Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 116

To compute S₁₁ that is the reflection coefficient of a network under the matched condition, the port‐2 is terminated in Z_0. Thus, Z_in = Z + Z₀ and the reflection coefficient at port‐1 is

(3.1.61)

Figure 3.15 Network of series impedance.

Likewise, to compute S₂₂, the port‐1 is terminated in Z_0. It gives Z_out = Z + Z₀ at the port‐2. The S₂₂ is

(3.1.62)

The total port voltage at the port‐1 is a sum of the forward and reflected voltages:

To compute S₂₁, i.e. the transmission coefficient from the port‐1 to the port‐2 under the matched termination, at first, the total port voltage at the port‐2 is obtained:

Therefore, from equations (i) and (ii):

However, the port voltage V₂ computed from the port current is

Finally, S₂₁ is obtained from equations :

(3.1.63)

Equations (3.1.61) and (3.1.63) provide the following relation:

(3.1.64)

The [S] matrix of the series impedance is

(3.1.65)

The attenuation and phase shift of a signal, applied at the input port‐1 of series impedance Z = R + jX, are computed below.

Using S₂₁ from equation (3.1.63), the attenuation offered by the series impedance is

(3.1.66)

The lagging phase shift of the signal at the output port‐2, due to the series element, is

(3.1.67)