Richard Clark wrote:
I see you have yet to respond to this very matter attended to quite at
length by Chipman.

I have recently realized that those terms in Chipman's equations are
interference terms. EM wave interference is not understood very well
by RF people although it is understood very well by optics people.

For instance, the superposing of two coherent voltages in a Z0
environment is well known.

Vtot = V1 + V2 (assume V1 and V2 are in phase)

Squaring both sides and dividing by Z0 yields the power.

Vtot^2/Z0 = (V1+V2)^2/Z0

Vtot^2/Z0 = V1^2/Z0 + V2^2/Z0 + (2*V1*V2)/Z0

Note that the first term to the right of the equals sign is the
power associated with the V1 wave and the second term is the
power associated with the V2 wave. The third term is the
interference term. If V1 and V2 are in phase, the third term
will be constructive interference.

If the phase angle between V1 and V2 is less than 90 degrees,
the interference is constructive, i.e. cos(theta) is positive.

If V1 and F2 were 180 degrees out of phase, the interference
would be destructive.

If the phase angle between V1 and V2 is between 90 degrees and
180 degrees, the interference is destructive, i.e. cos(theta)
is negative.

Interference is the reason for those extra terms in Chipman's
equations. It always happens when the sum of two voltages
are squared to get the power.

Reference: _Optics_, by Hecht.
--
73, Cecil http://www.qsl.net/w5dxp


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