# Characterize ferrite cores, e.g. core losses

How can I characterize ferrite cores? I can measure saturation, but how can I measure core losses so I can decide what frequency to run them at?

I could charge a primary winding to a certain current, then disconnect the primary and measure the current in a secondary across a resistor with my oscilloscope. Do I need e.g. different resistors to get data for different frequencies? Can I get the B/H curve that way and calculate from there? Would I need to measure ramp up in the primary, too, maybe with resistors? I can consider wire resistances.

Building an AC primary driver and measuring power in vs. power out is probably too challenging for me.

I have two big cores intended for a HV PS for a Farnsworth-Hirsch Fusor and I need a small MPPT PS for a 250 g solar model aircraft.

I may be able to find data for the two big cores, but I'd like to be able to characterize unknown cores.

Edit: My big cores are 1533 g and 298 g, and the core for the 250 g airplane should be <10 g, I guess. Would film capacitors be a good choice for the big cores, or are there suitable ceramic ones?

Actually, I would dare say AC power is the easier way to go here -- using RF techniques to measure absorption, and doing it at low frequencies is easy with an oscilloscope, function generator, and a few components.

For example, consider the calculator at the bottom (links to my website):
https://www.seventransistorlabs.com/Calc/RLC.html#cmatch

By setting up a network of low-loss capacitors (C0G ceramic preferred), the bulk of the resonant current, and thus the predominant imaginary component of the coil impedance, can be canceled out. The impedance of a typical winding might be quite high (or low), so that matching it to a 50Ω generator is at best challenging, and often comes at the expense of high losses (between generator and DUT) -- compare the above resistor-divider schemes for example, where the coil voltage is strictly less than the source. This way however, we can deliver a large fraction of the output power into the coil, and develop representative voltages in it.

A typical 15Vpk generator is capable of about a half watt. Not much in the grand scheme of things, but impressive to actually feel a component warming up due to what you've otherwise considered negligible signal power.

Why is voltage important?

Magnetics are nonlinear materials. In general, both losses and permeability vary with amplitude, so you get the most representative values by measuring as close to design conditions as possible. We don't need to replicate the waveform, as fundamental dominates -- even if the frequency exponent is rather unfavorable, it's unlikely that harmonics contribute more than 10% or so of overall losses, so the sine-wave fundamental approximation is a reasonable one.

Note that a large or lossy material requires more power to run at actual design level; a function generator won't work for everything. You can buy or build an amplifier, but do be careful to account for its output impedance: the value of a function generator is its carefully balanced resistive output. You can also build an amplifier with output impedance other than 50Ω, perhaps to better suit the load in question, or available power supplies.

You can also test a smaller article, and hope that the measurement remains representative when scaled up. This, too, is challenging with magnetics, as the strength of eddy currents is proportional to length scale. But the effects of individual particles/crystals of the magnetic material do not, so you end up with different e.g. modified Steinmetz (MS) parameters for different core materials, shapes and sizes.

Offhand, I suspect the eddy current limitation is small enough to ignore, as core materials tend to be low enough loss, and small in scale, to avoid it; manufacturers don't usually give different MS parameters between core sizes, just by material. (And at that, often they don't give different parameters between permeability grades of the same family; which, is surprising at best, but, I wonder what the error bars actually are. I would very loosely guess, they'd only do that if the variation is on the order of 10 or 20%, enough you aren't likely to be burned (hah, literally, we're talking about heat dissipation here..) by it. But who really knows, without all the data to back it up?)

Sine waves are most likely the best option here.

To do this with square waves, we would need a complete inverter (and perhaps rectifier) circuit, and some means of quantifying switching and conduction losses -- not impossible, but it makes things a whole lot harder to tell for sure, and we're looking for potentially quite small differences, particularly as the Q factor rises into the hundreds.

Or, for a more small-signal explanation: we could simply measure the complex impedance directly, by applying some voltage, measuring the current, and optionally, calibrating out phase shift and gain of the test jig. But this is quite difficult to do by oscilloscope:

• Oscilloscope measure features are often quite limited; the phase measurement might be calculated between zero-crossings, for example, so are very sensitive to noise near the zero crossing.
• The noise floor in general is typically quite poor, as receivers go; 8-bit converters are the most common (give or take "Hi-Res" modes or averaging, or higher-bit-depth models). Which is to say, the smallest resolvable instantaneous change, is a modest fraction of a percent, the same magnitude as the Q we're looking for (i.e. the difference in phase between Q = 100 and Q → ∞ is about 1%).
• Using an FFT mode, phase is often discarded (magnitude view only), so that such a vector measurement isn't possible at all.
• The data series is its strongest advantage; and a formidable one when used properly, but because of the above limitations, you may have to simply dump the waveform to PC and process it separately, which is a pain. (And, obviously this isn't of much help for those equipped with analog scopes..!)

