RF and Microwave Engineering: Fundamentals of Wireless Communications

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 Z₀₁ is the port reference impedance. Figure 5.7 shows the circuit for the calculation of s₁₁ on a two-port network. Port 2 is terminated by the port reference impedance Z₀₂.

Figure 5.7 Circuit for the calculation of reflection coefficient s₁₁.

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 ...