Cecil:

[snip]
The scaling is defined by the s-parameter specification. Nobody is
free "to scale them as you wish". For instance, a1 is defined as:

(V1+I1*Z0)/2*Sqrt(Z0)
--
73, Cecil http://www.qsl.net/w5dxp
[snip]

I like that definition best of all in a theoretical setting... but be
prepared...
there are many others to be found in the literature.

Even though I like the definition you have shown above, I find the
definitions...

a = v + Zo*i and b = v - Zo*i

To be very convenient in practice since they correspond to a very easy to
understand, visualize and manipulate single Operational Amplifier
reflectometer
circuit.

As long as the relationship between v and i and a and b are simple linear
combinations
without singularities, i.e. the transformation matrix M which allows you to
transform between
the [a, b] vectors and the [i, v] vectors is non-singular then you are just
fine, as long as
you remain consistent with your initial definition. You can perform
reliable and accurate
Engineering with any definition of the "waves" [a, b] that are a suitable
linear combination of the
"electricals" [i, v].

--
Peter K1PO
Indialantic By-the-Sea, FL.