The RF Link

1. SATELLITE
COMMUNICATION
LECTURE-6
THE RF LINK

2. ISOTROPIC TRANSMITTER
• Consider a radio wave propagating in free space from a point source P of
power 𝑃𝑡watts. The wave is isotropic in space, i.e., spherically radiating from
the point source P.
• The power flux density (or power density), over the surface of a sphere of
radius 𝑟𝑎 and 𝑟𝑏 from the point P, is given by-
𝑃𝐷𝐹𝐴 =
𝑃𝑡
4𝜋𝑟 𝑎
2
𝑃𝐷𝐹𝐵 =
𝑃𝑡
4𝜋𝑟 𝑏
2
• Ratio of power densities is given by-
𝑃𝐷𝐹 𝐴
𝑃𝐷𝐹 𝐵
=
𝑟 𝑏
2
𝑟 𝑎
2
• This is known as inverse square law of radiation: the power density of a radio
wave propagating from a source is inversely proportional to the square of the
distance from the source.

3. BASIC RF LINK
Now, generally the link is not isotropic and it has a gain 𝐺𝑡. So,
power flux density at any point P, at a distance R is given by-
𝑃𝐷𝐹𝑅 =
𝑃𝑡 𝐺𝑡
4𝜋𝑅2 (W/𝑚2)
Expressed in dB as-
𝑃𝐷𝐹𝑅= 10log (𝑃𝑡 𝐺𝑡) – 20 log R – 10 log (4𝜋)
= 10log (𝑃𝑡 𝐺𝑡) – 20 log R – 11
Effective Isotropic Radiated Power (EIRP)

4. BASIC RF LINK (CONTD.)
• Receiver power with effective aperture 𝐴 𝑒 is
𝑃𝑟= (𝑃𝐷𝐹𝑅) 𝐴 𝑒=
𝑃𝑡 𝐺𝑡
4𝜋𝑅2 𝐴 𝑒 (watts)
• Now, Receiver gain 𝐺𝑟 is related to effective aperture 𝐴 𝑒
by-
𝐺𝑟=
4𝜋
𝜆2 𝐴 𝑒
where, 𝐴 𝑒=
𝐺 𝑟 𝜆2
4𝜋
Thus, Receiver power 𝑃𝑟 can be written as-
𝑃𝑟 =
𝑃𝑡 𝐺𝑡
4𝜋𝑅2
𝐺 𝑟 𝜆2
4𝜋
𝑃𝑟 = (𝑃𝑡 𝐺𝑡) 𝐺𝑟
1
4𝜋𝑅 𝜆 2 (watts)
(EIRP) Path loss

5. BASIC LINK EQUATION
Receiver power = (EIRP) (𝐺𝑟)(Path Loss)
When expressed in dB, we have-
𝑃𝑟 (dB) =(EIRP) + (𝐺𝑟) - (Path Loss)
This result gives the basic link equation, sometimes referred to as the Link Power Budget Equation

6. SYSTEM NOISE
• Undesired power or signals (noise) can be introduced into the satellite link at all locations along the signal
path, from the transmitter through final signal detection and demodulation.
• The major contributor of noise at radio frequencies is thermal noise, caused by the thermal
motion of electrons in the devices of the receiver (both the active and passive devices). The noise
introduced by each device in the system is quantified by the introduction of an equivalent noise
temperature.
• The noise power, is given by –
𝑛 𝑁=𝑘𝑇𝐵 watts
where, 𝑘 = Boltzmann’s constant = 1.39 × 10−23
Joules/Kelvin = -198 dBm/K/Hz = -228.6 dBw/K/Hz
T = equivalent noise temperature of the noise source, K.
B = Noise Bandwidth, in Hz.
• Since, thermal noise is independent of the frequency of operation, it is often useful to express
the noise power as a noise power density (or noise power spectral density), 𝑁𝑜, of the form
𝑁𝑜=
𝑛 𝑁
𝐵
=
𝑘𝑇𝐵
𝐵
= 𝑘𝑇 watts/Hz

7. LINK PERFORMANCE PARAMETERS
CARRIER TO NOISE RATIO
• The ratio of average RF carrier power, c, to the noise power, n, in the same bandwidth, is defined as the
carrier-to-noise ratio (
𝑪
𝑵
).
• Let us define the losses on the link by two components, the free space path loss
𝑙 𝑓𝑠 =
4𝜋𝑅
𝜆
2
and all other losses, 𝑙 𝑜, defined as
𝑙 𝑜= (𝑜𝑡ℎ𝑒𝑟 𝑙𝑜𝑠𝑠𝑒𝑠)
where the other losses could be from the free space path itself, such as rain attenuation, atmospheric
attenuation, etc., or from hardware elements such as antenna feeds, line losses, etc.

8. CARRIER TO NOISE RATIO (CONTD.)
• The power at the receiver antenna terminals, 𝑃𝑟, is given by-
𝑃𝑟 = 𝑃𝑡 𝐺𝑡 𝐺𝑟
1
𝑙 𝑓𝑠 𝑙 𝑜
• The noise power at the receiver terminal, is given by –
𝑛 𝑟=𝑘𝑇𝐵 watts
• The carrier-to-noise ratio (
𝑪
𝑵
) at the receiver terminals is then-
𝑪
𝑵
=
𝑃𝑟
𝑛 𝑟
=
𝑃𝑡 𝐺𝑡 𝐺 𝑟
1
𝑙 𝑓𝑠 𝑙 𝑜
𝑘𝑇𝐵
=
(𝐸𝐼𝑅𝑃)
𝑘𝐵
𝐺 𝑟
𝑇
1
𝑙 𝑓𝑠 𝑙 𝑜
when expressed in dB,
𝑪
𝑵
= (𝐸𝐼𝑅𝑃) +
𝐺
𝑇
−(𝐿 𝑓𝑠 + 𝑜𝑡ℎ𝑒𝑟 𝑙𝑜𝑠𝑠𝑒𝑠 − 228.6 − 𝐵 𝑁
where the EIRP is in dBw, the bandwidth 𝐵 𝑁 is in dBHz, and k = −228.6 dBw/K/Hz
• The (
𝑪
𝑵
) is the single most important parameter that defines the performance of a satellite communications
link. The larger the (
𝑪
𝑵
) , the better the link will perform.