I am involved in the direct measurement of inductance of vacuum tube audio output transformers. Inductance levels vary from around 1 H to 50 H for the primary and down to just a few mH on the secondary. In this measurement method, I would like to be able to include copper and iron losses (copper losses are series R and iron losses are modeled as parallel R across the transformer windings). The purpose of these measurements are to help accurately model, using LTSpice, the vintage Acrosound output transformers that are so popular in Williamson type amplifiers. Any and all thoughts would be appreciated including LTSpice models of other transformers. Best regards, David.

  • \$\begingroup\$ It is not clear what you’re asking. Do you want to measure the inductance of each winding (unloaded), or do you want to measure core losses? Series/copper resistance as well as magnetic core losses have nothing to do with winding inductance. They’re not related. So just measure the winding inductance, that’s the inductance. You’re done. As for core losses, you definitely cannot model that as a parallel resistor. There are multiple loss mechanisms that behave differently (and differently from each other) depending on frequency. Being an audio transformer, that is non-trivial. \$\endgroup\$
    – metacollin
    Dec 8, 2017 at 4:32
  • \$\begingroup\$ The Williamson transformers are flat from 5Hz to 50,000Hz, if I recall rightly. The phase shift is key, so the small amount of feedback preserves waveforms. The iron-noise (just made up that term, as the domains flip) needs to be characterized. \$\endgroup\$ Dec 8, 2017 at 4:35
  • \$\begingroup\$ domain-wall noise is from hysteresis. \$\endgroup\$ Dec 8, 2017 at 5:23
  • \$\begingroup\$ Some tube audio uses transformers with a DC bias current. Are you using a suitable tester, that allows bias current? \$\endgroup\$
    – Whit3rd
    Dec 8, 2017 at 6:10

1 Answer 1


Just off the cuff...

  1. Measure DCR of primary and secondary and after max Vrms/Z(f)=I with load is known, you have I²R in both primary and secondary.
  2. Measure Lp/Ls to compute n² turns, voltage ratio.
  3. Measure Output Impedance with primary shorted using known source impedance to measure V drop and thus Zsc.
    • This can also be defined with the rated, Zr[Ohms] = [Vrms]²/[VA]
    • then Z load/ out is your dampening factor for the lowest bass f of interest with cathode Rc/n² added to Zsc in series = Zout
  4. Measure impedance by increasing both I and f as Eddy Current losses increase with Pec = k * (I*f)² by measuring impedance drop at 10k or 20kHz with rising current. This will not be just a fixed shunt R as EC losses are not constant.
    • If you don't have a Sig Gen , use Audacity.
    • Good CRGOS Silicon Steel with Silicate insulated lamination gives the lowest hysteresis
    • Bsat threshold for inductors and transformers is usually defined by 10% drop in L with applied V, but using a primary short circuit and driving the secondary is easier with a low power Amp and sig gen input. ( I think .hmm)

If the Laminate is good M6, the core losses can be less than 1.5W/kg at 50 Hz. Any interlayer shorts can reduce the overall core capacitance but also raise the B level closer to saturation.

I'd be very impressed if the transformer spanned more 3 decades in frequency with a flat response. I don't ever recall seeing any. But this could be a first with greater laminate gaps and lower mutual coupling.

  • 1
    \$\begingroup\$ Your concern is valid but the Williamson design paid unusually close attention to interleaving primary and secondary windings to achieve very high mutual coupling. I don't remember if it achieving a full 4 decades, but that's almost how long ago I read the articles... \$\endgroup\$ Dec 8, 2017 at 10:06

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