[Amps] surge limiter question

[TexasRF@aol.com]

Thanks for the several replies. I see that I left out some important info,  
as usual.
 
The tube being protected is a TH347, and is expensive, $3500 new, $1400  
rebuilt. I have lost one tube to turn on surges so would like to make sure the  
replacement is the last one!
 
The filament is rated for 6.0v, 34a so the current limiting has to be done  
in the transformer primary where the current is about 1.9 amps. The 
manufacturer  cautions that the filament current must be limited to 75 amps on the first  
cycle. I would like to limit the current to about 30 amps peak during the  
initial turn on period. There is a series connected 50 watt rheostat for voltage 
 adjustment after everything is up to temperature. There is also a relay in 
the  circuit that shorts out the NTC thermistor after about 10 seconds. The 
shorting  is done for several reasons; 1> to have a way for it to cool off and be 
ready  for a recycle, 2>to allow it to run cold nearly all the time for long 
life,  3> to eliminate the voltage drop across the device and 4> to help 
reduce  voltage variations due to variation in cooling air circulating around the  
thermistor.
 
The fact that the cold filament resistance is only about .0176 ohms makes  
the problem a bit more complex. The filament transformer is a 6.3vac, 50 amp  
unit from Dahl (34 amp would be a special build, costs more). 
 
Considering that primary current is about 1/18 of the secondary  current, I 
am looking for 30/18 amps there or about 1.666 amps. Assuming that  the cold 
filament resistance is .0176 ohms, then in a perfect transformer, the  reflected 
resistance will be 18^2 X .0176 or 5.7 ohms. The voltage at the  primary 
would need to be 1.666 X 5.7 or about 9.5v at turn on. If only a  resistor is used 
then it must drop the remainder of the line voltage. In the  case of 117vac 
the resistor would need to drop 107.5 volts. The resistor value  would be 107.5 
/ 1.666 or about 65 ohms.
 
After a few milliseconds the filament resistance will have increased. I  
found a reference about Tungsten resistance increasing at the rate of about .5%  
per degree C. Starting at room temperature the tube needs to reach about 2000  
degrees C so the question is how far on the way to 2000 degrees C will the 65  
ohm resistor allow?
 
I wrote a simple Basic program to iterate the filament resistance vs  
voltage/current and it shows the circuit to stabilize at 27.2a filament current,  
1.12a primary current, .041 ohm filament resistance and 325 degrees C. So far so  
good. BUT, if the resistor is shorted at this point the filament current will 
 jump to about 6/.041 or 146 amps! This is not good!
 
This is where the NTC thermistor was added to the mix. Actually, there are  
two of them in series, 120 ohms each so the starting current is very low and  
increases as the thermistors heat up. 
 
I don;t have a scope (and it would need to be a storage scope as things are  
changing quickly and I already know that the first cycle is not the one  
producing the most current). So the next approach was the one ohm primary  resistor 
with diode and 100 mFd storage capacitor. At turn on the capacitor is  
charged to the peak value across the one ohm resistor (less diode drop). My DVM  has 
a 10megohm input impedance so there is plenty of time to measure the  
capacitor voltage before the cap discharges.
 
I am moderately confident of this approach but was hoping for some help  with 
the mathematics involved with modeling the problem. I know that the  
thermistor resistance is dropping based on its temperature but I don't know how  to 
convert the amperes flowing into degrees C and how long it takes for all this  
to happen. A similar thing is happening in the filament structure but with the  
current limiting action this seems a lot more predictable as the temperature  
should be closely related to the filament volts X amps flowing at a given 
time  sample. The Basic program will give a fair accounting of the filament  
action.
 
Another slant on this is that the thermistors start out with maximum power  
dissipation per ac cycle and taper off to a low value per cycle; the filament  
starts out with minimum dissipation per cycle and ends up at maximum. I am  
trying to confirm that all is well at the crossover point.
 
Voltage regulation and adjustment is a whole different subject that gets  
dealt with after that relay shorts out the limiter circuit discussed above.  
Marv, W6FR has given some excellent input on a regulator circuit that will be  
very helpful when the current limiting problem is resolved.
 
Any help, suggestions or comments are appreciated.
 
Thanks/7,
Gerald K5GW