Re: NST power rating -- another perspective

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

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 



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

 > My C compilers don't have exponentiation, but in Fortran exponentiation
 > is "**". In BASIC it is "^".

To be trueful, I don't remember where ^^ notation came from.   Maybe it is
verililog. Anycase, it was common speak where I worked and I will change to
^ notation for this group.

 >  >  >  > the power across RL is:
 >  >  >  > PL = Vsec(oc)^^2  x   RL / [(sL)^^2 + sL(R + RL) + (R + RL)^^2]
 >  >  >
 >  >  > Power is not calculable so directly in this way. A product in the
time
 >  >  > domain is not a product of transforms.
 >  >
 >  > My VL, IL, and PL should have been expressed as VL(s), IL(s), and PL(s)
and
 >  > Vsec(oc) is assumed to be the transformed Vsec(oc).  I meant to keep
the
 >  > expressions in frequency domain. The power in frequency domain, I
believe,
 >  > will be the product of VL(s) and IL(s).  One can then take the inverse
 >  > Laplace transform to convert back to time domain (for the general
 >  > case).....or, one can do what you suggest below.
 >
 > To see that the general expression doesn't work, try to compute the
 > power when Vsec(s)=V/s, a step function (or DC), and L=0:
 > PL=(V/s)^2*RL/(R+RL)^2
 > The inverse Laplace transform of this is a ramp, not a constant as it
 > should be.
 > Note that to obtain the correct value making s=jw you have to consider
 > Vsec as a constant, a phasor, not the Laplace transform of Vsec(s)
 > when s=jw. A product of Laplace transforms is a convolution in time,
 > not a product. Power is a nonlinear function of the voltage, and can't
 > be calculated directly from these transforms, although, as you observed,
 > some simple tricks give the correct answers.
 >
 > Antonio Carlos M. de Queiroz

I shall try your case and review this more carefully.  In any case, I think
this expression is very useful within context.  Please try to compare the
polynomial results at a constant frequency with the results of the method
you think best.

Gerry R.
Ft Collins, CO