The idea of an amplifier that uses transformers instead of tubes or transistors, is an interesting one. Appreciably the SE magnetic audio transformers were used many years ago for various functions. Could such a system work, and more importantly provide a high quality music signal at the output?
Update November 11,2021
A complete circuit for a magnetic amplifier , or transformer based amplifier is found in the links below. Unfortunately, the amplifier has to have an AC current running through its coils, which rules it out for me: I will not deal with AC current at this time. It remains to be seen if some arrangement of transformers can be used to amplify an audio signal. At least one amplifier, the Lutek, uses magnetic amplifiers in its power stages:
Article on Magnetic Amplifier (1995)
Initial testing with one transformer was surprising : the sound of the music did increase in volume, but was distorted . The signal out of the headphone jack was in any case very low, so the sound did not provide encouraging results.
Further testing with two transformers would be very interesting.
The original 1960 patent is at this site:
https://worldwide.espacenet.com/publicationDetails/originalDocument?CC=US&NR=3131360&KC=&FT=E
An actual demonstration on You Tube of a transformer based amplifier (no tubes or transistors) is at this location. It works, apparently, and the sound quality is quite good from what I hear. There are several components involved though.
https://www.youtube.com/watch?v=ci9AI5KuToM
A discussion on DIY Audio is here:
https://www.diyaudio.com/forums/solid-state/115221-transformer-amplification-amplifier-2.html
Links:
The main site for magnetic amplifiers Sparkbang
Nuts and Volts Magazine:
https://www.nutsvolts.com/magazine/article/the_magnetic_amplifier
Sunpower site: Limitations of Magnetic Amplifiers:
https://www.sunpower-uk.com/glossary/what-is-magnetic-amplifier/
Contains a link to the book: https://alixus.wordpress.com/forgotten-magnetic-amplifiers/
Passive Pre-Amplifier using transformers
1960s Popular Mechanics Article about Magnetic Amplifiers in industry
Electronics Stack Exchange Q and A about Magnetic and Alternative Amplifiers