Transformer for driving high impedance headphones from a low impedance source?

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After seeing a talk by Nelson Pass regarding the B1 buffer amp with a transformer on the output, I was wondering if it would be feasible to use a transformer to drive high impedance headphones such as 650s directly from a source that can't produce enough voltage, e.g. an iPhone.

E.g., something with about 32 Ohm primary, and 300 Ohm secondary.

Is that doable, and can anyone recommend a suitable transformer?
 
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High fidelity audio signal transformers are expensive and can add harmonic distortion. Notably third order distortion. Easy to make less expensive than special transformer, a simple headphone amp with a JFET and MOSFET that can drive 600ohm headphones beautifully.

Pocket version:
xrk971 Pocket Class A Headamp GB

Desktop version:
xrk971 Desktop Class A (DCA) Headphone Amp

Plus you get a power boost. The problem with using only a transformer is that you are limited by conservation of energy through the transformer. An iPhone’s output is never going to be enough for truly satisfying headphone experience. A high impedance headphone requires higher voltage to actuate its voice coil. A transformer with higher voltage output has lower current inversely proportional to the voltage gain
 
If the transformer's specified with impedances for its windings that likely will mean its a signal transformer and those will probably have too high winding resistance to work well in this application. You could try to make your own trafo for driving headphones - you'd need a large-ish ferrite core (perhaps PQ40 would do). I've built several smaller trafos for headphones but never tried building a step-up, they've all been step-down. Could be the leakage inductance would turn out too high for good frequency response but it'd be worth a stab.
 
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