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# Understanding Core Loss Measurement

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## Understanding Core Loss Measurement

(OP)
Hello folks,

I'm looking for a way to measure core loss in RF transformers & inductors. I ran across this PhD dissertation:
https://vtechworks.lib.vt.edu/bitstream/handle/109...
which looks thorough and practical, but I'm having trouble understanding some of it. I've tried to contact the author with no success.

Chapter 3 (pg 65) looks like just the ticket. But I don't understand the derivation of eqn 3.1.
• Why does the core power depend on Ipp (capital I) and not ipp? Capital Ipp is just the current resulting from the magnetizing inductance, which will vary with Lm (fig 3.1), while ipp is the current step due to core loss.
• What does the duty cycle D have to do with core loss? Driving fig 3.1 with a square wave, Rcore sees approximately a rectangular wave across it and should dissipate the same power regardless of D. Where do the D terms come from?
In short, I pretty much don't get anything about eqn 3.1! Any help would be greatly appreciated, and then maybe I'll start understanding eqn 3.2...

Gerrit

### RE: Understanding Core Loss Measurement

Hi reson8or,
There's a typo. You're right, it isn't Ipp. It's ipp for eq 3.1. Looking at figure 3.3 If you split up ipp into i+ and i- and also split Vpp up into V+ and V- then, do algebra for 2 minutes, you'll come up with: P=D*(1-D)*Vpp*ipp which is the correct eq 3.1.
You will see something like figure 3.3 on your o-scope and it is pretty easy to estimate your core loss after applying eq 3.1.

Given a non-50% waveform (such as what you'll see in current sense transformers and phase-shift resonant inductors), I've had pretty good accuracy by splitting the core loss into two parts: #1 for the time and voltage of the positive swing and #2 for the negative swing. Use either the Steinmetz equations for your core material or, the charts of loss vs F & B given in the data sheets. For the positive swing, the frequency is 1/2 T1 and the Flux is 1/2 delta flux1. Do likewise for the negative swing. Multiply the loss of part #1 & #2 by their duty cycles then, sum the two. That's the total core loss.

I came up with the routine which I just described in the 90's. For a few evenings I wound various cores, applied a narrow non-50% pulse and recorded delta V and delta ipp from the scope, applied equation 3.1 and compared the two. The results where within about 20% of the equation, good enough for me to give the mechanical engineers some numbers which they needed to work with. A few years later I saw an paper at APEC in which the author did pretty much the same thing. He brought up some discrepancies in that simple equation which had to do with unequal flux density within the core geometry itself.

207 pages from Lee and the other Virginia Tech guys!!! Yikes! I know they could have simplified that into a few paragraphs but they go into a lot of detail, more than I need for my work.

Darrell Hambley P.E.
SENTEK Engineering, LLC

### RE: Understanding Core Loss Measurement

(OP)
Hi Darrell,

Thanks for your careful explanation. It's not intuitive that core loss would depend on D (at least to my intuition), but I can see how splitting the problem into + and - V partitions could lead to it. I'll draw some waveforms and see if I can improve my intuition.

The square wave drive measurement of ipp looks like an easy way to get directly to core loss. It would be worth building a high-speed, low-Z, variable-V pulse driver for it. Is that what you did?

Gerrit

### RE: Understanding Core Loss Measurement

#### Quote (reson8r)

It's not intuitive that core loss would depend on D (at least to my intuition)
See discussion on page 23

#### Quote (vtechworks page 23)

Many literatures have reported that the core loss under
rectangular excitation is different from sinusoidal excitation, and the duty cycle plays an important role to the loss. In 1978, by comparing the measured the core loss of various materials under these excitations, Chen [17][18] discovered that the core loss for square voltage excitation is lower than the sinusoidal excitation with the same AC flux amplitude. In 1991, by using Fourier analysis, Severns [19] analyzed the core loss for rectangular excitations under duty cycles other than 50%. At 50% duty cycle, the higher order harmonics are very small, so the core loss is dominated by the fundamental. The triangular excitationâ€™s fundamental amplitude is lower than sinusoidal, so its loss is lower than sinusoidal. As the duty cycle becomes smaller or bigger, the high order harmonics makes the core loss larger than the sinusoidal. This Fourier analysis helped the qualitative understanding of the core loss under non-sinusoidal excitations, but it is not quantitatively accurate...
See also Figure 1.4 which seems roughly proportional to 1/[D*(1-D)] with a minimum at D=0.5

=====================================
(2B)+(2B)' ?

### RE: Understanding Core Loss Measurement

(OP)
I guess that's what I get for skimming the material! Thanks, Electricpete. I'll read the paper more thoroughly.

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