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

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5.3 Scattering Parameters and Power

The power waves ai and bi of a two-port network are related by the following system of linear equations as

5.13 5.13

5.14 5.14

where the coefficients sij are the scattering parameters [4]. We can write the equations in matrix form as

5.15 5.15

where S is the scattering matrix. Matrix elements sii with equal indices are reflection coefficients describing reflection of waves at port i. Matrix elements sij with different indices ij are transmission coefficients, describing the transmission of waves from port j to port i.

From Section 3.1 we already know reflection coefficients r. In order to understand that the scattering parameters with two identical indices sii are reflection coefficients too, we look at Equation 5.13, which is given by b1 = s11a1 + s12a2. Let us assume that port 2 is terminated by an infinite transmission line with a characteristic impedance of Z02. On this transmission line no incident wave a2 exists. Hence, a2 = 0. (Alternatively, we can terminate port 2 with a resistor that equals the characteristic line impedance of that port R = Z02.) Due to Ohm's law the resistor enforces U2 = Z02(−I2). The minus sign stems from our definition of voltage ...

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