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Registered Member #61905
Joined: Sun Nov 12 2017, 03:27AM
Location:
Posts: 23
Uspring wrote ... Ok, but you might have some trouble winding that.
I've never seen a multi-strand TC secondary. While it would be more difficult to wind, it should work and give more skin area. You could even do 3-strands with some patience. I have done this for winding single layer toroid inductors, and it seems to work better than a single fat wire. If you wanted to try 3 wires, I would wind the first two together, then put down a thin layer of polyurethane to fix the windings, then wind the 3rd on top and more polyurethane. The 3rd wire would be a little longer than the first two, but should still reduce resistance of the coil.
This is a picture of the tri-filar inductor I mentioned:
With Vinp*Q/Zpri I got only 78% of Iprimax from Imax which I picked up for R=(4/pi)*Vmax/Imax to calculate Ca for calculation of n, load, B and k for my secondary+topload.
Antonio and myself are using slightly different definitions of Vinp. He is using peak voltage from a square wave input and I'm using peak voltage from a sinusoidal input. So the factor of 4/pi arises. Use 4/pi * Vinp in my equation instead of Vinp to account for a square wave input.
I'm almost sure I shouldn't use Qsec which is 1/k in Iprimax=Vinp*Q/Zpri and should use Qpri=(Qsec/k^2)*fpri*fsec/f^2*(1-f^2/fsec^2)
^2+fpri/fsec*1/(k^2*Qsec), right?
Yes, the Q in Iprimax=Vinp*Q/Zpri is the primary Q i.e. Qpri. With respect to the above, you should use Iprimax=4/pi*Vinp*Q/Zpri
Beside of this as I mention I made a spreadsheet and figured out that I still didn't get how to balance MMC and Lpri according to pack of formulas from Antonio's post.
The Ra in his webpage is the quantity relating input voltage and input current i.e. Ra = 4/pi * Vinp / Iprimax.
Antonios and my approach differ in one respect: He chooses the operating frequency of the coil to be at the secondary resonance. But usually the DRSSTCs operating frequencies are determined by primary current feedback to allow for zero current switching. The coil starts up at the primary resonance frequency and gradually changes to one of the poles of the system. The pole frequencies also change during the burst, since the arc adds capacitance to the secondary tank, shifting its resonance frequency. The equation
contains the operating frequency f explicitly, so it is more general. Sadly it depends strongly on f and f is not so well known. If we assume the coil to be running on one of the poles and also, that primary and secondary res frequencies are the same, then the above can be simplified to approximately
Qpri = Qsec + 1/(k^2*Qsec)
The lowest Qpri, i.e. the best transfer of power to the secondary and also the best effect of primary current limiting by the arc is achieved by selecting Qsec = 1/k. That gives a guideline to select secondary impedance, but Qsec depends on the arc load, which changes dramatically during arc growth. Assuming Qsec is chosen optimally, i.e. Qsec=1/k, then Qpri = 2/k. The effective input resistance is then
Zpri/Qpri = k/2 * 1/(2*pi*f*Cpri) and this is also equal to 4/pi * Vinp/Iprimax, so
Vinp/Iprimax = pi/8 * k * 1/(2*pi*f*Cpri)
That is more or less equal to the prescription
Vmax/Imax < k/(2*pi*f*C)
The latter equation is more conservatively chosen, since we have made a lot of assumptions on the way.
Registered Member #2694
Joined: Mon Feb 22 2010, 11:52PM
Location: Russia, Volgograd (Stalingrad).
Posts: 97
Uspring wrote ...
With Vinp*Q/Zpri I got only 78% of Iprimax from Imax which I picked up for R=(4/pi)*Vmax/Imax to calculate Ca for calculation of n, load, B and k for my secondary+topload.
Antonio and myself are using slightly different definitions of Vinp. He is using peak voltage from a square wave input and I'm using peak voltage from a sinusoidal input. So the factor of 4/pi arises. Use 4/pi * Vinp in my equation instead of Vinp to account for a square wave input.
I'm almost sure I shouldn't use Qsec which is 1/k in Iprimax=Vinp*Q/Zpri and should use Qpri=(Qsec/k^2)*fpri*fsec/f^2*(1-f^2/fsec^2)
^2+fpri/fsec*1/(k^2*Qsec), right?
