@pkvintage
I had a look at the Audionote website and the manual for your M6 Phono.
So 126mv for 1v out is 18db - that is the line stage specs.
The phono is quoted as 63db. If the phono is 63db then you should not need an SUT at all, there would probably be an internal SUT and the phono would have enough gain for your Koetsu straight in.
I think it is more likely the 63db quoted includes the 18db in the line stage. If this is the case then the phono alone has 45db gain ( 63 - 18 ). If the phono gain is 45db then you probably need a SUT with a gain ratio somewhere between 1:10 ( 20db ) to 1:15 ( 24db ).
I looked at your power amplifier the Audionote Conquest Silver Signature. There are 2 versions -
first one specs out at 250mv for full power. So given the preamp specs are for 1v out you can see the power amp is very sensitive and you have a bit of spare gain.
For this reason I would suggest you try a SUT with 1:10 gain ( 20db ).
Some folk will go on about loading, but my advice is to forget about that and focus on getting the correct gain. Too much and you’ll be running the volume pot too low which can mean channel imbalance more likely.
If your gain is too low, obvious you’ll have a higher noise floor.
There is a low gain version of the Conquest Silver Signature and this is spec’d out at 3.15V to full power. I doubt you have this version.
I can’t see why Audionote should be able to give you advice on this.
Given the quality of your system you want a decent SUT - Stevens and Billington, Tango, etc. Higher end vintage units can deliver bang for your buck eg Denon AU1000. The Zesto mentioned uses standard Jensen transformers which are very neutral, reasonable quality. Other folk consider the Llundahl transformers quite good. There are obvious other bespoke companies offering solutions - comes back to budget.
Hope this is useful for you.
