Re: DRSSTC design procedure - draft

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Bob (R.A.) Jones" <a1accounting-at-bellsouth-dot-net> 

  Hi,

Some more intersting equations after AQ intro.

 > Original poster: "Antonio Carlos M. de Queiroz" <acmdq-at-uol-dot-com.br>
 >
 > Very interesting observation. The ratio of maximum energies in Cb
 > and Ca really appears to converge to 4 as the mode gets higher.
 > This happens for cosinusoidal or sinusoidal excitation, and depends
snip
 > only on the mode.
 > in more energy in the primary than in the secondary capacitance.
 > This relation gives a quick estimate for the maximum input current,
 > given the bang size:
 >
 > If the ratio of energies in Cb and Ca is 4:
 > 0.5*Ca*Vamax^2 = Ebang/4
 > Vamax = sqrt(Ebang/(2*Ca))
 > Iinmax =~ Ca*2*pi*Frequency*Vamax
 >
 > Testing: The default design in the sstcd program is:
 > Mode: 18:19:20
 > Ca=   5.0000000000 nF
 > La=  86.0126111111 uH
 > Cb=  15.0000000000 pF
 > Lb=  28.2000000000 mH
 > kab=   0.1046489272
 > Output frequencies: 231829.58, 244709.00, 257588.42 Hz
 > Maximum VCa (V)=    -1700.52069 (0.00723 J) at t=19.40194 us
 > Maximum ILa (A)=       13.02961 (0.00730 J) at t=98.05981 us
 > Maximum VCb (V)=   -62289.94357 (0.02910 J) at t=38.81388 us
 > Maximum ILb (A)=        1.43719 (0.02912 J) at t=37.79378 us
 >
 > Using the formula:
 > Vamax = sqrt(0.02910/(2*5e-9))= 1706 V
 > Iinmax = 5e-9*2*pi*244709*1706 = 13.12 A
 > Very good agreement. The relation allows then an estimation of the
 > voltage on the primary capacitor and of the maximum input current,
 > from the bang energy and from the primary capacitance.
 > Actually, this maximum current is the minimum required, if the system
 > is perfectly tuned. Any mistuning (including operation at the
 > resonances) increases it.
 >

Voltage gain is given by Vg = Vin^2* (8/Pi*k)*sqrt(La/Lb)
Note: inversely proportional to k!!!

Also approximately Voltage gain  Vg = Vin (8/Pi*k)*sqrt(Ca/Cb)

Hence approx bang energy Eb =  Vin^2*32*Ca/(Pi*k)^2 or Vin^2*1945/*k^2

and max E for Ca is 1/4 of this.

So now  here is my design strategy:
 >From your break rate and power supply determine required bang energy or cost
of Ca
 >From max switching frequency and peak current determine the mode and
frequency
then determine the k something near 0.1 say from AQ's tables
then determine Ca from Ca = (Eb*(Pi*k)^2)/32*Vin^2

Finally the hard part select a top load that has the suitable C and break
out voltage for the bang energy
Ok yes you need say 10% equations/tables for C and break out voltage of the
top load, a fiddle factor for roughness and breakout voltage to peak factor
(Someone suggested 0.3 for the last one).

At this point a suitable coil length for the expected spark length could be
selected along with a diameter assuming H/D=5

Determine the total C using your favorite method.

Then determine La and Lb and your ready to start building.

Anyone want to start on WinSSTC?

Note all the above is assumes no break out and driving at the soft switching
frequency as described previously in this thread. ie the strategy is to
design a soft switching configuration that uses the max switching power and
max wall plug power to pump up the top load to a required voltage/bang
energy which then breaks out to form a streamer. i.e. I don't believe at
present the load characteristics after break are know sufficiently to have a
reliable stratigy. Though I know that the hard part as described above is a
long way from definitive.

Bob