Mini-review: Miyajima ETR-Stereo step-up transformer

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Yes, I spotted that too. 2.2pF would be the capacitance of just a few inches of cable, so that can't be right. Up to 2.2nF would make more sense, though the lower values (0.47nF) would still be a bit too small to do much with most LOMC cartridges. Maybe the values are uF as the manufacturer says. Up to 2.2uF does sound like a lot though.

As above, the capacitance is probably uF, not pF.

The numbers for this knob are actually the number of active turns used in the primary coil. The number of turns used determines the primary inductance which does relate to the cartridge coil impedance, in a way. Say for instance that the target for the LF cut-off of the transformer is 10Hz and the cartridge impedance is 5 ohms, a certain primary inductance (and therefore a certain number of turns) will be required to achieve that. If the cartridge impedance was only 2 ohms you wouldn't need so much primary inductance and could use fewer turns on the primary. If the cartridge impedance was 12 ohms you would need more primary inductance and therefore more turns.
However, that all relates to a certain LF cut-off, arbitrarily chosen at 10Hz. If you chose the LF cut-off point to be some other figure, the turns requirements would be different. But why not simply use the maximum number of turns and get the lowest possible LF cut-off? That would be the best option if the winding wire had zero resistance and there was zero coupling capacitance between windings, but wire like that doesn't exist. In practice it's best to use just enough turns of wire on the primary to keep winding resistance and capacitance down to a minimum.
The concept of a "correct" setting for any given cartridge impedance is a bit vague and subject to caveats, so I agree with Miyajima - "that the settings should be chosen by ear and not by rigid observation of guidelines".

That isn't really correct - it's the combination of input coil and output coil which determine the step-up ratio.
This knob, similar to the previous knob, selects the number of turns used in the secondary coil. The numbers are the number of turns used. Therefore both the "input knob" and the "output knob" are used to calculate the voltage gain. For example, selecting 120 for the input and 4000 for the output gives a turns ratio of 120:4000, or 1:33. Changing the input knob to 180 and leaving the output knob at 4000 would give you a turns ratio of 180:4000, or 1:22.

The last knob selects a value of resistance load which appears across the secondary coil and is in parallel with the 47k load of the following MM phonostage. Its effect will be mainly to damp ringing in the transformer.

Yes, the knobs aren't particularly easy to understand and using them is far from intuitive.

Crumbs! my head hurts!

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Sorry for any adverse effect on yer noggin
Yes, the maths/theory behind it might be a bit heavy but in practice it isn't so bad. Let me summarise:

1) The first knob affects the capacitive load seen by the cartridge. Even when set to zero the cartridge will see capacitance from a variety of sources, so the numbers can't be taken too seriously and the effects are somewhat unpredictable. Basically, suck it and see.

2) The second knob controls the number of turns on the primary winding. There really isn't a "correct" number of turns for a particular cartridge, so again, suck it and see.

3) The third knob controls the number of turns on the secondary winding. The ratio of primary turns to secondary turns gives you the turns ratio. Use this knob in combination with the previous knob to set the turns ratio you require. There's quite a bit of leeway when choosing the ratio and there really isn't any optimum or perfect match for any particular cartridge, so basically, suck it and see.

4) The fourth knob selects an additional load for the transformer (in addition to the 47k of the following mm phonostage). It will alter the load as seen by the cartridge and it will change the effects of inter-winding capacitance and leakage inductance on the transformer's frequency response. Without access to some measuring equipment the user cannot really know what effect the knob is having - other than listening for changes - so the only thing you can do is ... you guessed it ... suck it and see.

Looks like my random approach is the correct one then!

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Sorry for any adverse effect on yer noggin
Yes, the maths/theory behind it might be a bit heavy but in practice it isn't so bad. Let me summarise:

1) The first knob affects the capacitive load seen by the cartridge. Even when set to zero the cartridge will see capacitance from a variety of sources, so the numbers can't be taken too seriously and the effects are somewhat unpredictable. Basically, suck it and see.

2) The second knob controls the number of turns on the primary winding. There really isn't a "correct" number of turns for a particular cartridge, so again, suck it and see.

3) The third knob controls the number of turns on the secondary winding. The ratio of primary turns to secondary turns gives you the turns ratio. Use this knob in combination with the previous knob to set the turns ratio you require. There's quite a bit of leeway when choosing the ratio and there really isn't any optimum or perfect match for any particular cartridge, so basically, suck it and see.

4) The fourth knob selects an additional load for the transformer (in addition to the 47k of the following mm phonostage). It will alter the load as seen by the cartridge and it will change the effects of inter-winding capacitance and leakage inductance on the transformer's frequency response. Without access to some measuring equipment the user cannot really know what effect the knob is having - other than listening for changes - so the only thing you can do is ... you guessed it ... suck it and see.

Thanks for that Andrew (tbh, it's not that difficult to spin my noggin!), as Tom says , all part of the fun, suck it and see indeed, all in an evening's listening.
Getting the subtle changes in settings out of the cartridge, is for some of us, great fun.
A quality piece of equipment that i'm sure will give Tom many hours of audio pleasure.
Very nicely reviewed.