A similar process applies to vector voltmeters: we can apply a reference voltage, read the current, and pass it through an I/Q mixer to resolve the real and imaginary components directly. But component tolerances everywhere spoil the balance of this system, both in terms of cancellation or purity (1V∠0° might not resolve as exactly 1V amplitude, or exactly 0° phase), or orthogonality (1V∠90° might not resolve as 90°). A simple 2x2 matrix transformation suffices to calibrate this, but that's a lot to handle in terms of analog signal processing, and even with digital acquisition and calibration, that's four cal points needed per measurement frequency. Suffice it to say, such instruments are challenging to build accurately, so as to resolve large Q factors with small error bars.

So, anything we can do to make the job easier -- canceling out some of the reactance with a capacitor, for example -- reaps benefits in accuracy.

Fortunately, C0G capacitors are practically ideal -- it's really quite peculiar how ideal they are, for example connecting 10nF chips in parallel on a PCB, nearly touching each other, the "sloshing" resonant mode between them is still resolvable. (Try that with almost any other capacitor type, and ESR dominates this resonant mode, so that they effectively behave in parallel at all frequencies.) We do still introduce a measurement error, as losses are inevitable -- but with Q factors of 3000+ being typical, we expect a measurement error less than 10% for inductor Q factors up to 300, for example. That's not bad at all.

• +1. But one thing: even if the frequency exponent is rather unfavorable, it's unlikely that harmonics contribute more than 10% or so of overall losses, so the sine-wave fundamental approximation is a reasonable one. This is true when the duty-cycle is 50% only. Higher duty-cycles will bring higher losses even for the same frequency. I don't know if the OP's intended applications require higher duty-cycles but after characterisation or prediction the real application may end up with higher losses. Commented Mar 6 at 12:01
• Quite so. We prefer to avoid odd duty cycles when we can, but every so often they're required given other constraints, and we expect increased core losses in that case. In the limit, harmonics are equal amplitude and core loss might rise by, not just a percentage, but several fold or more. (The effect isn't sudden; for modest duty cycles, say 30-70%, the harmonic contribution might be in the 10-20% range.) Commented Mar 6 at 12:59

but how can I measure core losses

Well, I don't know your precision requirements but measuring core loss by yourself accurately can be a time-consuming and difficult process, and also open to make significant errors in measurements.

The only method I'd suggest requires accurate temperature measurement: You'll need to use a contact-base temperature measurement device (e.g. thermocouple). Also you'll need to isolate the entire setup (core & TC) thermally from the environment.

• Wrap a few turns around the core.
• Apply a voltage at a certain frequency (preferably sine wave).
• Calculate the flux swing (Faraday). Make sure the core doesn't saturate.

$$V_t = N \ A_e \ \frac{\Delta B}{\Delta t}$$

• Wait for some time for the temperature to stabilise (this can take minutes).
• Take the delta-T (temperature change) after stabilisation and multiply this by the ferrite material's (usually MnZn) specific heat (usually ~750), and with the core's mass (in kg). That will give you the energy dissipated as heat to rise the core's temperature.

$$c = \frac{Q}{m\cdot\Delta T}=750 \ \mathrm{\frac{Joules}{kg \cdot °C}}$$

• Divide this energy by the time duration you applied the wave for, and you'll get the power dissipation.

$$P = \frac{Q}{\Delta T}$$

• Divide this by the volume you'll get loss per volume $$P_V=\frac{P}{V_{core}}$$

You'll need to repeat the whole process for different frequencies. Also, you'll have to cool down the core to the room temperature (either by waiting or by applying forced air, for example).

Note that the loss data you collect here is for sinewaves only. For excitation with square wave, as stated in Tim's answer, the fundamental dominates the total loss but only when the duty cycle is 50%. The real loss will be higher when the duty cycle is higher than 50%.

Charging the inductor with current is possible, but it's much easier on the bench to charge capacitors, with their much longer and more forgiving time constant. I would get several different capacitors. Charge each to some voltage, then measure the ring-down on your scope when you connect them to an inductor wound on your unknown core. That will give you inductance and loss at various different frequencies.

The maths-heads amongst us might do an FFT, or a curve-fit, of the captured traces. However, you will get a lot of data from just estimating the frequency and the rate of decay by locating the peaks of the waveforms. Be prepared that the loss and inductance may change at different amplitudes, so assess different parts of the curve separately, or start with different amounts of energy stored in your capacitors.