and by substitution of (11) into (10), the scattering parameters are now found in terms of impedance matrix
Another approach by Jiang  and Mimani and Munjal  is based on an impedance matrix
, which is obtained by either plane wave analysis or the boundary or finite element method.
Consider, for example, the impedance matrix
representation of a system in which case we have
or Z-matrix is other useful method.
For fiber lining, the absorption is modeled using a complex impedance matrix
expressed in modal coordinates to describe the impedance of the lining on the acoustic cavity.
Figure 2(b) illustrates the condition number of the impedance matrix
for three EFIE schemes.
which is the inverse matrix of the impedance matrix
The microwave network is described by impedance matrix
Three-phase modeling of unbalanced distribution systems during open conductors and/or shunt fault conditions using the bus impedance matrix
While using an impedance matrix
to define a network might be more intuitive, it is actually more difficult to get the proper measurements; therefore, S-Parameters are the choice of the digital designer.
Rather than expressing the relationship between a's and b's in terms of a nonlinear large-signal scattering matrix S, we can alternatively express the relationship between voltages (V's) and currents (I's) in terms of a nonlinear large-signal impedance matrix
Z, as follows
The impedance matrix
, derived from the relations between voltage and current at z = -l and z = 0, is obtained as