Roy Lewallen wrote in
news
Keith Dysart wrote:
. . .
By substitution, it is easy to show that the rules used to
derive Vf and Vr results in
P(t)=Pf(t)-Pr(t)

So, while superposing powers, does not work in general, it does
for this case. Directional wattmeters take advantage of this
ideosyncracy to let the user compute the power being delivered
to the load.
. . .

And it works only if Z0 is purely real. When it's not, P(t) also
includes Vf*Ir and Vr*If terms which are neither "forward" nor
"reverse" power. It's unfortunate in a way that Z0 is close enough to
being real for decent lines at Amateur frequencies that these terms
are small. Otherwise they'd have to be confronted and some mistaken
assumptions abandoned.

While Zo of transmission lines might not be purely real, if the sampler
element is calibrated for V/I being real, then the power is given by
'forward power' - 'reflected power'. This is true even if the
calibration impedance is different to the transmission line in which the
measurements are made, though significant departure will impact
measurement uncertainty.

For example, if I insert a 50 ohm Bird 43 in a 75 ohm line at 1.8MHz,
and measure Pf=150W and Pr=50W, then the power is 150-50=100W. The
insertion VSWR due to the Bird 43 is trivial in this case, so it hardly
disturbs the thing being measured. Each of the power measurements is of
little value alone, no inference can be made (in this case) of the
actual line VSWR, but the difference of the Pf and Pr readings does give
the power at that point.

I discuss this in my article entitled "http://vk1od.net/blog/?p=1004" at
http://vk1od.net/blog/?p=1004 .

Owen