# Link budget calculations for SATCOM – Downlink

For discussions regarding SATCOM uplink, read here: Link budget calculations for SATCOM – Uplink

This post explains the mathematical equation used to calculate the SNR of SATCOM downlink, or in other words, SNR of satellite signal as received at ground terminal. The assumption is that reader is familiar with SATCOM link parameters including terminal G/T, Terminal Noise Temperature, Free Space Path Loss (FSPL), and Antenna Gain etc. And if you are not comfortable with these parameters, it is highly recommended to go through the details of SATCOM link parameters and their mathematical modelling, by reading these blogs:

- Free-Space Path Loss (FSPL) in Wireless Links
- Antenna Gain of ESA Terminal (Ground Station) in SATCOM
- Noise Temperature and G/T of Ground Terminal (Receiving System) in SATCOM

To start with, note that we are interested in Signal-to-Noise ratio at the input of the receiving system (ground terminal) and can be expressed as:

(SNR-per-Hz)_{ Down} = (C/N_{o})_{ Down} = (Carrier Power in 1-Hz BW)_{dBm} – (Noise Power in 1-Hz BW)_{dBm}

Where,

- Carrier Power is the Satellite signal power as received by the antenna of ground terminal
- Noise power is the input-referred noise power seen by ground terminal.

**Carrier Power in 1-Hz BW**

As mentioned earlier, Carrier Power is the Satellite signal power as received by the antenna of ground terminal. It can be expressed as follows:

** **Carrier Power in 1-Hz BW, dBm = (Satellite TX EIRP)_{ dBm} – 10*log10 (Satellite TX BW) – (FSPL)_{dB} – (Atmospheric Loss)_{ dB} + (Terminal Antenna Gain)_{ dBi}

where,

- (Satellite TX EIRP)
_{ dBm}= Satellite transponder Effective isotropic radiated Power in dBm. For details, read here: - Satellite TX BW= Satellite transponder Bandwidth in Hz
- (FSPL)
_{dB}= Free-space path loss in dB. It can be expressed as follows.

FSPL, dB = 20*log10(d,km) + 20*log10(f,GHz) + 92.45

For details, read here: Free-Space Path Loss (FSPL) in Wireless Links - (Terminal Antenna Gain)
_{ dBi}= Antenna Gain of Ground terminal in dBi. It can be expressed as follows:

G(dBi)= Peak Gain (dBi) – Cosine roll-off * 10 * log10(cos theta)

For details, read here: Antenna Gain of ESA Terminal (Ground Station) in SATCOM

**Noise Power in 1-Hz BW**

As mentioned earlier, Noise power is the input-referred noise power seen by ground terminal. It can be expressed as follows:

Noise Power in 1 Hz BW, dBm = 10*log10(k.T) + 30

- k= Boltzman’s constant = 1.381 x 10
^{-23 }J/K - T= Input-referred Noise temperature (in Kelvins) of the ground receiving systems/terminal, which includes the antenna itself and the RF chain, ending at the output of the LNB (low noise block downconverter), assuming there is sufficient gain to make any noise contribution after the LNB negligible. For details, read here: Noise Temperature and G/T of Ground Terminal (Receiving System) in SATCOM
- 30 is being added to 10*log10(k.T) for converting it from dBW to dBm.

**Calculating the SNR-per-Hz of Downlink**

(C/N_{o})_{ Down} = (Satellite TX EIRP)_{ dBm} – 10*log10 (Satellite TX BW) – (FSPL)_{dB} – (Atmospheric Loss)_{ dB} + (Terminal Antenna Gain)_{ dBi} – 10*log10(k.T) – 30

We can rewrite above equation as:

(C/N_{o})_{ Down} = (Satellite TX EIRP)_{ dBm} – 10*log10 (Satellite TX BW) – (FSPL)_{dB} – (Atmospheric Loss)_{ dB} + (Terminal Antenna Gain)_{ dBi} – [10*log10(k) + 10*log10(T) + 30 ]

Subtracting the transponder bandwidth from the full satellite EIRP gives the satellite transmit power in a 1 Hz bandwidth. Subtracting the FSPL and atmospheric attenuation, and then adding the Receive Antenna Gain provides the power at the input of receiving system (also in a 1 Hz BW).

[10*log10(k) + 10*log10(T) + 30] provides the input noise power (in dBm) for the terminal, where T is the noise temperature of the receiving system including antenna , RF chain and LNB – it accounts for the antenna noise as well as the input-referred noise contribution by the rest of the receiver . Finally, subtracting input noise floor (per Hz) of the receiver from the input carrier power (per Hz) produces the overall input signal-to-noise ratio in a 1 Hz BW.

Next, we can lump terminal Gain and noise-temperature parameters into a single entity called as terminal G/T. Finally, the downlink SNR equation takes the form as follows:

**(C/N _{o})_{ Down}** = (Satellite TX EIRP)

_{ dBm}– 10*log10 (Satellite TX BW) – (FSPL)

_{dB}– (Atmospheric Loss)

_{ dB}+ (Terminal G/T)

_{ dB/K}– 10*log10(k) – 30

- Where, (Terminal G/T)
_{ dB/K}= (Terminal Antenna Gain)_{ dBi }– 10*log10(T)

It can be observed that increasing terminal G/T improves the Downlink SNR.

*Learn more about this topic by taking the complete course ‘**RF System Design of Receivers, Transmitters & Transceivers – RAHRF409’**. Watch the course videos for more detailed understanding. Also checkout other courses on RF system and IC design on **https://rahsoft.com/courses/**. **Rahsoft also provides a certificate on Radio Frequency. All the courses offer step by step approach.*

*Learn more about this topic by taking the complete course ‘*

*RF System Design of Receivers, Transmitters & Transceivers – RAHRF409’*

*. Watch the course videos for more detailed understanding. Also checkout other courses on RF system and IC design on*

*https://rahsoft.com/courses/*

*.*

*Rahsoft also provides a certificate on Radio Frequency. All the courses offer step by step approach.*