Suppose you have two reciprocal (passive) devices, A and B, both described with S-parameters \$S_a\$ and \$S_b\$. With a VNA, you measure \$S_a\$ and \$S_{\rm tot}\$ (S-parameters of AB, both devices cascaded).
From circuit theory, we can convert both to its T-parameters, \$T_{\rm tot}\$ and \$T_a\$. Now we know that $$T_{\rm tot}=T_a T_b\,.$$
So we can obtain
$$ T_b = T_a^{-1} T_{\rm tot} , $$
and convert this to \$S_b\$.
There is just one problem: For my measurements, \$|S_{b,11}| \gt 1\$ or, in other words, the real part of the input port impedance of B (its resistance!) is less than zero.
This is clearly wrong because the devices are passive. How can this happen? Which sanity checks can be invoked to see where things/intermediate results are wrong (maybe which measurement point is off)? Intuitively, under which condition can this happen?
Additional Info: The measured results at 915MHz are:
$$ S_a = \begin{bmatrix} -0.0376-i0.2195 & 0.0949-i0.7257 \\ 0.0949-i0.7257 & -0.2423-i0.1649 \\ \end{bmatrix} . $$
\$S_a\$ is is a signal path on a PCB which includes (passing) RF switches, a discrete delay line and ac coupling caps. Parameters were measured using the method from https://ieeexplore.ieee.org/document/780284 with an Agilent VNA at -30dBm but large amount of averaging. The magnitues (return loss and insertion loss) make sense to me and are on the order of what I expect from simulations.
\$S_b\$ is actually a one-port (just a termination impedance), hence I only care about \$S_{b,11}\$. When I measure \$S_{\rm tot}\$, I can still treat it as two-port, just with \$S_{12}=S_{22}=0\$ and \$S_{21}\$ arbitrary. My measurements for \$S_{\rm tot}\$ are:
$$ S_{\rm tot} = \begin{bmatrix} -0.2285+i0.2936 & 0 \\ 1 & 0 \\ \end{bmatrix} . $$
Using this measured data and the approach from above, I obtain:
$$ S_{b,11} = −0.2194−i1.1959 . $$
Choosing a characteristic impedance \$Z_0=50\Omega\$, this corresponds to a negative input impedance: \$Z_{\rm b,in} = -8.2055-i40.997\Omega\$ (any \$Z_0\$ will result in a negative input impedance!). This is unphysical (it could only be generated by an active element). For comparison, the output impedance of block A is \$Z_{\rm a,out}=29.0993-i10.4982\Omega\$. As such, it is not possible to find an L-match to match the impedance between the two blocks.
