This document provides an introduction and overview of satellite link budgets. It begins with definitions of key terms used in link budgets such as antenna directivity, gain, effective isotropic radiated power (EIRP), free space path loss, noise figure, and signal-to-noise ratio (SNR). It then explains the Friis transmission equation and how it is used to calculate the received power in a satellite link. Additional factors that impact the link budget are also covered such as atmospheric losses, antenna noise temperature, and modulation schemes. The document concludes by outlining the procedure for calculating an example satellite downlink budget.

1. An Introduction
to
Satellite Link Budget
Dr. ing. Marco Lisi
(marco.lisi@ieee.org)
Space Challenges, Sofia, 2017

2. “(…) et homines dum docent discunt”
Lucius Annaeus Seneca (c. 4 BC – A.D. 65)
Epistulae Morales ad Lucilium, Liber I, 7-8
2

3. Outline
• What is a “budget”?
• The RF link
• Antenna directivity and gain
• Power Flux Density
• EIRP
• Free Space Path Loss and Friis equation
• Slant range
• Atmospheric attenuation
• Signal to noise ratio
• Shannon’s theorem
• Antenna noise temperature
• Noise Factor, Noise Figure, G/T
• Eb/N0, BER
• Link budget procedure
3

4. What is a Budget?
4

5. The Basic RF Link
5

6. Antenna Directivity (1/2)
6

7. Antenna Directivity (2/2)
7

8. Definition of Directivity
• The directive gain of an antenna measures the power
density the antenna radiates in one direction, versus the
power density radiated by an ideal isotropic radiator (which
emits uniformly in all directions) radiating the same total
power;
• The directive gain, D(θ, φ), depends on the direction;
• The directivity D of an antenna is the maximum value of its
directive gain;
• The directivity is usually expressed in dBi, which is ten time
the logarithm (base 10) of the ratio defined before:
D (dBi) = 10𝑙𝑙𝑙𝑙 𝑙𝑙10 (
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑖𝑖𝑖𝑖 𝑜𝑜𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖
)
8

9. Directivity Formula
D =
𝟒𝟒𝝅𝝅 𝑨𝑨𝒆𝒆
𝝀𝝀𝟐𝟐
where:
Ae = is the equivalent area of the antenna (in case of an
aperture antenna like a reflector or a patch is the
physical area of the antenna multiplied by the radiation
efficiency, η)
λ = the electromagnetic wave wavelength;
9

10. Directivity ≠ Gain
10
G = ηohmic D
in dB: G (dB) = D (dBi) - Lohmic (dB)

11. Power Flux Density
11

12. Effective Isotropic Radiated Power
12
EIRP (Effective Isotropic Radiated Power):
The amount of power that would have to be
applied to an isotropic antenna to equal the
amount of power that is being transmitted in a
particular direction by the actual antenna
EIRP = PtGt (watts)

13. Received Power (1/2)
13
PtGt watts PFD = EIRP/(4πR2)

14. Received Power (2/2)
14
Ae = ηAr
Pr= PFD * Ae

15. Friis Transmission Equation
15
Pr = PtGtGr
𝝀𝝀
𝟒𝟒𝝅𝝅𝝅𝝅
𝟐𝟐
FSPL = Lp =
𝟒𝟒𝝅𝝅𝝅𝝅
𝝀𝝀
𝟐𝟐
FSPL: Free Space Path Loss
Power Received =
𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 ∗𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹 𝑹𝑹𝑹𝑹 𝑹𝑹 𝑹𝑹 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑮𝑮𝑮𝑮𝑮𝑮𝑮𝑮
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳

16. GEO Satellite to Earth Slant Range
16

17. Friis Equation in Decibels
17
Pr = EIRP + Gr – Lp dBW
Each term must be in decibel notation:
• EIRP = 10 log (PtGt) dBW
• Gr = 10 log (4πAe/λ2) dB
• Lp = 20 log (4πR/λ) dB

18. Iso-gain or Iso-EIRP Contours
18
On the antenna footprint it is possible to trace the iso-gain
contours.
In case of satellites for TV broadcasting, it is usually reported
the EIRP (“Effective Isotropic Radiated Power”), in dBW, or
the corresponding needed diameter of the ground antenna.

19. What power levels are we speaking about?
19
• With reference to the previous iso-EIRP contour, let us
assume the satellite is transmitting at Ku band (12 GHz)
with an EIRP of 50 dBW;
• A user in Sofia is receiving with an antenna of 60
centimeters in diameter (efficiency 60%), so GR = 35 dB;
• Assuming a slant range of 36,000 kilometers (optimistic),
the Free Space Path Loss is equal to -205 dB;
PR [dBW] = EIRP [dBW] – FSPL [dB] + GR [dB] =
= 50 -205 +35 = - 120 dBW
PR [W] = 10−
120
10 = 10−12
= 1 picoW

20. Additional Path Losses
20
aLtot = Lp + La
La = attenuation in atmosphere (mostly rain)

21. Atmospheric Attenuation vs. Frequency
21

22. Statistical Rainfall Maps (ITU)
22

23. Satellite Communications Signal Path
23

24. Now that I know Pr ?
24
Throw it away!

25. Signal to Noise Ratio
25

26. Signal to Noise Ratio
26

27. Signal to Noise Ratio
27

28. Shannon, Father of the Information Age
28

29. Let us ask Shannon: why is Pr not enough?
29

30. Shannon’s Theorem and Equation
30
• C = maximum possible data rate that can be transmitted
without errors in a given communication channel (bits
per second, bps);
• B = effective bandwidth of the channel (Hz);
• S = total signal power (W);
• N = total noise power (W).
Nota Bene: Shannon’s theorem tells you the best you can
achieve, but NOT HOW you can achieve it!

