## Satellite Communications Receiving System Figure of Merit GT

figure of merit of a satellite communications receiving system, G/T, has been introduced into the technology to describe the capability of an earth station or a satellite to receive a signal. It is also a convenient tool in the link budget analysis.14 A link budget is used by the system engineer to size components of earth stations and satellites, such as RF output power, antenna gain and directivity, and receiver front-end characteristics.

G/T can be written as a mathematical identity:

where G is the net antenna gain up to an arbitrary reference point or reference plane in the downlink receive chain (for an earth station). Conventionally, in commercial practice the reference plane is taken at the input of the low-noise amplifier (LNA). Thus G is simply the gross gain of the antenna minus all losses up to the LNA. These losses include feed loss, waveguide loss, bandpass filter loss, and, where applicable, directional coupler loss, waveguide switch insertion loss, radome loss, and transition losses.

Tsys is the effective noise temperature of the receiving system and

Tant or the antenna noise temperature includes all noise-generating components up to the reference plane. The reference plane is a dividing line between the antenna noise component and the actual receiver noise component (Trecvr). The antenna noise sources include sky noise (Tsky) plus the thermal noise generated by ohmic losses created by all devices inserted into the system such as waveguide, bandpass filter, and radome. Trecvr is the actual receiver noise temperature, which has equivalence to the receiver noise figure. A typical earth station receiving system is illustrated in Figure 9.20 for a 12-GHz downlink. Earth stations generally have minimum elevation angles. At 4 GHz the minimum

14We called this path analysis in LOS microwave. Frequency = 12 GHz Figure 9.20 Model for an earth station receiving system.

elevation angle is 5°; at 12 GHz, 10°. The elevation angle is that angle measured from the horizon (0°) to the antenna main beam when pointed at the satellite.

Take note that we are working with noise temperatures here. Noise temperature is another way of expressing thermal noise levels of a radio system subsystem or component. In Section 9.2 we used noise figure for this function. Noise figure can be related to noise temperature by the following formula:

where Te is the effective noise temperature measured in kelvins. Note that the kelvin temperature scale is based on absolute zero.

Example. If the noise figure of a device is 1.2 dB, what is its equivalent noise temperature?

1.2 dB = 10 log(1 + Te/290) 0.12 = log(1 + Te/290) 1.318 = (1 + Te/290) 0.318 = Te/290 Te = 0.318 X 290 Te = 92.22 K

Antenna noise (Tant) is calculated by the following formula:

where la is the numeric equivalent of the sum of the ohmic losses up to the reference plane and is calculated by

where La is the sum of the losses in decibels.

Sky noise varies directly with frequency and inversely with elevation angle. Some typical sky noise values are given in Table 9.5.

Example. An earth station operating at 12 GHz with a 10° elevation angle has a 47-dB gain and a 2.5-dB loss from the antenna feed to the input of the LNA. The sky noise is 25 K developing an antenna noise temperature of 240 K. The noise figure of the LNA is 1.5 dB. Calculate the G/T.

Convert the 1.5-dB LNA noise figure value to its equivalent noise temperature. Use formula (9.20). For this sample problem Te = Trecvr.

Now we can calculate the G/T. Derive the net antenna gain (up to the reference plane—at the input of the LNA).

Gnet = 47 - 2.5 = 44.5 dB G/T = 44.5 dB - 10 log Tsys = 44.5 - 10 log 359.6 = +18.94 dB/K or just + 18.94 dB/K.

For earth stations operating below 10 GHz, it is advisable to have a link margin of 4 dB to compensate for propagation anomalies and deterioration of components due to aging. Such a margin gives a comfortable safety factor, but every decibel above and beyond

 Frequency Elevation Angle Sky Noise (GHz) O (K) 4.0 5 28 4.0 10 16 7.5 5 33 7.5 10 18 11.7 10 23 11.7 15 18 20.0 10 118 20.0 15 100 20.0 20 80

what actually needed to close the link costs money. Here is where good system design judgment is required.

