An Introductionto

Satellite Link Budget

Dr. ing. Marco Lisi(marco.lisi@ieee.org)

Space Challenges, Sofia, 2017

“(…) et homines dum docent discunt”

Lucius Annaeus Seneca (c. 4 BC – A.D. 65)Epistulae Morales ad Lucilium, Liber I, 7-8

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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

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What is a Budget?

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The Basic RF Link

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Antenna Directivity (1/2)

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Antenna Directivity (2/2)

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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) = 10𝑙𝑙𝑙𝑙𝑙𝑙10 (𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑝𝑝𝑟𝑟𝑑𝑑𝑑𝑑𝑟𝑟𝑑𝑑𝑝𝑝𝑑𝑑 𝑑𝑑𝑑𝑑 𝑝𝑝𝑑𝑑𝑝𝑝 𝑑𝑑𝑑𝑑𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑝𝑝𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑝𝑝𝑟𝑟𝑑𝑑𝑑𝑑𝑟𝑟𝑑𝑑𝑝𝑝𝑑𝑑 𝑑𝑑𝑑𝑑𝑝𝑝𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑟𝑟𝑖𝑖𝑖𝑖𝑑𝑑

)8

Directivity Formula

D = 𝟒𝟒𝝅𝝅 𝑨𝑨𝒆𝒆𝝀𝝀𝟐𝟐

where:

Ae = is the equivalent area of the antenna (in case of anaperture antenna like a reflector or a patch is thephysical area of the antenna multiplied by the radiationefficiency, η)

λ = the electromagnetic wave wavelength;

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Directivity ≠ Gain

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G = ηohmic D

in dB: G (dB) = D (dBi) - Lohmic (dB)

Power Flux Density

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Effective Isotropic Radiated Power

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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)

Received Power (1/2)

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PtGt watts PFD = EIRP/(4πR2)

Received Power (2/2)

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Ae = ηAr

Pr= PFD * Ae

Friis Transmission Equation

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Pr = PtGtGr𝝀𝝀

𝟒𝟒𝝅𝝅𝝅𝝅

𝟐𝟐

FSPL = Lp = 𝟒𝟒𝝅𝝅𝝅𝝅𝝀𝝀

𝟐𝟐

FSPL: Free Space Path Loss

Power Received = 𝑬𝑬𝑬𝑬𝝅𝝅𝑬𝑬 ∗𝝅𝝅𝒆𝒆𝑹𝑹𝒆𝒆𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹 𝑨𝑨𝑹𝑹𝑨𝑨𝒆𝒆𝑹𝑹𝑹𝑹𝑨𝑨 𝑮𝑮𝑨𝑨𝑹𝑹𝑹𝑹

𝑬𝑬𝑨𝑨𝑨𝑨𝑷𝑷 𝑳𝑳𝑳𝑳𝑳𝑳𝑳𝑳

GEO Satellite to Earth Slant Range

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Friis Equation in Decibels

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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

Iso-gain or Iso-EIRP Contours

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On the antenna footprint it is possible to trace the iso-gaincontours.In case of satellites for TV broadcasting, it is usually reportedthe EIRP (“Effective Isotropic Radiated Power”), in dBW, orthe corresponding needed diameter of the ground antenna.

What power levels are we speaking about?

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• With reference to the previous iso-EIRP contour, let usassume 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 60centimeters 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] = 10−12010 = 10−12 = 1 picoW

Additional Path Losses

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aLtot = Lp + La

La = attenuation in atmosphere (mostly rain)

Atmospheric Attenuation vs. Frequency

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Statistical Rainfall Maps (ITU)

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Satellite Communications Signal Path

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Now that I know Pr ?

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Throw it away!

Signal to Noise Ratio

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Signal to Noise Ratio

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Signal to Noise Ratio

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Shannon, Father of the Information Age

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Let us ask Shannon: why is Pr not enough?

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Shannon’s Theorem and Equation

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• 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 canachieve, but NOT HOW you can achieve it!

Shannon’s Limit

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C/B = log2 (1+ S/N) = log2 𝟏𝟏 + 𝑬𝑬𝒃𝒃𝑵𝑵𝟎𝟎

𝑪𝑪𝑩𝑩

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]

𝑬𝑬𝒃𝒃𝑵𝑵𝟎𝟎

= 𝑩𝑩𝑪𝑪𝟐𝟐 �𝑪𝑪 𝑩𝑩 − 𝟏𝟏 = 𝟐𝟐

𝜼𝜼−𝟏𝟏𝜼𝜼

Per η → 0 (B → ∞) Eb/N0 = - 1.59 dB

Satellite Communications Signal Path

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Thermal (Johnson) Noise

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• 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].

C/N (S/N) at Receiver Input

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NOTA BENE: “C” from now on means carrier power level, NOT the channel data rate in Shannon’s equation

C/N (S/N) at Receiver Input

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Receiving System C/N

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Antenna Noise Temperature, Ta

• The temperature of a hypothetical resistor that wouldgenerate the same output noise power per unit bandwidthas 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.

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Sources of Antenna Noise

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Noise Factor and Noise Figure (1/2)

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Noise Factor and Noise Figure (2/2)

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• 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)

Noise Factor an Noise Temperature

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• 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) + …

Receiving System C/N

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Quick and Dirty G/T Calculation

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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.

Receiving System C/N

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Example of G/T Calculation

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Digital Modulations Techniques

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BER vs Eb/N0 for Digital Modulations

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Summary of Link Equations

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Link Margin (dB)

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Satellite (Down)Link Budget Procedure1. 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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