Transformer Parameter Extraction & BH Curve Plotting

In addition to building a Spice model for a transformer, it’s also important to know whether the core can support the flux generated by the primary winding. This is similar to the inductor problem I mentioned there.

Small HV transformer with test winding
Small HV transformer with test winding

Measure the core’s area and path length. One  can reasonably expect all cores to have hard metric measurements these days: Yankees set those calipers to millimeters and get over it. Besides, you need metric units for everything that follows.

This transformer has two E-shaped core halves, so the center leg (the one with the windings on it) has twice the area of the outside legs, which are 7 mm thick and 5 mm wide. The central leg is twice that width: 10 mm.

Figure the stacking factor for a ferrite core is, oh, say, 0.9, making the effective core are:

Ac = 0.9 · 7 · 10 = 63 mm^2 = 0.63 cm^2

You need cm^2 here to get gauss later on.

The core is square, 30 mm on each side. Divide it in half, right down the middle of the center leg, then figure the mean path length around the middle of that rectangle:

MPL = 2 · (30 – 5) + 2 · (15 – 5) = 70 mm = 7 cm

Again, you need cm here to get oerstead down below.

Put a few turns Nt of fine wire around the core, outside all the other windings. This particular transformer has three small imperfections where the varnish / sealant didn’t quite bridge from the bobbin to the outer core legs, so I managed to sneak 20 turns of wire through the holes. Call this the test winding: Nt = 20.

Incidentally, that’s why you should always buy at least three units from surplus outlets: one to sacrifice, one to use, and one for a spare. I usually get five of anything.

Connect the transformer primary to a signal generator & oscilloscope Channel 1, connect the test winding to Channel 2, set the channels to maybe 100 mV/div. Set the signal generator for sine wave at maybe 1 kHz, crank on a few hundred millivolts, then read RMS voltages from both channels: Chan 1 = Vp, Chan 2 = Vt.

Knowing Vp and Vt and the number of turns Nt in the just-added extra winding, find the number of primary turns Np:

Vp / Vt = Np / Nt

136 / 40 = Np / 20

So Np = 68

Repeat that exercise, stuffing voltage into the transformer’s actual secondary winding (the HV winding):

4000 / 46 = Ns / 20

So Ns = 1739

Comfortingly, the turns ratio works out to what you’d expect from the voltage ratio measured while extracting those pi model parameters:

N = Np / Ns = 68 / 1739 = 0.039 = 1/25.6

(You may want the turns ratio as Ns/Np = 25.6. Either will work if you make the appropriate adjustments in the equations.)

Having measured the primary inductance as about 15 mH, the reactance at 60 Hz is:

5.6 Ω = 2 · π · 60 ·15e-3

So it’s reasonable to use a 100 mΩ current sensing resistor.

Plug a 6 VAC (not DC!) wall wart into the Variac and wire it to the primary through the resistor. Connect the oscilloscope X axis across the resistor, set the gain to maybe 10 mV/division.

Connect a 220 kΩ resistor in series with a 1 μF non-polarized capacitor, connect that to the normal HV secondary winding, connect the Y axis across the capacitor, set it for maybe 50 mV/div.

The capacitor voltage is the integral of the secondary voltage, scaled by 1/RC. The RC combination has a time constant of 220 ms, far longer than the 16.7 ms power-line period, so it’s a decent integrator.

Small HV transformer BH curve
Small HV transformer BH curve

Fire up the scope, set it for XY display, turn on the Variac, slowly crank up the voltage, and see something like this on the scope:

Tweak the offsets so the middle of the curve passes through the center of the graticule, maybe turn on the bandwidth limiting filters, adjust the gains as needed, then measure the point at the upper right at the end of the straightest section in the middle.

That point, as marked by the cursors, is more or less:

X = 6.5 mV

Y = 100 mV

Now plug all those numbers into the equations and turn the crank…

The magnetizing force H in oersteads:

H = (0.4 · π · Np · Ip) / MPL = (0.4 ·3.14 · 68 · Ip) / 7

H = 12.2 · Ip

Because the 100 mΩ current sensing resistor scales the current by 10 A/V, the scope X-axis calibration is:

H = 122 · Vsense

The core flux density B in gauss (noting that the turns is Ns and converting the peak Vcap voltage to RMS):

B =(0.707 · Vcap) · (R · C · 10^8) / (Ns · Ac) = Vcap · (220e3 ·1e-6 ·1e8) / (1739 · 0.63)

B = 14e3 · Vcap

Finally, at that point where the cursors meet in the upper right part of the curve:

H = 122 · 6.5e-3 = 0.8 Oe

B = 14e3 · 0.1 = 1400 G

Assuming there’s a straight line from the origin to that point (which is close to the truth), the B/H ratio gives the slope of the line and, thus, the core’s permeability:

µ = B / H = 1400 / 0.8 = 1700

It’s allegedly a ferrite core, so that’s in the right ballpark given the rough-and-ready approximations in the measurements.

The answer to the key question comes right off the scope without any fancy math, though. Just beyond the upper-right point the BH curve becomes horizontal, which means the slope is zero, which means the core is saturated, which means the circuit stops working.

Sooo, the maximum value of the primary current is pretty nearly:

Imax = 6.5 mV ·10 A/V = 65 mA

My back of the envelope for the high-voltage DC supply is that a peak of 30 mA will pretty much do the trick, so I’m in good shape. Might be a bit higher during startup, but it’ll sort itself out in short order.


