Cecil Moore wrote:
Gene Fuller wrote:
Where are the equations that describe this "delta-t" stuff that you
keep bringing up?

I made an error in my last reply and have canceled that reply.

delta-t is a mathematical term, Gene, related in the limit
to the differential dt. If you have to ask, I'm sure you
wouldn't understand the explanation.

Given the following experiment with two signal generators
equipped with circulators and load resistors - the generators
are phased-locked to ensure coherency:

[random s-parameter babble snipped]

How
long does it take to achieve b1 = s11(a1) + s12(a2) = 0?
I estimate that time to be delta-t which becomes dt
in the differential equation limit.

The principle of superposition allows us to observe that
s11(a1) and a12(a2) actually existed before they were
canceled.

Cecil,

That's typical; you don't have a clue about what you have dragged
yourself into.

Let's see. Delta-t is, uhhhh, delta-t. And of course we can replace
delta-t by the differential form, dt, if we choose. You haven't offered
the slightest justification for this bizarre formulation. Where are the
equations that include delta-t or dt? Sure, Maxwell's equations include
time derivatives, but somehow that does not seem to offer much help for
your delta-t dilemma. I always though that part of the utility of
s-parameters is that they do not have any time dependence in steady
state conditions. Is there some equation for ds11/dt that I missed?

I would sure like to see your definition of "the principle of
superposition" if it somehow says that something existed before it was
canceled. I cannot find that definition in any of my sources.

8-)

73,
Gene
W4SZ