Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 177

The circular polarization, shown in Fig. (4.10b), is obtained for two orthogonal field components of equal magnitude, and phase in quadrature. So, to get the circular polarization, two electric field components oscillate at the same frequency and meet the following conditions:

 Equal amplitude: The magnitudes of Ey and Ez are equal, i.e. |E0y| = |E0z| = E0.

 Space quadrature: The Ey and Ez field components are normal to each other.

 Time (phase) quadrature: The phase difference between the Ey and Ez field components are (φ = ± 90°), i.e. E0y = E0, and E0z = E0e±π/2 = ± j E0.

The phasor form of the E‐field vector of the circularly polarized waves, meeting the above conditions, could be written from equation (4.6.1a) as follows:

(4.6.4)

The e^jωt time‐harmonic factor is suppressed in the above equations. The time‐domain forms of the circularly polarized waves, using the instantaneous ‐field components, at any location in the positive x‐direction and also at the x = 0, i.e. in the (y‐z)‐plane, are expressed as follows:

(4.6.5)

The handedness, i.e. the sense of rotation of the ‐vector of the circularly polarized wave is determined by the direction of rotation of the ‐vector in the transverse (y‐z)‐plane with respect to time, whereas the EM‐wave propagates in the x‐direction. Therefore, using equation (4.6.5f), Fig. (4.10b) shows the anti‐clock rotation of the E‐field vector tracing a circle of radius E₀ in the (y‐z)‐plane. The sense of rotation is considered with respect to cos(ωt), taking t = 0. It shows the wave propagating in the positive x‐direction, i.e. the wave coming toward an observer standing on the positive x‐axis is the right‐hand circularly polarized wave (RHCP). Its field vector is given by equation (4.6.4b). Similarly, equation (4.6.5e) shows the clockwise rotation, i.e. the left‐hand circularly polarized wave (LHCP) propagating in the positive x‐direction. The magnetic fields of the RHCP and LHCP wave are obtained using equation (4.6.4) with equation (4.5.34a):

(4.6.6)

In the case of the wave propagation in the negative x‐direction, i.e. the wave moves away from the observer standing on the positive x‐axis, the role of RHCP and LHCP gets interchanged. Further, the handedness of circular polarization can be reversed by applying 180° phase‐shift to either the y or z component of the ‐field vector. The circular polarization could be further considered as a linear combination of two linearly polarized waves. Alternatively, the linear polarization can also be considered as a linear combination of the left‐hand and right‐hand circularly polarized waves [B.9].