Yes, the Q in Iprimax=Vinp*Q/Zpri is the primary Q i.e. Qpri. With respect to the above, you should use Iprimax=4/pi*Vinp*Q/Zpri
Beside of this as I mention I made a spreadsheet and figured out that I still didn't get how to balance MMC and Lpri according to pack of formulas from Antonio's post.
The Ra in his webpage is the quantity relating input voltage and input current i.e. Ra = 4/pi * Vinp / Iprimax.
Antonios and my approach differ in one respect: He chooses the operating frequency of the coil to be at the secondary resonance. But usually the DRSSTCs operating frequencies are determined by primary current feedback to allow for zero current switching. The coil starts up at the primary resonance frequency and gradually changes to one of the poles of the system. The pole frequencies also change during the burst, since the arc adds capacitance to the secondary tank, shifting its resonance frequency. The equation
contains the operating frequency f explicitly, so it is more general. Sadly it depends strongly on f and f is not so well known. If we assume the coil to be running on one of the poles and also, that primary and secondary res frequencies are the same, then the above can be simplified to approximately
Qpri = Qsec + 1/(k^2*Qsec)
The lowest Qpri, i.e. the best transfer of power to the secondary and also the best effect of primary current limiting by the arc is achieved by selecting Qsec = 1/k. That gives a guideline to select secondary impedance, but Qsec depends on the arc load, which changes dramatically during arc growth. Assuming Qsec is chosen optimally, i.e. Qsec=1/k, then Qpri = 2/k. The effective input resistance is then
Zpri/Qpri = k/2 * 1/(2*pi*f*Cpri) and this is also equal to 4/pi * Vinp/Iprimax, so
Vinp/Iprimax = pi/8 * k * 1/(2*pi*f*Cpri)
That is more or less equal to the prescription
Vmax/Imax < k/(2*pi*f*C)
The latter equation is more conservatively chosen, since we have made a lot of assumptions on the way.
So if:
Vinp=bus voltage
Qsec=1/k
Qpri=Qsec+1/(k^2*Qsec) i.e. Qpri=(1/k)+1/(k^2*(1/k))
if Rpri is not a Zpri then we are in endless loop because Rpri=(4/pi)*Vinp/Iprimax and Iprimax is what we looking for.
else
if Rpri is a Zpri then we are still in endless loop because Zpri=1/(2*pi*Fpri*Cpri), but Fpri is unknown so then Fpri=1/(2*pi*sqrt(Lpri*Cpri)), but Lpri is unknown so then Lpri=Lsec*Csec/Cpri+Cpri*Rpri^2, but Rpri is unknown so then Rpri=(4/pi)*Vinp/Iprimax and Iprimax is what we looking for.
Beside that, if:
k=sqrt(B^2/(2*Fsec^2+B^2))
B=Cpri*Rpri*sqrt(2)/(2*Pi*Lsec*Csec)
Rpri=4/
pi*Vinp/Iprimax
Iprimax=4/pi*Vinp*Qpri/
Zpri
and
Qpri=Qsec+1/(k^2*Qsec)
then we are in endless loop too because
in "k=sqrt(B^2/(2*Fsec^2+B^2))" we need to know "B" in "B=Cpri*Rpri*sqrt(2)/(2*Pi*Lsec*Csec)" we need to know "Rpri" in "Rpri=4/pi*Vinp/Iprimax" we need to know "Iprimax" in "Iprimax=4/pi*Vinp*Qpri/Zpri" we need to know "Qpri" and in "Qpri=Qsec+1/(k^2*Qsec)" we need to know "k"
"k", "B", "Rpri" or "La" should be defined for Iprimax could be resolved
Although, let the Fpri be equal Fsec and equal F=1/(2*Pi*sqrt(Lsec*Csec))
then
Qsec=1/k
Qpri=Qsec+1/(k^2*Qsec) i.e. Qpri=(1/k)+1/(k^2*(1/k))
Zpri=1/(2*pi*Fpri*Cpri) i.e. Zpri=1/(2*pi*(1/(2*Pi*sqrt(Lsec*Csec)))*Cpri)
k=sqrt(B^2/(2*Fsec^2+B^2)) i.e. k=sqrt((Cpri*Rpri*sqrt(2)/(2*Pi*Lsec*Csec))^2/
(2*(1/(2*Pi*sqrt(Lsec*Csec)))^2+(Cpri*Rpri*sqrt(2)
/(2*Pi*Lsec*Csec))^2))
and
B=Cpri*Rpri*sqrt(2)/
(2*Pi*Lsec*Csec) i.e. B=Cpri*Rpri*sqrt(2)/(2*Pi*Lsec*Csec)
and Rpri is unknown but Rpri=4/pi*Vinp/Iprimax but Iprimax is what we looking for.
