Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 134

The total series impedance and total shunt admittance of the shunt inductor loaded dispersive line, shown in Fig (3.27a), are given by

(3.4.12)

The series impedance and shunt admittance per unit length (p.u.l.) are

(3.4.13)

The complex propagation constant of the wave on the shunt inductor loaded line is

(3.4.14)

The propagation constant β for ω > ω_c is identical to equation (3.4.8). The attenuation constant α is obtained for ω < ω_c. The expressions for the phase velocity and group velocity follow from the expression of β as discussed previously. The characteristic impedance of the loaded dispersive transmission line Z_od(ω) is given by

(3.4.15)

For the case, ω < ω_c, the characteristic impedance Z_od is an imaginary quantity that stops the signal transmission through the line. The line behaves like a high‐pass filter (HPF). For the case ω > ω_c, the characteristic impedance Z_od is a real quantity that allows the signal propagation on the line. However, the characteristic impedance Z_od in the pass‐band is frequency‐dependent.