A 5 Volts power supply is a big limitation regarding to a current source 
compliance. I'd do the following:

1 - Decouple the outputs of the filters from the rectifiers, so as to have 
an output voltage referenced to 0 and up to 5 volt. The rectifiers act as 
peak detectors and your signal moves from 0 to 5V before clipping.
2 - Build a current mirror sink to ground, knowing beforehand that close 
tracking of discrete devices is an utopia, per output tube (I support the 
IN-13 advice).
3 - Inject the minimum bias current and sum up with a variable current to 
swing the total needed by the tube. This, done with simple resistors to +5V 
and the output to unity gain buffers (LM324 will work fine).

I'd try to make a schematic when I get time, but the circuits are very 
simple.

Gastón

On Monday, October 7, 2019 at 7:09:38 AM UTC-3, Mateusz Dziuba wrote:
>
> Hi again!
>
>
> After abandoning the project for a long time I came back to my IN-9 tubes. 
> I replaced the PSU (NE555 based -> MC34063A based), replaced transistors 
> for MJE340 (which will be used in final design) and did a bit of burning of 
> each lamp separately. Finally I get to the top of the tubes (well 9,5 mm). 
> It seems lamps required to be burned with higher current which my previous 
> PSU, current mirror and potentiometer arrangement was not able to provide. 
> I am blaming poorly designed PSU. 
> I would like to thank all of You for your time and advices.
>
> Now I am facing another problem.
>
> I built set of band-pass filters using LM324 with single supply 0-5VDC. As 
> the 2.5VDC is feed to non-inverting input of op-amps, and audio signal is 
> feed on inverting input, the value is oscillating around 2.5V (middle of 
> nixie). I was planning to use microcontroller and map the output voltage to 
> 0-5V by software and then feed on MJE340. in the end I decided to not use 
> microcontroller, and now I am stuck at point "How to get a 0-max swing of 
> the bar on the nixie?"
>
>>

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