Re: SSTC theory

["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 don't know the details of your simulation perhaps I missed something. For
 > a single frequency
 > excitation of a linear system at steady state the out put is also a single
 > frquency. In the case above in does not mater whether you drive at a
 > frequency in-between or not. i.e. the output must be a constant amplitude
 > sine
 > wave with he same frequency as the input at steady state if the transient
 > has
 > decayed

I am considering a lossless circuit. The transient never decays, and
adds
to the steady-state response. In the lossy cases, where a resistive
load was considered, the transient is what causes the output to ramp
instead of suddenly reaching the steady state value, what would be
impossible.

 > I suspect you may be observing the transient caused by the switch on of the
 > sine wave.  I believe the transient will excite the two poles and produce
 > the
 > two frequencies components of the classical beat envelope that then
 > exponentially decays.  The drive frequency component will  beat with the
 > two transient frequency components until they have decayed.

Yes. The transient is excited by the sudden application of the input
sinusoidal voltage (or square wave).

 > I had thought that it may be possible to utilize the transient in such a way
 > as to significantly increase the final output voltage while maintaining
 > maximum input during the build up phase by picking the appropriate driving
 > frequency. I believe one contributor may have already explored this but it
 > was not clear from his contribution what the relationship of the drive to
 > the two poles was.

At their geometrical mean. If this is not the optimum (apparently is) ,
is quite good.

 > It would be  interesting to analyze how a base current or field feedback
 > system oscillates  and what its transient behave is.
 >
 > My own interest is in zero crossing switching/feedback.  Meaning that with a
 > series resonant primary it should be possible to use the zero current point
 > to control the switches and hence guarentee soft switching. At least
 > initially
 > the driving voltage changes direction at the zero crossing points of the
 > input transient current. Such a method could be combined with peak current
 > control i.e.
 > stop switching at the next zero crossing when a given peak current is
 > exceeded.
 > Such a system may be less prone to self destruction and only requires
 > connection to the driver stage.

It appears possible to just look at the input current, reverting the
polarity of the input voltage at each change in direction of the
current.

 > It is  informative to consider steady state conditions and consider steady
 > state matching options. However it may be more important to consider the
 > transient conditions particular for SSTC's that have very high maximum
 > powers
 > relative to average wall plug power. In such systems a steady state
 > conditions may never be
 > reached. This may also be important if soft switching is required. as  even
 > if softswitching is achieved at steady state, will it also be soft during
 > the start up ???

The approach that I described works well too during the output voltage
rise. The driving frequency falls precisely at the geometrical mean of
the two resonances, and this forces resistive input impedance for any
resistive output load, including no load, and even during the initial
transient.

 > Consider the following approach. Lets assume some big beefy igfets say 600A
 > peak current and say an average wall plug current of 20A. Assuming direct
 > switching and pulsed operation with a triangular peak current profile  then
 > that's a 15 to 1 duty cycle. Then lets assume a pulse rate of 120Hz then
 > that's an on time of  556us.   Additionally lets assume interrupter type
 > operation as so the goal is to reach max secondary voltage.  So the matching
 > problem is what configuration will ramp up the driver current to 600Apk in
 > 556us. If we assume 100kHz frequency and a 5kW wall plug power which say
 > translates to a 30 x 6in secondary assume a standard flat primary with a
 > coupling round about 0.2.  How many turns on the primary  and what
 > size/rating of primary cap will get the approximately 42J in to the system
 > via an approximately 100kHz 310V  ramping up to 600Apk in 556us.

Trying a design:
Imax=600 A.
Vin=310 V peak, square wave.
The input resistance is then (4/pi*310)/600 = 0.6578 Ohms.
556 us corresponds to 55.6 cycles of 100 kHz. A bandwidth
around 100/55.6 = 1.7986 kHz would be adequate (not exact).
A problem is that with the matched design the output energy is
function of the bandwidth, and so it can't be specified independently
of the output energy.
The required bandwidth is:
B=(16/(pi^2*sqrt(2)))*Vin^2/(Rin*Energy)= 634.6 Hz (after dividing by
2pi).
The voltage gain is then determined by the output capacitance:
n=sqrt(sqrt(2)/(Cb*B*Rin))
Assuming 40 pF of secondary+terminal+streamers capacitance:
n=3672

The resulting element values:
Ca: 10.9 nF
La:  233 uH
Lb: 63.3 mH
kab: 0.00449
Cb: 40 pF

Then required bandwidth resulted too narrow, and so the coupling
between the coils become too loose. This doesn't look as a realistic
design...

To accumulate 42 J in a reasonable time, you need more input current.

Antonio Carlos M. de Queiroz