# Is my power supply calculation correct?

So I am trying to get into higher voltage projects, namely I got a bunch of nixie tubes very cheap. I was thinking of making my supply by connecting a 230v -> 9v transformer back to back with a 230v -> 12v transformer, which by my calculations should give me 171 volts of isolated AC, without counting in voltage losses. Is this correct? Then I would rectify it to give me around 170VDC.

Is that correct?

Also can I rectify the 9V AC in the middle and connect it to a common ground to power the logic?

So your V AC calculations are more or less right (9V AC in the middle, 171V AC at the output), but you need to multiply the rectified values by $\sqrt{2}$ to get the peak voltage and subtract off 2 diode drops for a typically 4 diode bridge rectifier.
Assuming you're using typical silicon diodes with $V_D \approx 0.7V$, the 9V AC becomes 11.3V peak and the 171V AC becomes 240.4V peak.
Also, you'll probably want some decent sized capacitors otherwise you'll end up with rectified waveforms which look like $abs(sin(t))$: 