1

Satellite Link Design

Joe MontanaIT 488 - Fall 2003

2

Agenda

• Basic Transmission Theory

• Review of Decibel

• Link Budget

• System Noise Power (Part 1)

3

Basic Transmission Theory

4

Link Budget parametersTransmitter power at the antennaAntenna gain compared to isotropic radiatorEIRPFlux density at receiverFree space path lossSystem noise temperatureFigure of merit for receiving systemCarrier to thermal noise ratioCarrier to noise density ratioCarrier to noise ratio

5

Isotropic Radiator

Consider an Isotropic Source (punctual radiator) radiating Pt Watts uniformly into free space.At distance R, the area of the spherical shell with center at the source is 4R2

Flux density at distance R is given by Eq. 4.1

24 R

PF t

W/m2

6

Isotropic Radiator 2

24 R

PF t

W/m2

Pt Watts

Distance R

Isotropic Source

Power Flux Density:Surface Area of

sphere = 4R2

encloses Pt.

7

Antenna GainWe need directive antennas to get power to go in wanted direction.Define Gain of antenna as increase in power in a given direction compared to isotropic antenna.

4/

)()(

0P

PG (Eqn 4.2)

• P() is variation of power with angle.

• G() is gain at the direction .

• P0 is total power transmitted.

• sphere = 4solid radians

8

Antenna Gain 2

Antenna has gain in every direction! Term gain may be confusing sometimes.Usually “Gain” denotes the maximum gain of the antenna.The direction of maximum gain is called “boresight”.

9

Antenna Gain 3

Gain is a ratio:It is usually expressed in Decibels (dB)G [dB] = 10 log10 (G ratio)

The world’s most misused unit ??(we will see more on dBs later)

10

EIRP - 1

An isotropic radiator is an antenna which radiates in all directions equallyAntenna gain is relative to this standardAntennas are fundamentally passive

No additional power is generatedGain is realized by focusing powerSimilar to the difference between a lantern and a flashlight

Effective Isotropic Radiated Power (EIRP) is the amount of power the transmitter would have to produce if it was radiating to all directions equallyNote that EIRP may vary as a function of direction because of changes in the antenna gain vs. angle

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The output power of a transmitter HPA is:Pout watts

Some power is lost before the antenna:Pt =Pout /Lt watts reaches the antenna

Pt = Power into antennaThe antenna has a gain of:

Gt relative to an isotropic radiatorThis gives an effective isotropic radiated power of:

EIRP = Pt Gt watts relative to a 1 wattisotropic radiator

EIRP - 2

HPA

Pout

Lt

Pt

EIRP

12

Power Flux Density - 1

We now want to find the power density at the receiverWe know that power is conserved in a lossless mediumThe power radiated from a transmitter must pass through a spherical shell on the surface of which is the receiverThe area of this spherical shell is 4R2

Therefore spherical spreading loss is 1/4R2

13

Power Flux Density - 2Power flux density (p.f.d.) is a measure of the power per unit areaThis is a regulated parameter of the system

CCIR regulations limit the p.f.d. of any satellite systemCCIR regulations are enforced by signatory nationsAllowable p.f.d. varies w.r.t. elevation angleAllows control of interferenceIncreasing importance with proliferation of LEO systems

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Received Power

The power available to a receive antenna of area Ar m2 we get:

(Eqs. 4.4, 4.6)24

x R

AGPAFP rtt

rr

222 W/m

44 R

GP

R

EIRPF tt

(Eqn. 4.3)

• We can rewrite the power flux density now considering the transmit antenna gain:

15

Effective ApertureReal antennas have effective flux collecting areas which are LESS than the physical aperture area.

Define Effective Aperture Area Ae: x e phyAA (Eqn. 4.5)

Where Aphy is actual (physical) aperture area.

= aperture efficiency Very good: 75%Typical: 55%

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Effective Aperture - 2

2

4

eA

Gain

• Antennas have (maximum) gain G related to the effective aperture area as follows:

Where: Ae is effective aperture area.

