where A and B are, respectively, called the net series impedance matrix and the net shunt admittance matrix
in the multilayer transmission line--both as per-unit-distance measures.
For the two cells in Figure 4 to be equivalent, they must have the same node equations (admittance matrix
) or the same normal modes.
It is pointed out in  that it is difficult to determine admittance matrix
elements analytically since they depend upon many physical properties, which are not identified easily.
For a given network with n nodes, the admittance matrix
is given by (3) in which the first two dimensions represent the bus admittance between two different nodes and the third dimension represent the frequency domain.
In effect, an admittance matrix
has larger size and symmetry properties of this matrix are lost.
This single impedance cannot be described by an impedance matrix but can be described by an admittance matrix
in the form
These were combined with a hybrid 3D/2D FEM analysis of the parallel plate structure to form a combined admittance matrix
. This analysis assumed that the transverse electromagnetic mode (TEM) was the only mode propagating in the via holes.
Next, the reconfigured equivalent circuit in Figure 2(a) is simplified forming a quadripole admittance matrix
, [Y.sub.R], of the closed-loop, while transformer, T, and admittance, [Y.sub.c], at the outer section are as depicted in Figure 3.
The Jacobian matrix is composed of 6x6 block matrices and has the same structure as the nodal admittance matrix
. By using this method, the Jacobian matrix can be updated faster than using conventional NR power flow method in the case of PQ buses.
Specifically, [Y.sub.s] is the admittance matrix
of the resistive grating, and it will be a full matrix (a tensor) if the resistive grating is inhomogeneous.
<x|x> denotes the inner product, M the number of uniaxial discontinuities, and [??] the self-adjoint admittance matrix
operator of the complete structure .