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>

 > Voltage gain(pk out V/square wave input V) =

(8/(Pi*k))*sqrt(Lb/La)

This is the -exact- expression for the mid-frequency case.

 > or
 > (8/(Pi*k))*sqrt(Ca/Cb)

Close.

 > A factor of 4/pi is required to determine the peak amplitude of the
 > fundamental of a square wave.

Ok. I forgot this.

 > It assumes that (La*s +1/Ca*s+Ra)(Lb*s+1/Cb*s+Rb) <<  Lab*s,  where s
 > Laplace operator.
 > This is a reasonable assumption when driving at the mid frequency and given
 > reasonable Q's (Ra*Rb<<(Lab*s)^2).
 > Then transfer function reduces to 1/(Lab*Cb*s^2) substitute k*sqr(La*Lb) for
 > Lab
 > Then assuming the La*Ca=Lb*Cb (only required to be closer than the split
 > frequencies) substitute (La*Ca*Lb*Cb) for s^2 and simplfy.

Why to include Ra?

 > At start up there is the steady state response and the transient response
 > which are initially equal and opposite and hence cancell. After a number of
 > cycles they sum at the output doubling the steady state response (similar to
 > the x4 thing with Ca and Cb).  So x 2 then x 4/pi for the square wave drive
 > factor.

I would say that this happens because the transformer is tuned at both
sides to the same frequency, and the turns ratio is n=sqrt(Lb/La)/k in
the model:

.                    1:n
. o--Ca--La(1-k^2)--+   +---+---+
.                   )   (   |   |
.                   )   (   Lb  Cb
.                   )   (   |   |
. o-----------------+   +---+---+

 > For the second version we can substitute the ratio of the L's with the ratio
 > of the C's.

But it happens that my design doesn't result in this !?
Using the tuning relation CaLa(1-k^2)=LbCb. The gain as function of
the capacitances would be:
Av=(8/pi)*sqrt(Ca/Cb)*sqrt(1/kab^2-1)
And indeed it is, exactly, but only for sinusoidal input. The other
formula works with cosinusoidal input too. Curious.

 > Its also useful to note that  Vmax(ca)= Vin(4/k*pi) = 6,338V

Works well too.

Antonio Carlos M. de Queiroz