On Jun 9, 6:44*am, Keith Dysart wrote:
Superposition works just fine for voltage and current, but is mostly
invalid for power. Attempting to apply superposition to power will
lead to inaccurate results.

It is invalid to try to use superposition on scalar values. There is a
particular way to obtain the total power from the superposition of two
EM waves. It's called the power density equation and contains an
interference term, the sign of which tells us whether destructive,
constructive, or zero interference results when the two EM waves are
superposed. It agrees perfectly with calculating the total power from
the voltage and current end products of superposition. It would
explain everything that Roy is missing in his food-for-thought
article. I first saw this equation in Dr. Best's QEX article.

Ptot = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

where A is the angle between the electric fields (voltages) of the two
superposed waves.

We get the same equation when we square the s-parameter equations.

(b1)^2 = (s11*a1 + s12*a2)^2, where (b1)^2 is the reflected power
toward the load.

(s11*a1 + s12*a2)^2 = (s11*a1)^2 + (s12*a2)^2 + 2(s11*a1)(s12*a2)

If it is not obvious, this is the same equation as the power density
equation above. The interference term in the squared s-parameter
equation contains phasors whose dot product involves cos(A), where A
is the angle between those two phasors. More s-parameter information
available below - Please note pages 16 and 17 involving powers.

http://www.sss-mag.com/pdf/hpan95-1.pdf
--
73, Cecil, w5dxp.com