It seems that "k" should be defined and Fpri should be equal Fsec else we did not get Iprimax defined for chosen Vinp, and then how we can correctly calc the "k" and Lpri?
And also for: Lsec=0,215587H Csec=0,00000000009258F Cpri=0,000001033333F k=0.1 Vinp=565 Iprimax=4/pi*Vinp*(1/k)+1/(k^2*(1/k))/(1/(2*pi*(1/(2*Pi*sqrt(Lsec*Csec)))*Cpri)) Qpri=(1/k)+1/(k^2*(1/k)) Zpri=1/(2*pi*(1/(2*Pi*sqrt(Lsec*Csec)))*Cpri) Rpri=4/pi*Vinp/Iprimax Lpri=Lsec*Csec/Cpri+Cpri*Rpri^2
I got only Vmax/Imax~0,23*k/(2*pi*f*C)
but you said is better to run at Vmax/Imax~0.5*k/(2*pi*f*C)
so it seems that I need a Cpri almost 0,0000022375F or so?
And if so then I don't understand why so because of if MMC becomes bigger then Lpri becomes smaller then Zpri becomes fewer then current grows faster and current growing will require fewer cycles for same current level and streamer will not be looking fat and tasty.
Or I understand it wrong again?
You wrote: "Primary rampup is a transient situation. Before a steady state is reached, primary current has to reach a significant level, then energy has to be transferred to the secondary, then the arc has to grow to its final length. Due to the slowness of the latter 2 processes, there might be a considerable overshoot of primary current. I've seen that in my coils. Slowing down rampup by increasing primary impedance avoids that to some extent."
So my question about "For fat long sparks will be better small MMC and lot of primary turns or huge MMC and a few primary turns?" was rather about to know how much cycles is need for "slowing down rampup by increasing primary impedance" and for streamer then can looks fat and for it can grow slowly for it can have a bit more length with same current due to a bit less branching due to streamer edge can be a terminal in most (but not all) part of time. for example: One, Two
EDIT: this is a bit strange but, in compare to "Vmax/Imax < k/(2*pi*f*C)", the "Vinp/Iprimax = pi/8 * k * 1/(2*pi*f*Cpri)" shows me 0,46 instead of 0.23 for same Cpri=0,000001033333F. Vinp/Iprimax=~0.46*k*pi/8*1/(2*pi*f*Cpri). It seems I'm make something wrong again.
if Rpri is not a Zpri then we are in endless loop because Rpri=(4/pi)*Vinp/Iprimax and Iprimax is what we looking for.
Zpri determines, how fast current will rampup in the primary. It does not tell you, how far it will go up. You need an effective Qpri for this, i.e. Iprimax=4/pi*Vinp*Qpri/Zpri.
You shouldn't mix Antonios and my equations. Antonios prescription starts from the idea to design a maximally flat frequency response of the coil. That leads to constraints on how primary and secondary frequencies relate and also on the coupling constant. He also makes the assumption, that the coil runs on the secondary resonance frequency. I've remarked on this in my previous post.
My approach is different. It centers on the idea to obtain a best as possible match between the bridges capabilities and the coils input properties. I'd choose the coupling as large as possible, usually a value of around k=0.2 is feasible wrt flashovers. The ratio between secondary and primary fres is best determined experimentally by tapping the primary, often tuning the primary low by 10 to 20% is best.
but you said is better to run at Vmax/Imax~0.5*k/(2*pi*f*C) so it seems that I need a Cpri almost 0,0000022375F or so?
That seems a bit large, what value of k did you use?
"For fat long sparks will be better small MMC and lot of primary turns or huge MMC and a few primary turns?" was rather about to know how much cycles is need for "slowing down rampup by increasing primary impedance" and for streamer then can looks fat and for it can grow slowly for it can have a bit more length with same current due to a bit less branching due to streamer edge can be a terminal in most (but not all) part of time.
For fat sparks you need long burst times on the order of several hundred us. Branching might be a bit less for slower rampup coils but for straight sparks you need a QCW coil with burst length of maybe 10ms and a very slow rampup, which is only achievable by ramping up bus voltage with e.g. a buck converter.
