# 5.5 Calculation of S-Parameters

The calculation of scattering parameters is similar to the calculation of impedance parameters and follows the common rules of circuit analysis (Ohm's Law, Kirchhoff's law, …). It is important to terminate all ports by their port reference impedance *Z*_{0i} during calculation.

*5.5.1 Reflection Coefficients*

We have already calculated reflection coefficients in Section 3.1. So we can directly adopt the relations from our previous discussion.

The reflection coefficient *s*_{ii} at port *i* is given by

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where *Z*_{ini} is the input impedance of port *i* and *Z*_{01} is the port reference impedance. Figure 5.7 shows the circuit for the calculation of *s*_{11} on a two-port network. Port 2 is terminated by the port reference impedance *Z*_{02}.

*5.5.2 Transmission Coefficients*

In order to calculate the transmission coefficient from port *i* to port *j* we connect an equivalent voltage source (ideal voltage source *U*_{0i} and internal resistance *Z*_{0i}) to port *i*. All other ports are terminated by their port reference impedances. The transmission coefficient *s*_{ji} is then given by

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Figure 5.8 shows the corresponding circuit ...