I use current-regulation on my nixie designs, and I've done cathode-side as 
well as anode-side regulation.  Where you decide to regulate the current 
depends upon the driver you select. So far, all of my designs use 
direct-drive (non-multiplexed).

My 'Tomorrowland' clock uses HV5532 drivers (it has fourteen IN-18 tubes), 
so I regulate current on each anode. Yes, there are 14 current 
regulators.... My wristwatch uses NPN transistors to drive the cathodes, so 
I regulate the current on each segment.

Since 10mA fuses really aren't available, I size the resistor in the 
current-regulator so that it will operate at about 1/2 it's rated power 
during normal operation. For example, an 0805 SMT resistor is rated for 1/8 
Watt, so I try to design for around 50-60mW. If a gross failure in the 
regulator occurs, the resistor should overheat and open. I have not tested 
it, though. I have a fuse on the power supply, and use the smallest value 
that will handle max operating current.

If you really want to be paranoid, monitor all of your anode currents with 
a multi-channel ADC. I've never done that, but it sounds like a fun project.

For cathode current-regulation, you would use an NPN or NMOS transistor; 
anode-side would use a PNP or PMOS. I found that high-voltage PMOS devices 
aren't nearly as common as NMOS.

If you use MOS devices, I'd recommend a zener-diode across gate-source and 
also very-high resistors (10Meg +) across drain-source to protect from ESD 
or unanticipated voltage spikes. It's probably overkill but SMT devices are 
so cheap and small it's worth the cost to me.

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