Convert S21 to impedance, don't understand the derivation.

http://www.home.agilent.com/agilent/....00&id=1536926
in the link above,

it explain how equation below is possible.
Z=(2Zo(1-S21 )) / S21

the first thing in the explanation is the assumption that

"Since the relationship between the Vs and the V1 is Vs = 2 x V1"

why is Vs=2V1?

In my humble knowledge...by voltage division.....
V1=(Z1*Vs)/(Z1+Z0) ...... where Z1 is impedance of Source V1....
now here i guess the assumption is that both sources have same impedance to offer... Z0=Z1..therefore
V1=(Z0*Vs)/(Z0+Z0)...
V1=Z0*Vs/2Z0
V1=Vs/2..
or Vs=2V1

I maybe wrong

V1 is not the voltage in a node.
It is the incident wave sensed by the directional coupler. It is the voltage that would be in the node in the case that there is matching (i.e. not reflected vawe); considering this, in that case can be seen by voltage division that V1=Vs/2.
Regards

Z