UPDATE 2016_04_12. This circuit is now toleranced and should work OK with the revised mains input voltages specified in post #202: 230V-5% to 240V+5% and 110V-5% to 115V+5%. (just for the record, this translates to the voltage on the 55V RMS windings being, 57.25V RMS +- 9% total worst case)
Hy fire,
Here is the latest incarnation of the mains transformer cold cathode tube PSU. I managed to simplify the design because the secondary voltages of the transformer are specified under full load conditions rather than the more normal off load conditions. While the tube supply line voltage is a bit on the low side (170V optimum) the latest design does eliminate one expensive and bulky capacitor.
NOTES
(1) The reservoir capacitor (C2) (3m3F= 3300uF) shown is for a full compliment of 100 tubes, all taking 12ma, which will give a ripple voltage of 5V peak to peak maximum worst case. The reservoir capacitor can be scaled down in proportion to the number of tubes actually used, but the minimum value of reservoir capacitor is 100uF. C2 can be made up from any number of individual capacitors in parallel. The capacitors do not have to be the same value or maximum voltage so long as the their voltage rating meets or exceeds the voltage stated on the schematic. The wire connecting the capacitors should be as short as possible and substantial.
(2) C2 ripple current rating should be 71mA RMS minimum.
(3) D1, D8, D9, & D10 form a bridge rectifier. A 10A minimum, 400V to 600V schottky bridge rectifier module can be used instead.
(4) For 115 V RMS supply operation connect the transformer pin 1 to pin 3, and pin 2 to pin 4 (parallel).
(5) RC1 to RC100 are essential to protect the transistors from any problems with the tubes (flash over) and to reduce the transistor dissipation.
(6) The interconnecting wire from the transformer secondarys up to the reservoir capacitor should be substantial (100s of amp peaks will flowing in the rectifier circuit). This will help keep the DC supply line voltage up.
(7) Follow the wiring connections for the tube supply line indicated on the schematic. ie the tube supply lines connect directly to the terminals of the reservoir capacitor. If more than one capacitor is used connect to the highest value capacitor terminals.
(8) The transistors must be in a position to allow a good flow of cool air all around them by convection. The transistor ambient air temperature should be as cool as possible.
(9) Solder the transistors to substantial PCB traces to help conduct heat away. The transistors should be mounted about 3mm proud of the PCB to allow good air circulation.
(10) The collector resistors should also be mounted in as cools as possible ambient air temperature.
(11) The collector resistors should be mounted about 4mm off the PCB to allow a free flow of cool air all around them by convection.
(12) The tubes should also be mounted to allow adequate air flow for convection cooling.
ERRATA
(1) Add one 100nf low loss capacitor across the tube supply line for every 5 tubes. Suitable capacitors are ceramic and polycarbonate metal film.
(2) Higher current, 10A minimum, 400V to 600V PIV schottky rectifiers should be used to keep the supply line voltage up by lowering the diode forward drop.
(3) Change RC1 to RC100 from 3K3 to 5K6.
(4) QV1 to QV100 are transistor types 2N6517.
(6) Supply line voltage should read, '152V MINIMUM PEAK, 175V MAXIMUM PEAK. RIPPLE VOLTAGE= 5V PEAK TO PEAK MAXIMUM.'
DATA SHEETS & SOURCES
(1) Transformer
https://www.farnell.com/datasheets/1945759.pdf
(2) Transistor
https://www.onsemi.com/pub_link/Collateral/2N6515-D.PDF