De embed a network using s2tf or T-matrix - discrepancy?

Dear Community,

I am trying to de-embed a 2-port network (fixture) from a measurment to sinf its s21 or transfer function and I found 2 ways to do it.

my setup is a fixture followed by a diode laser. with the diode laser I can assume s12 = 0 and s22 = 1.

using the s2tf vs old fashined Tmatrix to de-embed I get a discrepancy

from s2tf:

I can use the equation below to calculate the tf from the source to the load (may be arbitrary).

tf = VlVs = S21(1+Γl)(1−Γs)/(2(1−S22Γl)(1−ΓinΓs))

assuming a perfect load, Γs becomes 0 and we are left with:

tf = VlVs = S21(1+Γl)/(2(1−S22Γl))

(S21 and S22 are the scattering parameters of the 2-port network in between the ports, or the fixture in my case).

With this I have the transfer function from the source to the load allowing any arbitrary load - I would like to assume it as my diode laser.

I could also ask what would be the s21 from the source to the diode laser with trying to de-embed the 2-port network.

If I take on de-embedding with Tmat method and work out the algebra, I can write the total s21 as:

With this I find a discrepancy in the numerator: vs (or )

I am aware to the fact that the relation from the transfer function to s21 should also include the impedance and might include a factor of 2 (due to defenition of the voltage source).

Can someone help to sort this?

Is the problem assuming the arbitrary load in the s2tf has this directional property?

Thanks!

Matan

[Matan]

s2tf https://www.mathworks.com/help/rf/ref/s2tf.html