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RF and Microwave Engineering: Fundamentals of Wireless Communications by Frank Gustrau

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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 Z0i 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 sii at port i is given by

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where Zini 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.

5.7

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 U0i and internal resistance Z0i) to port i. All other ports are terminated by their port reference impedances. The transmission coefficient sji is then given by

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Figure 5.8 shows the corresponding circuit ...

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