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The magnitudes are related by E HZ0, where Z0 120p The direction of the line traced out by the tip of the electric field vector determines the polarization of the wave Keep in mind that the electric and magnetic fields are varying as functions of time The magnetic field varies exactly in phase with the electric field, and its amplitude is proportional to the electric field amplitude, so it is only necessary.

to consider the electric field in this discussion. The tip of the E vector may trace out a straight line, in which case the polarization is referred to as linear. Other forms of polarization, specifically elliptical and circular, will be introduced later. In the early days of radio, there was little chance of ambiguity in specifying the direction of polarization in relation to the surface of the earth. Most transmissions utilized linear polarization and were along terrestrial paths. Thus vertical polarization meant that the electric field was perpendicular to the earth s surface, and horizontal polarization meant that it was parallel to the earth s surface. Although the terms vertical and horizontal are used with satellite transmissions, the situation is not quite so clear. A linear polarized wave transmitted by a geostationary satellite may be designated vertical if its electric field is parallel to the earth s polar axis, but even so the electric field will be parallel to the earth at the equator. This situation will be clarified shortly. Suppose for the moment that horizontal and vertical are taken as the x and y axes of a right-hand set, as shown in Fig. 5.2a. A vertically polarized electric field can be described as Ey y Ey sinwt (5.1)

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where y is the unit vector in the vertical direction and Ey is the peak value or amplitude of the electric field. Likewise, a horizontally polarized wave could be described by Ex x Ex sinwt (5.2)

These two fields would trace out the straight lines shown in Fig. 5.2b. Now consider the situation where both fields are present simultaneously.

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(a) Figure 5.2 (b) (c)

These would add vectorially, and the resultant would be a vector E (Fig. 5.2c) of amplitude 2E2 E2, at an angle to the horizontal given by x y a arctan Ey Ex (5.3)

E varies sinusoidally in time in the same manner as the individual components. It is still linearly polarized but cannot be classified as simply horizontal or vertical. Arguing back from this, it is evident that E can be resolved into vertical and horizontal components, a fact which is of great importance in practical transmission systems. The power in the resultant wave is proportional to the voltage 2E2 E2 , x y squared, which is E2 E2 . In other words, the power in the resultant x y wave is the sum of the powers in the individual waves, which is to be expected. More formally, Ey and Ex are said to be orthogonal. The dictionary definition of orthogonal is at right angles, but a wider meaning will be attached to the word later. Consider now the situation where the two fields are equal in amplitude (denoted by E), but one leads the other by 90 in phase. The equations describing these are Ey Ex y E sinwt x E coswt (5.4a) (5.4b)