Keith Dysart wrote:

Only partly. If you look at the element on an instrument
like a Bird 43, you will find that it is both capacitively
and inductively coupled to the line. The capactive
coupling is sensitive to the total voltage on the line
at the point of the element, while the inductive coupling
is sensitive to the total current in the line.

The subtraction (or addition) is done in the element
where the voltage sample and the current sample
(scaled by Z0) are subtracted before being applied
to the diode. The output of the diode is the
rectified instantaneous difference of the voltage and
scaled current from the equations originally provided.
This is fed to an average responding meter which has
a scale marked to show (Vf**2)/Z0 (i.e. power).
. . .

Another common directional wattmeter circuit is the Bruene type circuit.
This uses an ordinary current transformer to get the current sample and
a direct connection for the voltage sample. The voltage sample is
reduced to the correct proportional value via a transformer or
capacitive voltage divider. It shouldn't be hard to find a diagram of
one on the web.

Roy Lewallen, W7EL