Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 78

Figure (2.12a) shows the series‐connected voltage source V_S at x = 0. The location x = 0 is a junction of two transmission lines – line #1 open‐circuited finite‐length line and line #2 infinite length line. The lines at the left‐hand and right‐hand sides of the voltage source can be replaced by the equivalent impedances Z⁻ and Z⁺, respectively. It is shown in the equivalent circuit, Fig (2.12b). Again, the voltage waves on both lines, excited by a series voltage source, could be determined.

The voltages across loads Z⁻ (Z₁) and Z⁺ (Z₂), shown in Fig (2.12b), are obtained as follows:

(2.2.18)

Line #1 is open‐circuited and line #2 is of infinite extent. Therefore, their input impedances at x = 0⁻ and x = 0⁺ are

Figure 2.12 A series voltage source at the junction of two‐line sections.

(2 2 19)

The voltage at x = 0⁺ from equations (2.2.18c) and (2.2.19) is

(2.2.20)

For a lossy transmission line, the above equation could be written as follows:

(2.1.21)

The voltage wave on the infinite extent lossy line #2 is

(2.2.22)

The voltage at x = 0⁻ on the lossless line #1 is

(2.2.23)

However, the voltage at x = 0⁻ on a lossy line #1 is

(2.2.24)

The voltage wave on the open‐circuited lossless line #1 is obtained from equations (2.2.16) and (2.2.23):

(2.2.25)