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Old April 1st 07, 02:34 PM posted to rec.radio.amateur.antenna
Cecil Moore[_2_] Cecil Moore[_2_] is offline
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First recorded activity by RadioBanter: Mar 2007
Posts: 3,521
Default Is the Superposition Principle invalid?

Keith Dysart wrote:

The impedance
encountered by the reflected wave at the generator is the
same as the generator's source impedance.


No, the generator's source impedance is *NOT* the
impedance encountered by the reflected wave. Please
reference w2du's article again.

http://www.w2du.com/r3ch19a.pdf

Forget about the conjugate match and concentrate on the
non-dissipative source resistance being different from
what you are calling the generator's source impedance.
An *active* source creates a source impedance looking back
into the source that is *different* from what you are
calling the generator impedance.

Secondly, the "directional wattmeter" uses superposition
to compute Vf and Vr from which it computes Pf and Pr. You,
like many others seem willing to subtract Pr from Pf to
obtain Pnet.


One can directly add and subtract powers under certain
conditions. One condition is if two waves are not coherent.
Another condition is if two coherent waves have no effect
on each other. Since the forward wave and the reflected
wave have no effect on each other (except in the human
mind) reflected power can simply be subtracted from from
forward power to obtain power delivered to the load but
that is NOT superposition of powers. It is a simple
addition/subtraction of scalars based on the conservation
of energy principle.

But this would only seem to be valid if
superposition works for power. So why are people who accept
that superposition does not work for power, prepared to
accept that Pnet = Pf - Pr?


You seem to have forgotten the definition and rules of
superposition. Superposition applies to fields and waves.
Superposition doesn't apply to scalars. Power is a scalar.
Or another way to express it is:

V1 + V2 = V3 (vectors or phasors)

(V1 + V2)^2 = V3^2 (scalars)

V1^2 + V2^2 V3^2 (scalars)

It's a pretty simple principle of mathematics. The square
of the sum is NOT equal to the sum of the squares.
--
73, Cecil http://www.w5dxp.com