tion 7.55, where Pm is the maximum ERP. P = r2s2Pm (7.55) The three-dimensional radiation pattern can be more fully represented in two dimensions by a family of polar patterns, each contour line joining directions having equal ERP. Polarization The polarization of an electromagnetic wave defines the time-varying behavior of the elec- tric field vector at a point. Linear Polarization When the electric vector lies wholly in a single plane, the wave is said to be linearly polar- ized. In terrestrial communications, when this plane is parallel to the surface of the Earth, the wave is defined as horizontally polarized and, when the plane is perpendicular to the surface of the Earth, the wave is defined as vertically polarized. Circular Polarization A wave is said to be circularly polarized where the electric field vector rotates in the plane normal to the direction of propagation such that the locus of the extremity of the vector Chapter 7 Electromagnetic Waves Rotating Electric Field Vector Direction of Propagation: Normal to Plane XOY Fig. 7.14 Polarization ellipse and circumscribing rectangles. describes a circle. The agreed convention for defining the sense of rotation of the electric vector is in terms of the direction of rotation for an observer looking; in the direction of propagation (i.e., toward the receiver). Clockwise rotation is often called right-hand circular polarization; counterclockwise, left-hand circular polarization. The electric field vector rotates at the angular frequency, W, of the wave and describes one revolution in the period 2/w. Elliptical Polarization A wave is defined as elliptically polarized where the electric field vector rotates in the plane normal to the direction of propagation while its amplitude varies such that the locus of the extremity of the vector describes an ellipse. The vector rotates by one revolution during the period of oscillation, 2/w, of the source, though the angular velocity is not constant throughout the revolution, as it would be for circular polarization. Elli