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·驻波换算 ·天线计算 |
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ANTENNA INTRODUCTION / BASICSRULES OF THUMB: １.The Gain of an antenna with losses is given by:
2. Gain of rectangular X-Band Aperture G = 1.4 LW Where: L = length of aperture in cm W = width of aperture in cm 3. Gain of Circular X-Band Aperture
4. Gain of an isotropic antenna radiating in a uniform spherical pattern is one (0 dB).
5. Antenna with a 20 degree beamwidth has a 20 dB gain. 6. 3 dB beamwidth is approximately equal to the angle from the peak of the power to the first null(see figure at right). 7. Parabolic Antenna Beamwidth:
ANTENNA BASICS
Quite often directivity and gain are used interchangeably. The difference is that directivity neglects antenna losses such as dielectric, resistance, polarization, and VSWR losses. Since these losses in most classes of antennas are usually quite small, the directivity and gain will be approximately equal (disregarding unwanted pattern characteristics). Normalizing a radiation pattern by the integrated total power yields the directivity of the antenna. This concept in shown in equation form by:
Another important concept is that when the angle in which the radiation is constrained is reduced, the directive gain goes up. For example, using an isotropic radiating source, the gain would be 0 dB by definition (Figure 2(a)) and the power density (Pd) at any given point would be the power in (Pin) divided by the surface area of the imaginary sphere at a distance R from the source. If the spacial angle was decreased to one hemisphere (Figure 2(b)), the power radiated, Pin, would be the same but the area would be half as much, so the gain would double to 3 dB. Likewise if the angle is a quarter sphere, (Figure 2(c)), the gain would be 6 dB. Figure 2(d) shows a pencil beam. The gain is independent of actual power output and radius (distance) at which measurements are taken.
Converting from radians to degrees, and converting to dB, the above equation reduces to (with 4 square radians [steradians] = 4 x (57.3)2 = 41253 representing the equivalent number of "square degrees" in a sphere):
Beam area is also defined as:
All antennas, except wire antennas, have a physical aperture area. That area can be normalized with an area by , such that
Note: Equation is approximate since aperture efficiency isn't included as is done in equation [7]. Substituting equation [4] and [5] into equation [2] gives:
The efficiency (discussed later) will reduce the gain by a factor of 30-50%. Antenna size and beamwidth are also related by the beam factor defined by: Beam Factor = (D/ where D = antenna dimension in wavelengths. The beam factor is approximately invariant with antenna size, but does vary with type of antenna aperture illumination or taper. The beam factor typically varies from 50-70 degrees. The upper plot of Figure 4 shows the values of gain for equation [1] for a square antenna aperture. The lower plot of Figure 4 shows a typical antenna with an efficiency of 70%.
The previous discussion presumes we know the shape and magnitude of the antenna pattern. Frequently we do not know this, but have other information available to us. The Gain of an antenna with losses is given by:
Note that the gain is proportional to the aperture area normalized by the square of the wavelength. For example, if the frequency is doubled, (half the wavelength), the aperture could be decreased four times to maintain the same gain. APERTURE EFFICIENCY, The Antenna Efficiency, (1) Illumination efficiency which is the ratio of the directivity of the antenna to the directivity of a uniformly illuminated antenna of the same aperture size, (2) Phase error loss or loss due to the fact that the aperture is not a uniform phase surface, (3) Spillover loss (Reflector Antennas) which reflects the energy spilling beyond the edge of the reflector into the back lobes of the antenna, (4) Mismatch (VSWR) loss, derived from the reflection at the feed port due to impedance mismatch (especially important for low frequency antennas), and (5) RF losses between the antenna and the antenna feed port or measurement point. The aperture efficiency, Items (3), (4), and (5) above represent RF or power losses which can be measured. The efficiency varies and generally gets lower with wider bandwidths. EFFECTIVE CAPTURE AREA Effective capture area (Ae) is the product of the physical aperture area (A) and the aperture efficiency (
APERTURE ILLUMINATION (TAPER) The aperture illumination or illumination taper is the variation in amplitude across the aperture. This variation can have several effects on the antenna performance: (1) reduction in gain, (2) reduced (lower) sidelobes in most cases, and (3) increased antenna beamwidth and beam factor. Tapered illumination occurs naturally in reflector antennas due to the feed radiation pattern and the variation in distance from the feed to different portions of the reflector. Phase can also vary across the aperture which also affects the gain, efficiency, and beamwidth. CIRCULAR ANTENNA GAIN Solving equation [6] in dB, for a circular antenna with area D2/4, we have: [9] 10 Log G = 20 Log (D/ This data is depicted in the nomograph of Figure 5. For example, a six foot diameter antenna operating at 9 GHz would have approximately 44.7 dB of gain as shown by the dashed line drawn on Figure 5. This gain is for an antenna 100% efficient, and would be 41.7 dB for a typical parabolic antenna (50% efficient). An example of a typical antenna showing the variation of gain with frequency is depicted in Figure 6, and with antenna diameter in Figure 7. The circle on the curves in Figure 6 and 7 correspond to the previous (Figure 5) example and yields 42 dB of gain for the 6 ft dish at 9 GHz.
Example ProblemIf the two antennas in the drawing are "welded" together, how much power will be measured Multiple choice: a. 16 dBm Answer: The antennas do not act as they normally would since the antennas are operating in the near field. They act as inefficient coupling devices resulting in some loss of signal. In addition, since there are no active components, you cannot end up with more power than you started with. 10 dBm - 3 dB - small loss -3 dB = 4 dBm - small loss If the antennas were separated by 5 ft and were in the far field, the antenna gain could be used with space loss formulas to calculate (at 5 GHz): 10 dBm - 3 dB + 6 dB - 50 dB (space loss) + 6 dB -3 dB = -34 dBm (a much smaller signal). >>欣航威波 |
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The antenna equations which follow relate to Figure 1 as a typical antenna. In Figure 1, BW
is the azimuth beamwidth and BW
is the elevation beamwidth. Beamwidth is normally measured at the half-power or -3 dB point unless otherwise specified. See Glossary. The gain or directivity of an antenna is the ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions.
Real antennas are different, however, and do not have an ideal radiation distribution. Energy varies with angular displacement and losses occur due to sidelobes. However, if we can measure the pattern, and determine the beamwidth as shown in Figure 3, it can be shown that:
)(Beamwidth)
, is a factor which includes all reductions from the maximum gain. 
can be expressed as a percentage, or in dB. Several types of "loss" must be accounted for in the efficiency,
:
a, is also known as the illumination factor, and includes items (1) and (2) above; it does not result in any loss of power radiated but affects the gain and pattern. It is nominally 0.6-0.8 for a planer array and 0.13 to 0.8 with a nominal value of 0.5 for a parabolic antenna, however can vary significantly. Other antennas include the spiral (.002-.5), the horn (.002-.8), the double ridge horn (.005-.93), and the conical log spiral (.0017-1.0).
) or:
) + 10 Log (
) + 9.94 dB ; where D = diameter
