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A MESFET switched line phase shifter. (From http://parts.jpl.nasa.gov/mmic/3-IX.PDF)
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and control electrode provides the RF coupling between input and output. Thus, this is basically a contactless switch. As mentioned earlier, it is also possible to alter the phase shift by altering the propagation coefficient. By definition, a sinusoidal electromagnetic wave experiences a phase change of 2 rad over distance of one wavelength l, and therefore the phase change coefficient can be written simply as 2 l (6.45)
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This will be in radians per meter with l in meters. As noted earlier, the connection between wavelength l, frequency f, and phase velocity vp is lf vp. It is also known that the phase velocity on a transmission line having a dielectric of relative permittivity r is vp c/ 2er, where c is the free space velocity of light. Substituting these relationships in Eq. (6.43) gives: 2 f 2er l c (6.46)
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This shows that, for a fixed length of line, a phase change can be obtained by changing the frequency f or by changing the relative permittivity (dielectric constant) er.. In one scheme (Nishio et al., 2004) a method is given for phasing a base station antenna array by means of frequency change. The modulated subcarrier is fed in parallel to a number of heterodyne frequency mixers. A common local oscillator (LO) signal is fed to each mixer to change the subcarrier up to the assigned carrier frequency, the output from each mixer feeding its own element in the antenna array. The phase change is introduced into the LO circuit by having a different, fixed length of line in each branch of the LO feed to the mixers. Thus the output from each mixer will have its own fixed phase angle, determined by the phase shift in the oscillator branch. Phase change can also be effected by changing the relative permittivity of a delay line. Efforts in this direction have concentrated on using ferroelectric material as a dielectric substrate for the delay line. Whereas the dielectric constant of a printed circuit board may range from about 2 to 10, ferroelectrics have dielectric constants measured in terms of several hundreds. The ferroelectric dielectric constant can be changed by application of an electric field, which may be in the order of 2000 kV/m. Thus to keep the applied voltage to reasonable levels, a thin dielectric is needed. For example, for a dielectric thickness of 0.15 mm and an electric field of 2000 kV/m the applied voltage
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is 2000 10 0.15 10 300 V. The characteristic impedance of a microstrip line is given by Z0 > 2er, where Z0 is the impedance of the same line with an air dielectric. The characteristic impedance increases as a function of h/W, where W is the width of the line and h the thickness of the dielectric. Thus thinner dielectrics lead to lower characteristic impedance, and this combined with the high dielectric constant means that the line width W has to be narrow. Values given in De Flaviis et al. (1997) for the ferroelectric material barium modified strontium titanium oxide (Ba1 x Srx TiO3) show a dielectric constant in the region of 600, dielectric thickness between 0.1 and 0.15 mm, and line width of 50 m, for a characteristic impedance of 50 . The bias voltage is 250 V. The ferroelectric dielectric is used in a number of different ways. In the paper by De Flaviis et al., the material was used simply as the dielectric for a microstrip delay line. It has also been used as a lens to produce scanning by deflecting an antenna beam (see Ferroelectric Lens Phased Array at http://radar-www.nrl.navy.mil/Areas/Ferro). The lens is shown in Fig. 6.37. The ferroelectric dielectric in each column is biased to provide a progressive phase shift so that an incident plane wave normal to the edges of the dielectric columns will emerge from the opposite edges in a direction determined by the phasing in the lens. A single lens produces one dimensional scanning. Ferroelectrics are also employed in reflectarrays described next. 6.20 Re ectarrays A reflectarray, as the name suggests is an array of antenna elements that acts as a reflector. A reflector array incorporates a planar array as a reflector, as shown in Fig. 6.38. The planar array basically replaces the parabolic reflector shown in Fig. 6.13. Reflected waves from each of the elements in the array can be phased to produce beam scanning; Fig. 6.38b shows the construction. The reflected wave is actually a combination of reflections from the antenna elements and the substrate. Figure 6.38c shows the polar diagram for a 784 element array. Further details of this array will be found in Pozar (2004). A number of methods of producing beam scanning have been proposed. Fig. 6.39 shows a 2832 element, 19-GHz reflectarray which employs ferroelectric phase shifters for the elements. Further details will be found at www.ctsystemes.com/zeland/publi/TM-2000-210063.pdf. Varactor diodes have also been used to provide a phase shift that is controlled by an applied bias. A varactor is in effect a voltage controlled capacitor, and changes in the capacitance introduce a corresponding phase shift. Figure 6.40 shows one arrangement for a five-element array.
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