Single-to-differential converter for a Gilbert mixer

I am designing a double-balanced mixer and think I need a balun to be implemented in the RF input for characterization purposes, and found this circuit that converts from single-to-differential.
I simulated it and got the differential output expected.

- How this circuit works, if there is no input signal in one of its inputs ?
- Input signal is applied in M1, with a DC value in order to bias this MOS,
in simulation I needed M2 to be biased too, is it correct ?
- Why there is a little phase shift in the output signals ?
- Is this a good way to implement an active balun ?

has someone worked with single-to-differential circuits ?

Thanks.

maybe you can serch ieee paper
key word "active balun"