Electrical – Turns ratio of multi winding transformer

It sounds like you're dealing with a SPICE simulator.

In SPICE, you define a transformer as a coupled inductor, with the following ratio:

\$\dfrac{N_1}{N_2} = \sqrt{\dfrac{L_1}{L_2}}\$

There's also a coupling factor K that comes into play.

The magnetizing inductance of a transformer is the inductance you measure across the primary winding with the secondaries open-circuit (floating). It's a function of the core material and geometry, air gap and number of turns.

Your \$L_1\$ and \$L_m\$ should be one and the same.

Here (from Wikipedia) is a fairly complete linear model of a transformer:

Note the magnetizing inductance Xm across the primary. If that inductance is too low, you'll get excessive current flowing even with no load on the secondary.

While a single-turn primary is certainly possible, with sensibly-sized cores it implies either a very low voltage (for example, a current transformer, which is typically toroidal) or a very high frequency (or both).

The inductance is proportional to the number of turns squared, and a small 120/240V 50/60Hz mains transformer primary might be some hundreds of turns, so you can see how far off a single turn is. At a fraction of a volt, or higher frequencies at relatively low voltage, a single-turn primary might make some sense.