7.2 Design and practice of ESA |
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Real impedance (Ω)
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εr = 2 |
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160 |
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140 |
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εr = 2.75 |
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εr = 4 |
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120 |
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εr = 7 |
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100 |
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h/Rin
Figure 7.118 Real impedance with respect to h/Rin for εr = 2, 2.75, 4, and 7 ([49], copyrightC 2007 IEEE).
Gain (linear)
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ª2.2 GHz |
εr = 1 |
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3.5 |
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εr = 2.2 |
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2.5 |
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εr = 4.2 |
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Frequency (Hz) |
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Figure 7.119 Simulated gain for a spiral with εr = 1, 2.2, and 4.2 ([49], copyright C 2007 IEEE).
0.1 < h/Rin < 1 for εr < 7 in Figure 7.118. The impedance for smaller h/Rin tends to (1/2) Z0, corresponding to no substrate case (meaning in free space), and for larger h/Rin, to (1/2) Z0/ √εr .
7.2.2.1.4.3.2 Gain
Measured and FDTD simulated gains of the spiral antenna of = 79◦, Rin = 2.5 mm, Rout = 0.12 m are illustrated in Figure 7.119, where a sequence of gain variation for various substrates with εr from lowest to highest 1, 2.2, and 4.2 is given. Gain G can be evaluated as
√
G = π εact (7.65)
where εact is effective permittivity of the active region ring in the spiral. The active region is a part that contributes to radiation, which occurs in a curved structure having circumference one wavelength or in a straight wire or edge with length of one-half