The power waves *a*_{i} and *b*_{i} of a two-port network are related by the following system of linear equations as

5.14

where the coefficients *s*_{ij} are the *scattering parameters* [4]. We can write the equations in matrix form as

5.15

where **S** is the *scattering matrix*. Matrix elements *s*_{ii} with equal indices are *reflection coefficients* describing reflection of waves at port *i*. Matrix elements *s*_{ij} with different indices *i* ≠ *j* 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 *s*_{ii} are reflection coefficients too, we look at Equation 5.13, which is given by *b*_{1} = *s*_{11}*a*_{1} + *s*_{12}*a*_{2}. Let us assume that port 2 is terminated by an infinite transmission line with a characteristic impedance of *Z*_{02}. On this transmission line no incident wave *a*_{2} exists. Hence, *a*_{2} = 0. (Alternatively, we can terminate port 2 with a resistor that equals the characteristic line impedance of that port *R* = *Z*_{02}.) Due to Ohm's law the resistor enforces *U*_{2} = *Z*_{02}(−*I*_{2}). The minus sign stems from our definition of voltage ...

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