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Aperture Antennas

Typical values of :-Reflectors: 50-60%-Horns: 65-80 %

2D

Gain

4

22 D

rAphy

22

44 phyeAA

Gain

• Aperture antennas (horns and reflectors) have a physical collecting area that can be easily calculated from their dimensions:

• Therefore, using Eqn. 4.7 and Eqn. 4.5 we can obtain the formula for aperture antenna gain as:

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Aperture Antenna Types

HORNEfficient, Low Gain, Wide Beam

REFLECTORHigh Gain, Narrow Beam, May

have to be deployed in spaceLet’s concentrate on the REFLECTORS in the next slides

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Reflector Types

Symmetrical, Front-Fed Offset, Front-Fed

Offset-Fed, Cassegranian Offset-Fed, Gregorian

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Reflector Antenna -1

DdB

753 degrees (Eqn. 3.2)

• The approximation above, together with the definition of gain (previous page) allow a gain approximation (for reflectors only):

• A rule of thumb to calculate a reflector antenna beamwidth in a given plane as a function of the antenna dimension in that plane is given by:

EdBHdBdB

Gain33

22

3

7575

EdBHdBdB

Gain33

23

000,30000,30

• Assuming for instance a typical aperture efficiency of 0.55 gives:

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Antenna BeamwidthPeak (i.e. maximum) GAIN

Angle between the 3 dB down points is the beamwidth of the antenna

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Back to Received Power…The power available to a receive antenna of effective area Ar = Ae m2 is:

(Eqn. 4.6)24

x R

AGPAFP ett

rr

Where Ar = receive antenna effective aperture area = Ae

2

4

e

r

AG

• Inverting the equation given for gain (Eq. 4.7) gives:

Inverting…

4

2r

e

GA

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Back to Received Power…

• Substituting in Eqn. 4.6 gives:

2

4

RGGPP rttr

(Eqn. 4.8)

Friis Transmission Formula

• The inverse of the term at the right referred to as “Path Loss”, also known as “Free Space Loss” (Lp):

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R

Lp

Therefore…

p

rttr L

GGPP

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More complete formulation

rotherpolrataap

rttr LLLLLLL

GGPP

Demonstrated formula assumes idealized case.Free Space Loss (Lp) represents spherical spreading only.Other effects need to be accounted for in the transmission equation:

La = Losses due to attenuation in atmosphere

Lta = Losses associated with transmitting antenna

Lra = Losses associates with receiving antenna

Lpol = Losses due to polarization mismatch

Lother = (any other known loss - as much detail as available)Lr = additional Losses at receiver (after receiving antenna)

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Transmission Formula

rotherpolrataapt

rtout

rotherpolrataap

r

rotherpolrataap

rttr

LLLLLLLL

GGP

LLLLLLL

GEIRP

LLLLLLL

GGPP

x

Some intermediate variables were also defined before:Pt =Pout /Lt EIRP = Pt Gt Where:

Pt = Power into antennaLt = Loss between power source and antennaEIRP = effective isotropic radiated power

•Therefore, there are many ways the formula could be rewritten. The user has to pick the one most suitable to each need.

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Link Power Budget

Transmission:HPA PowerTransmission Losses (cables & connectors)Antenna Gain

EIRPTx

Antenna Pointing LossFree Space LossAtmospheric Loss (gaseous, clouds, rain)Rx Antenna Pointing Loss

Rx

Reception:Antenna gainReception Losses (cables & connectors)Noise Temperature Contribution

Pr

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Review of Decibel

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Why dB?

There is a large dynamic range of parameters in satellite communications

A typical satellite antenna has a gain of >500Received power flux is about one part in 100,000,000,000,000,000,000of the transmitted power

Wouldn’t it be nice to have a better way to write these large numbers?dB also lets many calculations be addition or subtraction!

That’s a lot of zeros!

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What is a dB?

Decibel (dB) is the unit for 10 times the base 10 logarithmic ratio of two powersFor instance: gain is defined as Pout/Pin (where Pout is usually greater than Pin)

in dB:

Similarly loss is:

dB log10

in

out

P

PG

dB log10

out

in

P

PL

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A Dangerous Calculation in dB!dB ratios must NEVER be calculated as 20 times the base 10 logarithmic ratio of voltagesUnless of course its more convenient, in which case

you must be very, very careful. Here’s why:

out

in

in

out

out

in

in

out

in

in

out

out

in

out

out

outout

in

inin

R

R

V

V

R

R

V

VG

RV

RV

P

PG

R

VP

R

VP

log10log20log10log10

log10log10

2

2

2

2

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This term is usually forgotten (with tragic

results!)

If these calculations are performed for say a (passive)transformer with winding ratios of 4 output turns perinput turn, Vout = 4 when Vin = 1. If the last term isneglected, the gain appears to be G = 20log(4) = 12 dB.This is a curious result for a passive device!If the last term is used, Rout = 16 for Rin = 1, so thelast term is -12 dB. This restores the balance at G = 0as expected for an ideal passive device.

