reggie wrote:
"I would like to build baluns with non-conventional ratios,---"

"Conventional" may mean a coil balun such as was common for TV reception
not so long ago. These were essentially transformers with a two to one
turns ratio which provides an impedance ratio of the square, or four to
one. This is similar to a center-tapped coil. The TV balun gives a
75-ohm coax connection to a 300-ohm balanced twin-lead connection.

My 1987 efition of the ARRL Handbook shows how to use RF transformers to
step up / step down impedance in Chapter 16. Also, ON4UN shows how to
match high-impedance to coax on page 6-14 of the 2nd edition of
"Low-Band DXing", an ARRL published book.

Best regards, Richard Harrison, KB5WZI