## Main telecom equation

The power of the signal from the probe at the output of the receiving antenna Pr is determined by

PtGt Sr

where Pt is the RF power of the probe transmitter, Gt the gain of the transmitting antenna, Sr the effective area of the receiving antenna, R the distance from probe to receiving station and •1 the losses. Two other forms of this equation are

PtGtGr^2 PtStSr nnn\

Although these equations are just different forms they show some features important for the probe link design.

First, given the transmitting-antenna gain and the area of the receiving antenna, the signal power does not depend on wavelength, i.e. on the frequency band. That is why the signal power in the DTE or relay link with omnidirectional or low-gain antennas on the probe and a high-gain antenna on the Earth station or orbiter does not depend on the frequency band.

Second, given the gains of the transmitting and receiving antennas, the received signal power is proportional to the square of the wavelength. That is why in the relay link with omnidirectional or low-gain antennas on both ends (probe and orbiter), UHF and even VHF bands have been used on all entry probes.

Third, given the areas of the transmitting and receiving antennas, the received signal power is inversely proportional to the square of the wavelength. That is why in the DTE link with high-gain antennas on both ends (probe and Earth station) shorter wavelengths from L-band to X-band have been used on all entry probes.

Practical application of these statements depends also on other factors: availability and efficiency of the on-board transmitters, the frequency bands of the ground stations, the wavelength dependence of absorption in the planetary atmosphere, etc.

A number of factors contribute to the signal losses •. We will list some of them; detailed description would be beyond the scope of this book.

Atmospheric losses include atmospheric absorption and atmospheric refraction losses in the atmospheres of Earth and of the destination planet. Refraction losses do not depend on wavelength and usually are a fraction of a dB for local elevation angles of the line-of-sight (both for the Earth station and for the probe on the planet) greater than 10-20°. Absorption losses could be wavelength dependent and usually increase with the link frequency. On Earth the most important source of absorption is precipitation. In the deep atmospheres of Venus and Jupiter pressure-induced absorption of carbon dioxide (Venus) and absorption of ammonia (Jupiter) are the greatest contributors at short wavelengths. For example, absorption of the X-band signal from a probe on the Venus surface is dB.

Antenna pointing losses, being a fraction of a dB for the Earth-based antennas, could be significant for the probe and relay orbiter antennas. Use of omnidirectional antennas is a cure that sacrifices the overall link budget.

Polarization losses are of order 0.2-0.3 dB for antennas with matched polarizations (linear or circular with appropriate orientation and rotation). They might increase to 3 dB if the received signal has linear polarization while the receiving antenna has circular, or vice versa (it usually happens at the edges of the antenna pattern of low-gain antennas). In unmatched circular polarization (one left-handed - another right-handed) the polarization losses may exceed 10 dB.

Hardware losses on the probe, in cables, diplexer, filters, etc., are usually of the order of fractions of a dB. The receiving system contributes to other losses that will be described later.

Actually the main parameter of the communication link is the ratio of the received signal power to the spectral density of noise at the output of the linear part of the receiver. Usually the output noise has a flat spectrum in signal bandwidth ('white' noise). The spectral density of the noise PN0 can be calculated as where k is the Boltzmann constant (1.38 X 10-23 W KT1 Hz-1), Teff the effective temperature of the system and N the noise-factor. The noise power is where 1F is the appropriate bandwidth.

The effective temperature includes several components: noise radiation received from the ionospheres, tropospheres and surfaces of the Earth and the planet; the radiation of the galaxy; the Sun, and the noise of the system components - receiver (mostly noise from the input low-noise amplifier), waveguides, cables, etc.

Radiation received from atmospheres, the galaxy and the surface of the Earth depends strongly on the wavelength, the direction of the antenna pointing (both elevation and azimuth), local weather and other factors. Galactic noise increases with wavelength while noise from the troposphere decreases. This combined noise has a minimum in the S-band - one of the reasons why the S-band was selected for deep-space communications in the early stages.

A planet's radiation does not contribute significantly to the system noise if the receiving antenna beamwidth is much larger than the angular size of the planet. In the opposite case, if the receiving antenna beamwidth is less than the angular size of the planet (which could be the case for orbiter relay antennas or Earth antennas in the Ka-band) the radiation of the planet may become a major contributor to the system temperature, which may reach 400-600 K for Venus in 1-8 GHz and 10000 K for Jupiter in the UHF. In general, if the solid angle of a planet as seen from the receiving station is 0p and the solid angle of the antenna beam is 0a, the contribution of the planet's radiation to the system noise temperature is

where Tp is the equivalent temperature of the planet's radiation.

The ratio of signal power to nose spectral density has dimensions of energy. Finally,

p no 4nR2kTeff or

Ps PtGG

Pno (4^,r)2teff where •2 = additional losses in the receiving system which include losses in high-frequency components (waveguides, cables, filters, diplexers) and signal processing losses (carrier, subcarrier and symbol synchronization losses, etc.). In modern ground stations these losses are usually of order 1-3 dB.

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