Bracerightbig this clearly has the form of an

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bracerightBig This clearly has the form of an elliptically polarized wave with a semimajor (semiminor) axis ˆ x ( ˆ y ), amplitude E + ( E ), and phase angle φ . As time t or position z advances, the electric field vector sweeps out the path of the ellipse. The sense of rotation depends on the signs of E + and E and ultimately on the original value of ψ . 2.4.4 Helical antennas The antennas considered so far all emit linearly polarized signals. Elliptical and circular polarization can be achieved by combining two or more linearly polarized antennas and exciting them out of phase with one another. Crossed dipoles driven 90 degrees out of phase are often used to transmit and receive circularly polarized signals, for example. Similarly crossed Yagi antennas (parasitic arrays of dipoles discussed in the next chapter) are commonly used for higher gain. Hybrid networks facilitate the feeding of the antennas. However, there are antennas that are elliptically or circularly polarized natively. One of these is the helical antenna or helix. D S z S I Figure 2.13: Section of a helical antenna with diameter D and turn spacing S . To the right is a normal mode model of a turn of the helix. Figure 2.13 shows a section of a helical antenna. The total length of an antenna with n turns is nS . The cir- cumference C of the turns is πD . The behavior of the helical antenna depends on whether its dimensions are large or small compared to a wavelength. When D,nS λ , the helix is electrically small and operates in the so-called ‘normal’ mode. When C,S λ , the helix operates in the ‘axial’ mode. While the radiation fields can be determined by calculating the vector potential directly as in previous examples, experience has shown that the performance of the helix is well approximated by some simple models. In the normal mode, each turn of the antenna behaves like the superposition of an elemental electric dipole and an elemental magnetic dipole antenna, as shown in Figure 2.13. Since the antenna is electrically small, the current is uniform along the length of the antenna. Since the turns are closely spaced compared to a wavelength, each contributes equally to the far field, and it is sufficient to consider the contribution from a single turn. The contributions from the 46
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electric and magnetic dipoles are, respectively: E e = jZ kIS sin θ e jkr 4 πr ˆ θ E m = π 4 Z k 2 ID 2 sin θ e jkr 4 πr ˆ φ with the total far-zone field being the vector sum of the two. Both components share the same sin θ spatial dependence, and so the radiation pattern is broadside and wide. The two components are, however, 90 out of phase, and the polarization of the signal is consequently elliptical and the same in all directions. The polarization becomes circular in all directions when the ratio of the amplitudes | E θ | | E φ | = 2 λS C 2 is equal to 1. This occurs when the circumference of the helix is the geometric mean of the wavelength and the turn spacing, C = 2 λS .
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