The impedance for a half wave antenna is high at both ends. Around 3 kΩ.
For a 50Ω coax feed line a 50x (2,5kΩ) to 70x (3,5kΩ) impedance transformer is needed.

A winding ratio of 4 (for example) transforms the voltage a factor 4 up and the current a factor 4 down (equal power). This means the impedance transformation is the square of the turn / winding ratio. So in this example a impedance transformation of 16, giving a 800Ω output impedance.

Primary and secondary windings are bifilar wound (and loosely twisted).

As the 30m band is CW-only, I will skip this band for the moment. I'm not (yet) a CW guy.

Leaving 17m an 12m to combine in one antenna.

Considerations

How to make the antenna resonant for both bands. The frequencies relate to each other as 3 to 4.

On the Internet there's lot of discussion about this End Fed.
One thread uses a full wave for 12m a coil and after that a wire of less than a meter to make 17m and 30m resonant. But how dus this work in theory?

So I dicide to start with one band: 17m.

Base

End-Fed antenna for 20m, 10 meter in length.
FT-140-43 ferrite toroid impedance transformer (UnUn).

Extension

To make it a multi band (10/20/40/80m) antenna when little space is available: