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Calculating primary ring-up time in DRSSTC

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Goodchild

Sat Oct 23 2010, 06:56AM

Registered Member #2292 Joined: Fri Aug 14 2009, 05:33PM
Location: The Wild West AKA Arizona
Posts: 795

As the title state is there an equation for calculating the amount of time it take the primary LC circuit to ring-up in DRSSTC?

This much I do know it should have something to do with the surge impedance of the LC circuit (Z surge). As a high Z (low C, high L) make
for a longer ring-up time time than an LC with a low Z (high C low L).

So how about it?

ScotchTapeLord

Sat Oct 23 2010, 03:47PM

Registered Member #1875 Joined: Sun Dec 21 2008, 06:36PM
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I've been trying to derive a formula for this sort of stuff, but it's over my head. The surge impedance dictates the initial current, and I believe that value of current gets added to to the waveform every half cycle. Then you have to factor in the power that is lost to the secondary... which isn't too bad, you just have to factor in the coupling. The part that gets me is the energy transferred back to the primary from the secondary...

However, since coupling is small, I guess you could just model it as a plain ideal LC circuit without a secondary. Not terribly sure of this, but if you can do that, then (V/Z)*(2*cycles) = Imax

V=Bus Voltage
Z=Surge Impedance
cycles=Number of full sine waves
F=Resonant Frequency of system

time = (1/F)*cycles

... so (V/Z)*2*time*F = Imax

time = (Imax*Z)/(2VF)

This should give you the time it takes to ring up to the maximum current you want, but it doesn't factor in losses, so the current won't get as high as you want, but should get close for an efficient system.

But then, this is all a guess, and I just woke up, so... yeah.

Steve Conner

Sat Oct 23 2010, 07:08PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

You can't model it, because nobody has a mathematical model for streamer loading.

If there were no secondary coil, the tank capacitor voltage would increase by the DC bus voltage (or 4/pi times it, or whatever) every half cycle, and the tank current would increase in proportion to that and the surge impedance. This would continue until it reached infinity or something blew. (Resistive losses can be ignored in a well-made coil: they're certainly not enough to keep the primary current down to a safe level.)

Energy transfer over to the secondary (either to feed the sparks, or to ring up the secondary) causes a back EMF to be induced into the primary, that opposes the inverter's output voltage and slows the primary current ringup. A DRSSTC can reach a steady state where the back EMF is equal and opposite to the inverter's output voltage, and the primary current settles to a steady value.

But again, without a mathematical model of streamers, you can't calculate the size of this effect.

ScotchTapeLord

Sun Oct 24 2010, 01:47AM

Registered Member #1875 Joined: Sun Dec 21 2008, 06:36PM
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Guess we just have to trust our CTs, then...

Goodchild

Sun Oct 24 2010, 06:18AM

Registered Member #2292 Joined: Fri Aug 14 2009, 05:33PM
Location: The Wild West AKA Arizona
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Hmm.. I kinda was thinking this at first to but I guess I just didn't want to believe it.

The reason I want to calculate this effect is because I'm working on a similar system to Steve Ward's. This type of systems use the high Z of the primary to limit the current over the supper long ontime pulse 10mS+. I know that VTTC also take advantage of this high Z current limiting effect. Without a way to calculate primary current ring up time I guess determining how high to make the Z is going to turn into a guessing game.

On top of what you said about the ring up time being depended partly on buss voltage, this type of system uses a ramping bus voltage which throws another hole monkey wrench into equation.

ScotchTapeLord

Sun Oct 24 2010, 06:37AM

Registered Member #1875 Joined: Sun Dec 21 2008, 06:36PM
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In the case of the QCW, towards the end of the cycle, the load probably looks almost completely like the streamer, in which case my proposed formulas are completely irrelevant.

That's interesting. Perhaps a device in which "the primary current settles to a steady value" like Steve describes can help us model the streamer if careful attention is paid to the waveforms and measurements in the primary? Perhaps the QCW has potential to some doors to new knowledge like this.

Goodchild

Sun Oct 24 2010, 06:16PM

Registered Member #2292 Joined: Fri Aug 14 2009, 05:33PM
Location: The Wild West AKA Arizona
Posts: 795

ScotchTapeLord wrote ...