31. Shannon’s Limit
31
C/B = log2 (1+ S/N) = log2 𝟏𝟏 +
𝑬𝑬𝒃𝒃
𝑵𝑵𝟎𝟎
𝑪𝑪
𝑩𝑩
where (assuming R, transmission rate, bps equal to C,
channel capacity, bps):
Eb = S/R = S/C [Joule per bit];
N0 = noise power density [W/Hz];
C/B = η = spectral efficiency [bits/seconds/Hz]
𝑬𝑬𝒃𝒃
𝑵𝑵𝟎𝟎
=
𝑩𝑩
𝑪𝑪
𝟐𝟐 �𝑪𝑪
𝑩𝑩 − 𝟏𝟏 =
𝟐𝟐𝜼𝜼−𝟏𝟏
𝜼𝜼
Per η → 0 (B → ∞) Eb/N0 = - 1.59 dB

32. Satellite Communications Signal Path
32

33. Thermal (Johnson) Noise
33
• All single port components (e.g. a resistor) generate an
electric noise, with an associated delivered power equal
to:
Pn = kTB
where:
Pn : noise power in watts [W];
k : Boltzmann’s constant = 1.379*10-23 [J/K] ([W/(Hz*K)]);
T : physical temperature of the component in Kelvin;
B : measurement bandwidth, [Hz].

34. C/N (S/N) at Receiver Input
34
NOTA BENE: “C” from now on means carrier power
level, NOT the channel data rate in Shannon’s
equation

35. C/N (S/N) at Receiver Input
35

36. Receiving System C/N
36

37. Antenna Noise Temperature, Ta
• The temperature of a hypothetical resistor that would
generate the same output noise power per unit bandwidth
as that at the antenna output at a specified frequency;
• The antenna noise temperature depends on antenna
coupling to all noise sources in its environment as well as
on noise generated within the antenna.
37

38. Sources of Antenna Noise
38

39. Noise Factor and Noise Figure (1/2)
39

40. Noise Factor and Noise Figure (2/2)
40
• Real electronic devices in a signal chain provide gain
(or attenuation) which act on both the input signal and
noise
 These devices add their own additional noise, resulting in
an overall degradation of S/N
• Noise Factor: Quantifies the S/N degradation from the
input to the output of a system
F = (S/N)i / (S/N)o
• Noise Figure = 10 log (F)

41. Noise Factor an Noise Temperature
41
• So = GA Si
• No = GA Ni + NA
• By convention, Ni = noise equivalent to 290 K
(Ni = N290 = kB 290 K)
F = 1 + NA/(GA N290) = 1 + Te/To
• For cascaded devices:
F = FA + (FB-1)/GA + (FC-1)/(GAGB) + …
• In terms of of system noise temperature degradation
using cascaded components:
Tsys = TA + TB/GA + TC/(GAGB) + …

42. Receiving System C/N
42

43. Quick and Dirty G/T Calculation
43
1. Consider antenna gain G at antenna terminals
(neglecting ohmic losses);
2. Consider LNA noise figure (neglect following
elements in the receiver chain, if LNA gain is high
enough);
3. Estimate all ohmic losses between antenna terminals
and LNA input (feed line, band-pass filter, etc.);
4. Add losses in dB to LNA noise figure in dB;
5. Calculate the equivalent noise temperature at antenna
interface from previous value;
6. Get G/Ts in dB/K.

44. Receiving System C/N
44

45. Example of G/T Calculation
45

46. Digital Modulations Techniques
46

47. BER vs Eb/N0 for Digital Modulations
47

48. Summary of Link Equations
48

49. Link Margin (dB)
49

50. Satellite (Down)Link Budget Procedure
1. Select carrier frequency;
2. Estimate satellite transmit power (including losses to antenna);
3. Calculate transmit antenna gain towards ground station;
4. Calculate space loss, determined by satellite orbit and ground
station location;
5. Estimate propagation absorption loss (rain attenuation) for the
desired link availability;
6. Estimate ground station antenna gain and noise temperature;
7. Estimate cumulative noise figure and equivalent noise
temperature of the receiver chain at antenna interface;
8. Calculate ground station G/TS;
9. Calculate Eb/N0;
10.Look up Eb/N0 required to achieve desired BER for the selected
modulation and coding technique (add 1-2 dBs for
implementation losses);
11.Calculate link margin;
12.Readjust design parameters to reach wanted positive margin.50

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