Exact design for lossless SSTCs

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

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

Hi all:

I made some further investigations about the theory of "sstc"s,
and found how to design the LC part of the system so complete
energy transfer occurs without breakout, as can be done for a
capacitor-discharge system.

I considered the system:

.               kab
.    o----Ca---+   +----+-----o
.              |   |    |
.             La  Lb   Cb
.              |   |    |
.    o---------+   + ---+-----o

The objective is to apply an alternating voltage to the input,
and after a determined number of cycles have all the energy that
entered the system in Cb, without voltage in Ca or currents in
La or Lb. I considered the input voltage as a cosinusoid or as
a sinusoid. A square wave input makes little difference.

I could (so far) identify three different possibilities:

a) cosinusoidal input: the two natural oscillation frequencies
of the network and the excitation frequency must be in a ratio
of three integers with odd difference (as 9:10:11 or 9:10:13),
with the excitation frequency being at the center. I found
this solution first, almost by chance when looking at other
problem. The solution exists only for the 4th-order system.

b) sinusoidal input: The three frequencies must be in a ratio
of three odd integers with double odd differences (as 9:11:13
or 9:11:17). The excitation is at the central frequency.
The design is just a bit more tricky, and produces the best
networks for practical use, with practically perfect "soft
switching" if the integers differ by just 2. The design
procedure allows also the generation of structures of higher
order, as an "sstc magnifier", that operates with four
simultaneous oscillations instead of the three of a capacitor-
discharge magnifier.

c) sinusoidal input: Similar to (b), but the excitation is
at the upper frequency. Less practical because the switching is
not soft. There is no solution with excitation at the lower
frequency.

There are many possibilities for the choice of the three
integers, as to choose the three integers so the excitation
is arbitrarily close to one of the resonances, what results
in a rise with "bumps", but the switching is not soft, and the
idealized waveforms can be quite different from what a real
circuit generates.

Interestingly, the resulting networks (b) are practically
identical to the ones generated from a Butterworth filter
(see my page at http://www.coe.ufrj.br/~acmq/tesla/sstc.html),
but the voltage gain (without load) is a bit higher.

I will set up a page with some examples and more details, but
if you want to try, I have implemented the design procedure
in the program "sstcd", that can make the calculations and
plot the waveforms. The program (for Windows) is available at:
http://www.coe.ufrj.br/~acmq/programs

Antonio Carlos M. de Queiroz