Jim Kelley wrote:

Cecil Moore wrote:
Jim Kelley wrote:
Perhaps I just understand the meaning of zero better than you do?

OTOH, perhaps not. If my bank balance is zero, does that
mean there have been zero debits and zero credits over
the entire previous month?

Nope. Keep trying though. You'll get it if you really put your mind to
it.

It is a gross confusion of cause and effect to say:
"If two waves superpose to zero, those two waves
don't exist." If the component waves being emitted
by a Yagi antenna don't exist, then it is a waste
of time and money to put up a Yagi antenna.

Maybe you should notify HP that they are wasting their
time publishing the following equation since s11*a1
and s12*a2 don't exist.

b1 = s11*a1 + s12*a2 = 0

That equation does *not* imply that s11*a1 and s12*a2
must equal zero. In fact those non-zero values are easy
to calculate. Square each and you have the power associated
with each of those components.

The irradiance equation from optical physics can be
derived by squaring the s-parameter normalized voltage
equation. Since (a1*a2) is a phasor term in that equation,
the phase angle between a1 and a2 must be included in the
result.
--
73, Cecil http://www.w5dxp.com