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Using Decibels - 1

Rules:Multiply A x B:(Add dB values)

•Divide A / B:

(Subtract dB values)

dB)(

dBdB

)(log10)(log10

)/(log10

1010

10

BA

BA

BA

BA

dB)(

dBdB

)(log10)(log10

) x (log10

1010

10

BA

BA

BA

BA

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Using Decibels - 2

Rules:Squares:(Multiply by 2)

)dBin ( x 2

)(log20

)(log10 x 2

)(log10

10

10

210

A

A

A

A

•Square roots:

(Divide by 2)

)dBin ( x 2

1

)(log2

10

)(log10

10

10

A

A

A

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Thinking in dB

Its useful to be able to think in dBNote that 18 is 2*3*3.Since: 2 = 3 dBand: 3 = 4.8 dByou can find 18 in dBin your head by adding3 + 4.8 + 4.8 = 12.6You don’t even need acalculator!This is really handy forchecking link budgetsquickly.

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References in dB

dB values can be referenced to a standardThe standard is simply appended to dBTypical examples are:

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Link Budget

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Translating to dBsThe transmission formula can be written in dB as:

This form of the equation is easily handled as a spreadsheet (additions and subtractions!!)

The calculation of received signal based on transmitted power and all losses and gains involved until the receiver is called “Link Power Budget”, or “Link Budget”.

The received power Pr is commonly referred to as “Carrier Power”, C.

rrotherrapolaptar LGLLLLLLEIRPP

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Link Power Budget

Transmission:+ HPA Power- Transmission Losses (cables & connectors)+ Antenna Gain

EIRPTx

- Antenna Pointing Loss- Free Space Loss- Atmospheric Loss (gaseous, clouds, rain)- Rx Antenna Pointing Loss

Rx

Reception:+ Antenna gain- Reception Losses (cables & connectors)+ Noise Temperature Contribution

Pr

Now all factors are accounted for as additions and subtractions

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4 Easy Steps to a GoodLink Power Budget

First, draw a sketch of the link pathDoesn’t have to be artistic qualityHelps you find the stuff you might forget

Next, think carefully about the system of interestInclude all significant effects in the link power budgetNote and justify which common effects are insignificant here

Roll-up large sections of the link power budgetIe.: TXd power, TX ant. gain, Path loss, RX ant. gain, RX lossesShow all components for these calculations in the detailed budgetUse the rolled-up results in build a link overview

Comment the link budgetAlways, always, always use units on parameters (dBi, W, Hz ...)Describe any unusual elements (eg. loss caused by H20 on radome)

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Simple Link Power Budget

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Why calculate Link Budgets?System performance tied to operation thresholds.Operation thresholds Cmin tell the minimum power that should be received at the demodulator in order for communications to work properly.Operation thresholds depend on:

Modulation scheme being used.Desired communication quality.Coding gain.Additional overheads.Channel Bandwidth.Thermal Noise power.

We will see more on these items in the

next classes.

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Closing the LinkWe need to calculate the Link Budget in order to verify if we are “closing the link”.

Pr >= Cmin Link Closed

Pr < Cmin Link not closed

Usually, we obtain the “Link Margin”, which tells how tight we are in closing the link:

Margin = Pr – Cmin

Equivalently:Margin > 0 Link ClosedMargin < 0 Link not closed

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Carrier to Noise RatiosC/N: carrier/noise power in RX BW (dB)

Allows simple calculation of margin if:Receiver bandwidth is knownRequired C/N is known for desired signal type

C/No:carrier/noise p.s.d. (dbHz)Allows simple calculation of allowable RX bandwidth if required C/N is known for desired signal typeCritical for calculations involving carrier recovery loop performance calculations

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System Figure of Merit

G/Ts: RX antenna gain/system temperatureAlso called the System Figure of Merit, G/Ts

Easily describes the sensitivity of a receive systemMust be used with caution:

• Some (most) vendors measure G/Ts under ideal conditions only

• G/Ts degrades for most systems when rain loss increases

– This is caused by the increase in the sky noise component

– This is in addition to the loss of received power flux density

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System Noise Power

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System Noise Power - 1

Performance of system is determined by C/N ratio.Most systems require C/N > 10 dB. (Remember, in dBs: C - N > 10 dB)

Hence usually: C > N + 10 dBWe need to know the noise temperature of our receiver so that we can calculate N, the noise power (N = Pn).

Tn (noise temperature) is in Kelvins (symbol K):

2739

5320 FTKT 2730 CTKT

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System Noise Power - 2System noise is caused by thermal noise sources

External to RX system• Transmitted noise on link• Scene noise observed by antenna

Internal to RX system

The power available from thermal noise is:

where k = Boltzmann’s constant = 1.38x10-23 J/K(-228.6 dBW/HzK),

Ts is the effective system noise temperature, andB is the effective system bandwidth

(dBW) BkTN s

We will see more on calculating Ts next class.