically 8.7 MHz where the measurements show it's about 13 MHz. The measured low frequency (100 Hz) resistance is about 0.2 ohms, 0.16 ohms using a 4-wire DC ohm meter which is close to the published 0.174 ohms DC resistance.

The graph below compares the Coilcraft inductance versus frequency graph in their PDF data sheet against measured data. The results are pretty close, but the measured data is slightly better than the published graph.

In my experience of comparing component published data with measured data, Coilcraft published data was pretty good. I'm guessing the published data is conservative so designers will have a good experience with their products.

• Yeah I would love to measure them myself as well, I might not have impedance analyzers but I think I might be able to get away with using my nano VNA analyzer from china. It does a good job with antennas. Commented Sep 20, 2023 at 9:19
• @ChristianidisVasilis I've found that the HP 4195 network analyzer is fine for measuring impedance in the few ohms to 1k ohm range since it's a 50 ohm system. I would assume the inexpensive VNAs have the same limitation. An impedance analyzer like the HP 4194 has a much wider range. EBay is a good source for such test equipment of yore at a reasonable price as long as you're motivated to do minor repairs.
– qrk
Commented Sep 20, 2023 at 13:32

I am starting to think that maybe the impedance does not change (much) up to a certain point in the given graphs, that is why it is not shown.

In fact, impedance does not change [from proportional], when Q factor is very large.

There is an underlying fundamental here: the Kremers-Kronig relations. Indeed, to the extent we can model/measure a component as a one-port (that is, it has two terminals, and behaves with no reference to any other connection ground or otherwise, current into one pin is perfectly balanced by current out the other, there are no common mode effects), the fact that it is a real component necessitates causality/analyticity and therefore the real, imaginary, or magnitude aspects are all related uniquely, i.e. you only need to measure one.

Granted, since derivatives are involved, this relation is highly susceptible to measurement error, so you can't expect an accurate Q or ESR plot from fitting the above inductance curves.

A good way to play around with this, may be the conversion/synthesis tool I wrote some time ago [links to my website]:

Coilcraft SPICE Model Converter | Calculators | Seven Transistor Labs, LLC

Along with similar discussion at the bottom, you can adjust parameters in the interactive calculator (also click-and-drag on values for fast adjustment!) and see the effect on all measurement aspects: |Z|, R, X, Q, etc.

A consequence of the K-K is, a lossy reactive component has an impedance slightly less than proportional (or inversely) with frequency. Anywhere you see an inductor with some Q factor; or for a capacitor with ESR and Z plotted and the two track as parallel asymptotes, the ratio of those two curves (reactance X / resistance R) gives the Q factor; then the slope of impedance |Z| on a log-log plot will lie at a flatter angle, determined by that Q factor. In other words, real lossy components are not $$\Z \sim F\$$, but $$\Z \sim F^{1-\epsilon}\$$, where $$\\epsilon\$$ is a small value when Q is modest to large.

I haven't actually worked out the exact relation, as it's not important to me, other than to note that the important element in the above calculator has equal portions (i.e. Q = 1) and therefore a slope of 1/2 (i.e., $$\R = X \sim \sqrt{F})\$$. Or, let's say... applying K-K to the sub-proportional $$\F^\alpha\$$ ($$\-1 < \alpha < 1\$$) case is an exercise for the student. :)

Finally, the application to modeling, is that we can approximate such an element over a finite frequency range, with finitely many dissipative elements: a geometric series of RC or RL networks. Which, intuitively, has the effect of connecting more capacitance or inductance in parallel, reducing the apparent value of L, or increasing C, as frequency goes up. This can only occur over a finite range, because the impulse response of such an (ideal lossy) element settles very slowly over time, i.e. the difference between the element and a lossless or perfectly lossy element (we only have R, L and C to build lumped-equivalent networks from) diverges at both short and long time scales (high and low frequencies).

Fortunately, real components are finite as well, as inductor DCR dominates at LF, and EPR and C at HF; or capacitor leakage at LF, and ESR and ESL at HF.

Regarding the data in qrk's answer (original research, splendid!), we might possibly see confirmation of the very fitting errors I identified on the above page -- the published flatter curve may be a curve-fitted result, perhaps using the very same parameters used in their SPICE models (the older ones); the fact that it's flatter (decreasing less as frequency rises), implies higher Q than measured -- indeed higher Q than is physically possible given other constraints (namely, losses at high and low frequencies; the fact that the curve ticks up towards 10MHz at a certain rate, also dictates how much it rises, or how quickly it can decline, in the 0.1-1MHz range!).

In other words, what you will find (or, what I've found from testing, anyway), is using their model parameters as a starting point (which, remember, use nonphysical elements: pure resistances and inductances that vary with frequency), a reasonable fit can be had, but it will always be an approximation of the given model, whether by compromising more on L(F) droop, or overestimating Q at LF and HF while underestimating Q at MF (middle frequencies).

For a more dramatic illustration of X and R interdependence, you might look at some ferrite bead curves, perhaps even curve-fit some yourself (set up an RLC network and tweak values and topology until the curves match; this is a good exercise for getting used to whatever simulator you're working in, as well). I've published a few model created in this way myself, e.g. HI0603P600R-10.ckt (fitted using above calculator tool), or MI1206L391R.ckt (fitted by hand, arbitrary network) [links to my website; plain text files].

• Thank you! everyone's answers have been helpful. I will check your models in the future for sure Commented Sep 20, 2023 at 9:18