In the case of the QCW, towards the end of the cycle, the load probably looks almost completely like the streamer, in which case my proposed formulas are completely irrelevant.

That's interesting. Perhaps a device in which "the primary current settles to a steady value" like Steve describes can help us model the streamer if careful attention is paid to the waveforms and measurements in the primary? Perhaps the QCW has potential to some doors to new knowledge like this.

You could be right about this, the only problem I see is that streamers from a QCW and from a regular DR seem to be a different "bread" of spark. The streamers from a regular DR seem wispier and QCW are thick and wight.

My logic tells me that the thicker sparks from the QCW will load the secondary down more than the sparks from a regular DR. When I do get this working I will have to collect some data from the system and maybe derive a usable equation for ring up time and also to find the point were the current levels out.

Luca

Mon Oct 25 2010, 01:31PM

Registered Member #2481 Joined: Mon Nov 23 2009, 03:07PM
Location: ITALY
Posts: 134

The best that you can do is to simulate the system with a circuit simulator as Pspice... The only problem, as Steve Mc Conner said, is that there is not an accurate model for streamers loading... A rough approximation is to use a resistor as streamer loading, the value of this resistor is something in the range 100-300kOhm. This is an approximation but at least it gives you a qualitative idea of the order of magnitude of voltages/currents in the system.
Reagrds,

Luca

ScotchTapeLord

Mon Oct 25 2010, 08:39PM

Registered Member #1875 Joined: Sun Dec 21 2008, 06:36PM
Location:
Posts: 635

This is an article by Terry Fritz that suggests a model with a resistance of 220k ohm in series with a 5 pf capacitor to ground. I guess for larger systems you could raise those values.

I know it's not perfect, but perhaps in time mankind will stumble upon a better model.

Steve Ward

Fri Oct 29 2010, 05:35PM

Registered Member #146 Joined: Sun Feb 12 2006, 04:21AM
Location: Austin Tx
Posts: 1055

Eric, your enthusiasm is great, but honestly, there isnt any simple equation thats gonna work very well.

My QCW system is well behaved due to the streamer loading, the primary impedance simply helps control how much power i try to push into the sparks. The other factor to consider is the coupling coefficient between the coils. Lower coupling means more circulating energy in the primary as only a fraction of it gets transferred to the secondary on each cycle (i dont recall if this is a straightforward relationship to coupling or not).

As to modeling, using "Terry's 220k + 1pF/foot in series" model is pretty crude, but is better than nothing! For a QCW system like mine it aint even close, not by a long shot, and you will get the wrong "answer" by a factor of 2 or easily more.

To model the spark for my QCW system i basically used +/-30kV voltage clamp with a series resistance equal to the secondary impedance at operating frequency (so about 40k ohms as i recall). Basically, when the secondary output voltage is low, there isnt much streamer to eat power, so modeling it as unloaded is ok (the zener diodes arent conducting yet). Once there is about 50kV the zeners start to clamp the top voltage, with an impedance equal to the secondary. This seems to be a decent approximation and gives "answers" closer to the real deal, but it still aint quite right. I dont bother publishing any of this stuff because there really isnt much good science behind it other than "i had some feeling that it acts this way, and it sort of models well".

The real spark is both non-linear (its not just some fixed resistance and capacitance) and time varying as it grows and the temperature and space charge change. You dont even learn enough in EE undergraduate studies to tackle problems of this nature (not to say that you cant figure it out on your own, just making an example of how difficult it really is). Ive tried spark models where the resistance varies with voltage squared (that is, the higher the output voltage, the lower the spark impedance), which seemed to work well, but the model was characterized for 1 particular system and only works in some small range of operating voltage etc... all extremely case-specific and non-universal (other than the concept of it).

My logic tells me that the thicker sparks from the QCW will load the secondary down more than the sparks from a regular DR.

This appears to be true, but what "logic" do you have? My guess is because the channel conductivity increases with time because there is more volume of hot gas (more energy went into it), compared with a "transient" coil, which as noted only has enough time to produce thin channels and requires far higher electric fields to get the same length of spark propagation.

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