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JGHzu where fGHz is the carrier frequency in GHz, and D is the antenna diameter in m.*

* Equation (13-19)yieldsa beamwidth about 20% greater than A/D (Chap. 9). This accounts for the nonuniform illumination of the parabola by the feed.

The antenna gain is approximately 27,000/02 obtained by combining Eqs. (13-7) and (13-19), and assuming T) = O.SS. A noncircular antenna has an elliptical beam with the half-power beamwidth along the major axis equal to 9X and the half-power beam-width along the minor axis equal to 6y The gain of the noncircular beam antenna can be estimated:

where Qx and Qy are in deg, and G is in dBi. For example, an antenna with a 1 deg by 2 deg elliptical beam has the same gain as a circular antenna with a beamwidth of 1.4 deg. Gain calculated in this manner is generally accurate to within 25% (1.2 dB) for beamwidths less than 150 deg. The beamwidths Qx or 8y can be estimated from Eq. (13-19) with D equal to the major axis or minor axis diameters.

The above gain equations are for peak gain. However, a receive antenna might not be located at the center of the transmitter antenna beam, or vice versa. With narrow beamwidths, small errors in pointing the antenna (introduced by wind gusts on the ground or satellite stabilization errors, for example) can lead to significandy reduced gain. The following equation estimates the reduction from peak gain, Le, in dB caused by a pointing offset from beam center:

where 0 is the antenna half-power beamwidth, and e is the pointing error. For example, for e equal to 912, the pointing loss is 3 dB. In calculating a link budget, we would subtract this pointing loss from the antenna gain.

Converting into dB, this gives:

Ls = 20 log (3 x 108) _ 20 log (4?t) - 20 log S - 20 log/ (13-23a)

where S is the path length in m, and/is the frequency in Hz.

The system noise temperature, Tp is the sum of a number of individual contributions from various sources. We have divided the noise sources into two groups. Those originating ahead of the antenna aperture (e.g., in the atmosphere) we call the antenna noise temperature, Tant- These noise sources are external to the ground station, except for the antenna itself, and include:

• Galactic noise

• Noise radiated by clouds and rain in the propagation path

• Solar noise (either in the antenna main beam or sidelobe)

• Presence of the Earth (typically 290 K) in a sidelobe

• Man-made noise (either in the antenna main beam or sidelobe)

• Contribution of nearby objects, buildings, radomes, etc.

• Temperature of blockage items in antenna subsystem such as booms or feeds

Figure 13-7 shows the estimated noise temperature from various external sources as a function of frequency. Note the necessity of keeping the receive antenna from pointing toward the Sun when the beamwidth is narrow (< 5 deg). Otherwise the Sun will significantly increase the antenna noise temperature.

A: Estimated median business area man-made noise B: Galactic noise

C: Atmospheric noise, value exceeded 0.5% of time

D: Quiet Sun (1/2 deg beamwidth directed at Sun)

E: Sky noise due to oxygen and water vapor (very narrow beam antenna);

upper curve, 0-deg elevation angle; lower curve, 90-deg elevation angle F: Black body (cosmic background), 2.7 K G: Heavy rain (50 mm/hr over 5 km)

A: Estimated median business area man-made noise B: Galactic noise

C: Atmospheric noise, value exceeded 0.5% of time

D: Quiet Sun (1/2 deg beamwidth directed at Sun)

E: Sky noise due to oxygen and water vapor (very narrow beam antenna);

upper curve, 0-deg elevation angle; lower curve, 90-deg elevation angle F: Black body (cosmic background), 2.7 K G: Heavy rain (50 mm/hr over 5 km)

Fig. 13-7. Minimum Expected External Noise From Natural and Man-made Sources, 10 MHz to 100 GHz [Ippolito, 1986].

All noise sources between the antenna terminal and the receiver output are lumped together and called receiver noise temperature, Tr. Receiver noise originates from

• Transmission Lines and Filters—equal to (1 -L)T, where L=P0/P,is the ratio of output power (P0) to input power (P,) and 7" is the component temperature in K.

• Low Noise Amplifier—equal to (F - 1) 290 K, where F is the noise figure from Eq. (13-24).

An additional contribution from subsequent amplifier stage noise exists, but is a small contributor because it is divided by the low noise amplifier gain. The noise figure, F, of the receiver is defined as:

To where Tr is the noise temperature of the receiver itself, and 7q is a reference temperature, usually 290 K. The noise figure is often expressed in dB (that is, 10 log F). For example, a cryogenically cooled receiver for reception of telemetry signals from a space probe may have a noise figure of 1.1 (0.4 dB) for a noise temperature of 29 K.

Adding the antenna noise and receiver noise gives us the system noise temperature, Ts. To find we add the noise contribution of the transmission line and bandpass filter which connect the antenna to the receiver's low-noise amplifier. Thus:

where Lr is the line loss between the antenna and receiver, expressed as a power ratio. The second term in Eq. (13-25) is the noise contribution from the transmission line, and the third term is the contribution from the receiver. The receiver noise temperature is the sum of these two terms. These noise temperatures are referred to the antenna terminal by dividing by Lr. Continuing with our cooled receiver example, assume the line loss is 03 dB, making Lr = 0.89. Then the noise contribution from the line loss is 36 K and the receiver noise is 33 K, both referred to the antenna terminal. Then Ts is Tam + 69 K.

Table 13-10 shows typical noise temperatures for satellite systems using uncooled receivers. When a narrow satellite-antenna beam looks at Earth, the uplink antenna noise temperature is the temperature of the Earth, about 290 K. In the future, improvements in design of low-noise amplifiers will reduce the receiver noise figures, especially at higher frequencies.

TABLE 13-10. Typical System Noise Temperatures In Satellite Communication Links In Clear Weather. The temperatures are referred to the antenna terminal. [See Eq. (13-25)1.

Noise Temperature

Frequency (GHz)

Downlink

Crosslink

Uplink

0 0

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