The ideal symmetrical transformer, as shown in fig. 9.3, is determined by the following equations which introduce two more unknowns in the MNA matrix.
The new unknown variables and must be considered by the six remaining simple equations.
The matrix representation needs to be augmented by two more new rows and their corresponding columns. For DC and AC simulation it is:
Using the port numbers depicted in fig. 9.3, the scattering parameters of an ideal, symmetrical transformer with voltage transformation ratio (number of turns) and , respectively, writes as follows.
An ideal symmetrical transformer is noise free.