Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 176

Figure (4.10a) shows E_y and E_z field components of the EM‐wave propagating in the x‐direction. The E‐electric field vector in the (y‐z)‐plane could be written in the phasor form as follows:

(4.6.1)

The e^jωt time‐harmonic factor is suppressed in the above equation (4.6.1a). Equation (4.6.1b) shows the magnitude of the E‐field, and equation (4.6.1c) computes its inclination with respect to the y‐axis. For y‐polarized wave, E_0z = 0, and for the z‐polarized wave, E_0y = 0. In general, the field components E_0y and E_0z are complex quantities. For the in‐phase field components, these are expressed as E_0y=|E_0y| e^jφ and E_0z=|E_0z| e^jφ. The instantaneous field components are considered to trace the movement of the tip of the ‐vector:

(4.6.2)

In the above equations, both field components have an identical phase (ωt + φ). Figure (4.10a) shows the slant or inclined linearly polarized wave with the in‐phase E_y and E_z components. The tip of the electric vector () moves along line A‐O‐B with respect to time. However, the slant angle θ does not change with time. If both the E‐field components are either in‐phase (A − O − B) or out of phase (A^/ − O − B^/) and have the same magnitude, i.e. E_0y = E_0z = E₀, the corresponding inclination angle of the linear polarization trace, with respect to the y‐axis, is θ = 45° and 135°, respectively. For the linear polarization, the total E‐field given by equation (4.6.1a) could also be written as follows:

(4.6.3)