Registered Member #2694
Joined: Mon Feb 22 2010, 11:52PM
Location: Russia, Volgograd (Stalingrad).
Posts: 97
Uspring wrote ...
For fat sparks you need long burst times on the order of several hundred us. Branching might be a bit less for slower rampup coils but for straight sparks you need a QCW coil with burst length of maybe 10ms and a very slow rampup, which is only achievable by ramping up bus voltage with e.g. a buck converter.
No, I'm not going so far with thickness of streamer to go into QCW. I'm saying only about DR. several hundred uS will give a different cycles number if fres will be different. About number of cycles there is no any rule of thumb more precisely than several hundred uS?
Uspring wrote ...
That seems a bit large, what value of k did you use?
same 0,1
Uspring wrote ...
I'd choose the coupling as large as possible, usually a value of around k=0.2 is feasible wrt flashovers.
Why not 0.15 or 0.1? won't 0.2 deliver a voltage stress and racing sparks?
Uspring wrote ...
My approach is different. It centers on the idea to obtain a best as possible match between the bridges capabilities and the coils input properties. I'd choose the coupling as large as possible, usually a value of around k=0.2 is feasible wrt flashovers. The ratio between secondary and primary fres is best determined experimentally by tapping the primary, often tuning the primary low by 10 to 20% is best.
Okay, thanks on that!
Although in returning to desirable Vmax/Imax=~0.5*k/(2*pi*f*C) if I use
Why not 0.15 or 0.1? won't 0.2 deliver a voltage stress and racing sparks?
Yes, it can. Wrt racing sparks it's not anything I can contribute to from a theoretical point of view. You'll have to try this out and e.g. change coupling when you run into problems.
whichever I choose k or Cpri, relation of 4/pi*Vinp/Iprimax is always equal 0.5*k/(2*pi*Fpri*C). It is okay or I do something wrong?
This is so, because you have taken equations from the derivation to e.g calculate Iprimax and then entered that into the final result of the derivation. That will just lead to a confirmation of the final result. From the different numerical results, you should use that, which best applies to your coil, e.g. the k=0.2 and Iprimax=684A. That would put your Cpri to about 0.5uF. For a smaller coupling, smaller Cpris would be better.
Registered Member #2694
Joined: Mon Feb 22 2010, 11:52PM
Location: Russia, Volgograd (Stalingrad).
Posts: 97
Uspring wrote ...
Why not 0.15 or 0.1? won't 0.2 deliver a voltage stress and racing sparks?
Yes, it can. Wrt racing sparks it's not anything I can contribute to from a theoretical point of view. You'll have to try this out and e.g. change coupling when you run into problems.
Ok. Thanks!
Uspring wrote ...
I think, your topload Csec is too big (90pF).
oh, again I made a mistake and did not notice this. Yep, topload isn't 90pF. It seems like 44.35pF according to fresh JavaTC calculation. And with a 1920 turns of 0.81mm on 315mm tube Csec is about a 52.82pF.
Uspring wrote ...
whichever I choose k or Cpri, relation of 4/pi*Vinp/Iprimax is always equal 0.5*k/(2*pi*Fpri*C). It is okay or I do something wrong?
This is so, because you have taken equations from the derivation to e.g calculate Iprimax and then entered that into the final result of the derivation. That will just lead to a confirmation of the final result. From the different numerical results, you should use that, which best applies to your coil, e.g. the k=0.2 and Iprimax=684A. That would put your Cpri to about 0.5uF. For a smaller coupling, smaller Cpris would be better.
Registered Member #2694
Joined: Mon Feb 22 2010, 11:52PM
Location: Russia, Volgograd (Stalingrad).
Posts: 97
Uspring wrote ...
I think, your topload Csec is too big (90pF).
Is too bad if skeleton-type toroid will be made from chrome plating iron\steel? It is better to throw out the finished steel toroid and make aluminum or steel is fine too?
Registered Member #2694
Joined: Mon Feb 22 2010, 11:52PM
Location: Russia, Volgograd (Stalingrad).
Posts: 97
Uspring wrote ...
Regarding to my strange traction to use 26AWG which I already have and avoid to buy any other wire while I already have one, will it be acceptable\reasonable to winding two 26AWG wires in parallel?
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26 or 18 awg for 315*1650mm secondary (and Balancing MMC and Primary on chosen Secondary in DR)
