Re: DRSSTC design procedure - draft

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

Original poster: "Antonio Carlos M. de Queiroz" <acmdq-at-uol-dot-com.br> 

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

 >   I notice that the output energy is approximately 4 x the max energy in the
 > primary  C (Ca).
 >
 > Is this generally true for the configuration/mode your suggesting?

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
only on the mode.
It's possible to obtain more by using modes as x:x+1:x+4, but
these modes result in hard switching.
Low modes also result in greater ratio, up to 12.8 for mode 1:2:3
(cosinusoidal input), but this mode results in too high k.
In the other hand, excitation at the resonances easily results
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.

I will see if I can obtain the exact expression for the factor.

Antonio Carlos M. de Queiroz