I note that any textbook I pick up shows that VSWR=(1+rho)/(1-rho) where
rho is the magnitude of Gamma (Gamma=(Z-Zo)/(Z+Zo)); rho=abs(Gamma)).

Now, reading TL theory texts can be confusing because of the sometimes
subtle swithes to and from an assumption of lossless line (under which
rho cannot exceed 1).

Since VSWR is the ratio of the magnitude of the voltage at a maximum in
the standing wave pattern to the magnitude of the voltage at a minimum
in the standing wave pattern, if we are to infer SWR at a point on a
line (if that makes sense anyway) from rho (which is a property of a
point on a lossy line), isn't the formula VSWR=abs(1+rho)/abs(1-rho)
correct in the general case (lossy or lossless line)?

Given that rho cannot be negative (since it is the magnitude of a
complex number), the general formula can be simplified to
VSWR=(1+rho)/abs(1-rho).

Seems to me that texts almost universally omit the absolute operation on
the denominator without necessarily qualifying it with the assumption of
lossless line.

If VSWR=(1+rho)/abs(1-rho), then doesn't it follow that rho is not a
function of VSWR (except in the lossless line case where
VSWR=(1+rho)/(1-rho) and therefore rho=(VSWR-1)/(VSWR+1))?

Thoughts?

Owen