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[[File:SymmetricCondensedNode.png|thumb|320px|right|A 3D symmetric condensed node]]
Most problems in electromagnetics require a three-dimensional computinggrid. As we now have structures, that describe TE and TM-field distributions, intuitively it seemseems possible to providedefine a combination of shunt and series nodes, which will provideproviding a full description of the electromagnetic field. Such attempts have been made, but they proved not very useful because of the complexity of the resulting structures they proved to be not very useful. Using the normal analogy, that was presented above, leads to calculation of the different field components at physically separated points. This causes difficulties in providing simple and efficient boundary definitiondefinitions. A solution to these problems was provided by Johns in 1987, when he proposed the structure, known as the '''symmetrical condensed node''' (SCN), presented in the figure on the right. It consists of 12 ports, because two field polarisations are to be assigned to each of the 6 sides of a mesh cell.
The topology of the SCN can notcannot be analysed using Thevenin equivalent circuits. More general energy and charge conservation principles are to be used.
The electric and the magnetic fields on the sides of the SCN node number ''(l,m,n)'' at time instant ''k'' may be summarised in 12-dimensional vectors
: <math>_k\mathbf{b}_{l,m,n}=\frac{1}{2\sqrt{Z_F}}{_k\mathbf{E}}_{l,m,n}-\frac{\sqrt{Z_F}}{2}{_k\mathbf{H}}_{l,m,n}</math>
where <math>Z_F = \sqrt{\frac{\mu}{\varepsilon}}</math> is the field impedance, <math>_k\mathbf{a}_{l,m,n}</math> is the vector of the amplitudes of the incident waves to the node, and <math>_k\mathbf{b}_{l,m,n}</math> is the vector of the scattered amplitudes. The relation between the incident and scattered waves is given withby the matrix equation
: <math>_k\mathbf{b}_{l,m,n} = \mathbf{S}_k\mathbf{a}_{l,m,n}</math>
The scattering matrix '''S''' maycan be calculated. For the symmetrical condensed node with ports defined as in the figure the following result is obtained
: <math>\mathbf{S} = \left[
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