Correction: I did a total arithmetic faceplant in the previous version. I think this is now correct, but you should always cross-check anything you find on the InterWeb, fer shure!

14 thoughts on “Transformer Parameter Extraction & BH Curve Plotting

  1. That looks like Goldmine G16821, and you do mention it’s surplus. Amusingly, I had bought five of these myself, following the same logic you did. I’m hoping to whomp up a power supply for small CRTs out of ’em. I quite like your “grab some clip leads and start from basic principles” approach. Good on ya!

    1. Goldmine G16821

      The very one!

      “grab some clip leads and start from basic principles”

      Damn straight: if it can’t stand some dangling wire, you probably can’t make it work in real life!

      Which can’t be taken to extremes and you really want a stable layout for careful measurements, but there’s a lot to be said for quick-and-dirty measurements when a project’s in the doodling stage.

  2. As I have a fair number of these and I’ve started building things out of them*, it occurred to me to write Chung Hing (the manufacturer of the transformer) and ask them if they had a record of the specifications. They very nicely wrote back and included a PDF of the entire build sheet for it. And it verifies your numbers nicely. Winding #1 is 68 turns of AWG#34, and winding #2 is 1700 turns of AWG#41. If Goldmine still sold these, I’d send the information on to them.


    1. it verifies your numbers

      Whew! I love it when a plan comes together!

      Did they give the winding inductances and core properties, too? I’ve gotten too many “datasheets” from the usual eBay suppliers giving just mechanical details and none of the electrical info I needed…

      1. It’s a little uneven – lots of details about the actual construction (type of insulating paper, copper tape, varnish, etc.) but dribs and drabs about the actual electrical properties. They give the core as EE30 #OJ-43007-EC which means little to me – it doesn’t even say whether it’s gapped or not. They give the inductance of the secondary as “6 H Min AT 1KHz 1Vrms”, the DC resistances (pri 3.57Ω max, sec 600Ω max), the turns ratio (as 68:1700, which I might have simplified to 1:25), the hipot testing parameters, and the winding direction (primary begins on pin 2, secondary begins on pin 8). Weirdly, the other lead on the secondary (the flying lead) is labeled as “5” on the schematic. Additional research on my part reveals that this part was used by both Xerox and Northgate Technologies (a medical equipment manufacturer), and the part was second-sourced by Summit Magnetics. I’m curious as to what your driving circuit looks like – my current one is a a pulse generator driving a single MOSFET. I can send you the spec sheet if you like.

        1. 68:1700, which I might have simplified to 1:25

          And then third shift would wrap exactly one primary turn around a few thousand bobbins!

          I used those things in two projects: a dosimeter charger and an ESR tester. Both were sufficiently low power that I didn’t need much drive.

          The ESR tester used push-pull PWM to stuff a 10 Vpp square wave into the transformer’s secondary winding. That produced a 400 mV output from the primary winding with enough oomph for a low-ESR cap: 20 mA input could drive half an amp out! (Ignoring, as we always do, the primary resistance…)

          I’m down to my last three of those things, but I can add the datasheet to the post for completeness.

          Thanks for the info!

  3. This is exactly the type of article I was looking for!
    But can I ask about measuring unknown cores (let them be ferrite or metal), as easily as possible, as little of winding as possible? So that I dont have to put together and take apart the EI cores all the time?
    I have a digital osciloscope at hand as well, and a chinesse inductor meter.

    1. as little of winding as possible

      Because inductance varies with the square of the turns, you don’t need many turns to get a reasonable reading. Wrap a dozen or so turns around the core, read the inductance, and then work from turns and inductance to find the AL value.

      Knowning AL and the dimensions, you can probably get a good idea of the material in the core.

      Knowing the inductance at a low frequency, pick a capacitor that will resonate it somewhere near the frequency you need in your actual circuit, then use a signal generator to find the resonance. That gives you a better idea of the core properties.

      That post may also be helpful, although it presumes you have a coil or transformer already wound.

      Good hunting!

      1. Thank you so much for the reply! How would I find out the permeability? I need it for calculations. I have some books on transformers and I know some theory from school, but still I am struggling to calculate a transformer, let say a microphone input transformer for my tube preamplifier. I do not mind if it will be big. All the companies like jensen, cinemag, lundhall, which make these transformers make them very small, for various purposes, from quality permaloy materials, but I just want a reasonable home build transformer. Could you give me some hints on finding out the permeability and maybe calculation of such transformers? I have a lot of cores but I don know their parameters, and I want to build the transformer right, so it wont be saturated or the impedance ration will be bad. thaks!

        1. finding out the permeability

          Some search-fu turns up that useful page, which gives a version of the familiar formula:

          L = (N^2 * mu * A) / MPL

          You wound N turns on the core and measured L. Guesstimate both A and the Mean Path Length around the core, then solve for the absolute permeability mu (if you used the right units!). Divide mu by mu-sub-zero to get the material’s relative permeability, then cross-check with some manufacturer’s datasheet to see if you’re in the right ballpark.

          so it wont be saturated

          That depends on the core material and dimensions, but you probably want to measure it using the same technique I used. You will need a substantial number of turns to get enough flux, but you’ve already weeded out the useless cores (knowing AL), so you won’t wind too many before you find one that might work in your application.

          You must ensure the core has enough material to support the flux at low frequencies, because the flux varies inversely with frequency. That’s why audio transformers tend to be so bulky: they must support the flux over a frequency range spanning three or four orders of magnitude. It’s worth spending some time with the basic equations to make sure you understand how that works.

          Hope that gets you started…

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