Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 178

Two orthogonal field components, in the space quadrature, of unequal magnitude and arbitrary phase angle (φ) between them, generate the elliptical polarization, i.e. the resultant E‐field vector rotates in the plane of polarization such that its tip traces an elliptical path as shown in Fig. (4.10c). The instantaneous orthogonal E‐field components in the x = 0 plane are given below:

(4.6.7)

Using the above equation and identity the following equation of the ellipse is obtained:

(4.6.8)

The semi‐major axis OA, the semi‐minor axis OB of the ellipse shown in Fig. (4.10c), and the axial ratio (AR) of the polarization ellipse are given below [B.9, B.29]:

(4.6.9)

The tilt angle θ of the polarization ellipse, i.e. inclination of the major axis OA with y‐axis is [B.9, B.29]:

(4.6.10)

For φ ≠ π/2, the polarization ellipse is inclined with respect to the y‐axis. The linear and circular polarizations are obtained as special cases from the elliptical polarization. For instance, for E_z(t) = 0 the wave is horizontally polarized in the y‐direction. For E_0y = E_0z = E₀ and φ = ± π/2, the LHCP/RHCP wave is obtained as equation (4.6.9) is reduced to an equation of a circle with OA = OB. For the linear polarization, AR is infinity. However, for the circular polarization, AR is unity. In the case E_0y = E_0z = E₀ and φ ≠ π/2, the wave is not circularly polarized and its AR is cotφ/2. For a practical circularly polarized antenna, the axial ratio is frequency‐dependent and its axial ratio bandwidth is defined as the frequency band over which AR ≤ 3dB.