This discussion considers the effect of the aperture field distribution on the beam and aperture efficiencies.
For many applications, the fraction of the total radiated energy that is in the main (null-to-null) antenna beam is important. This quantity is called the beam efficiency (21). The beam efficiency can be used to judge the ability of the antenna to discriminate between signals received through its main lobe and those through the minor lobes.
Before we go into this subject, it is helpful to review some fundamentals. The main beam is comprised of the solid angle
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4я _ 4л |
where Ap is the physical area of the aperture. The aperture efficiency is defined as the ratio of the effective aperture area, Ae, to the physical aperture, or
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Ae An |
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(29) |
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ap |
so that the ratio of the aperture and beam efficiencies is (8)
(30)
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k0X2 ap^m |
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Ae^A ap^m |
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where Пм is the main beam solid angle (sr), HA the total beam solid angle (sr), and k0 the free space wavenumbers (k0 = 2w/A). It is important to recognize, then, that beam efficiency and aperture efficiency are related to each other. In terms of the radiated intensity E( в, ф) of a pencil beam with boresight at (в = 0, ф = 0), the beam efficiency can be defined by (14) |
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/0n Г фп -9n v —Фп |
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E(0, ф)E(0, ф)* sin 0 dф d0 |
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(31) |
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По = |
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B |
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p п p 2n / / E(0^)E(0, ф)* sin 0 dф d0 J0 J0 |
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(26) |
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:0НРфЕ |
where вНР and фНР are the half-power beam widths (HPBW) in the two principal planes, minor lobes being neglected.
The (total) beam area HA (or beam solid angle ПА) consists of the main-beam area (or solid angle) plus the minor-lobe area (or solid angle). Furthermore, the ratio of the main-beam area to the (total) beam area defines what is called the beam where вп is the angle from boresight to first null in в and фп the angle from boresight to first null in ф. Also, E(Q, ф)* denotes the conjugate of E(a, ф).
In general, the aperture and beam efficiencies must both be multiplied by a gain-degradation factor due to phase errors given by (22)
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(32) |
kg = e-(2n/)
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Figure 13. Coordinate system used to analyze a circular aperture of diameter Dw. |
where S is the rms phase error over the aperture. It is assumed that the correlation intervals of the deviations are greater than the wavelength. The controlling effect of the taper on the efficiencies (beam and aperture) tends to decrease as the phase error increases. The efficiencies are also reduced by the presence of the phase error.
The curves of Fig. 15 show that the beam efficiency tends to increase with an increase in taper but the aperture efficiency decreases. Maximum aperture efficiency occurs for a uniform aperture distribution, but maximum beam efficiency occurs for a highly tapered distribution. In most cases a taper is used that is intermediate between the two extremes.