9.3.6.3 Typical Down-Link Power Budget. A link budget is a tabular method of calculating space communication system parameters. The approach is very similar to that used for LOS microwave links (see Section 9.2.3.4). We start with the EIRP of the satellite for the downlink or the EIRP of the earth station for the uplink. The bottom line is C/N0 and the link margin, all calculated with decibel notation. C/N0 is the carrier-to-noise ratio in 1 Hz of bandwidth at the input of the LNA. (Note: RSL or receive signal level and C are synonymous).

Expressed as an equation:

— = EIRP - FSLdB - (other losses) + G/Tm/K - k, (9.23)

where FSL is the free-space loss to the satellite for the frequency of interest and k is Boltzmann's constant expressed in dBW. Remember in Eq. (9.9) we used Boltzmann's constant, which gives the thermal noise level at the output of a "perfect" receiver operating at absolute zero in 1 Hz of bandwidth (or N0).15 Its value is -228.6 dBW/Hz. "Other losses" may include:

• Pointing losses, terminal and satellite (0.5 dB each)

• Off-contour loss (depends on satellite antenna characteristics)

• Gaseous absorption loss (varies with frequency, altitude, and elevation angle)

• Excess attenuation due to rainfall (for systems operating above 10 GHz)

The loss values in parentheses are conservative estimates and should be used only if no definitive information is available.

The off-contour loss refers to spacecraft antennas that provide a spot or zone beam with a footprint on a specific geographical coverage area. There are usually two contours, one for G/T (uplink) and the other for EIRP (downlink). Remember that these contours are looking from the satellite down to the earth's surface. Naturally, an off-contour loss would be invoked only for earth stations located outside of the contour line. This must be distinguished from satellite pointing loss, which is a loss value to take into account that satellite pointing is not perfect. The contour lines are drawn as if the satellite pointing were "perfect."

Gaseous absorption loss (or atmospheric absorption) varies with frequency, elevation angle, and altitude of the earth station. As one would expect, the higher the altitude, the less dense the air and thus the less loss. Gaseous absorption losses vary with frequency and inversely with elevation angle. Often, for systems operating below 10 GHz, such losses are neglected. Reference 3 suggests a 1-dB loss at 7.25 GHz for elevation angles under 10° and for 4 GHz, 0.5 dB below 8° elevation angle.

Example of a Link Budget. Assume the following: a 4-GHz downlink, 5° elevation angle, EIRP is +30 dBW; satellite range is 25,573 statute miles (sm), and the terminal G/T is +20.0 dB/K. Calculate the downlink C/N0.

15Remember that geostationary satellite range varies with elevation angle and is minimum at zenith.

First calculate the free-space loss. Use Eq. (9.4):

LdB = 96.6 + 20 log FGhz + 20 log Am = 96.6 + 20 log 4.0 + 20 log 25, 573 = 96.6 + 12.04 + 88.16 = 196.8 dB.

EIRP of satellite +30 dBW

Free-space loss -196.8 dB

Satellite pointing loss -0.5 dB Off-contour loss 0.0 dB Excess attenuation rainfall 0.0 dB

Gaseous absorption loss -0.5 dB

Polarization loss -0.5 dB

Terminal pointing loss -0.5 dB

Terminal GIT +20.0 dB/K

Sum -148.8 dBW Boltzmann's constant (dBW) -(-228.6 dBW)

### CIN0 79.8 dB

On repeatered satellite systems, sometimes called "bent-pipe satellite systems" (those that we are dealing with here), the link budget is carried out only as far as C|N0, as we did above. It is calculated for the uplink and for the downlink separately. We then calculate an equivalent C|N0 for the system (i.e., uplink and downlink combined). Use the following formula to carry out this calculation:

+2 -3

### Responses

• John
What is the figure of merit {gt} receiving earth station?
8 years ago
• Rosa McMahan
How to calculate the figure of merit of the earth station example?
7 years ago
• freddie
Why is g/t refernced to lna input?
6 years ago
• Katja
What is figure of merit satellite?
2 years ago
• aatifa
How to calculate downlink availability for earth station?
1 year ago
• Darcy Campbell
How to calculate satellite antenna receive G/T?
2 months ago