1 satellite link design – part ii joe montana it 488 – fall 2003

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Satellite Link Design – Part II

Joe MontanaIT 488 – Fall 2003

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Agenda

• System Noise Power (Part II)

• Numerical Examples

3

Acknowledgements:

• Dr. James W. LaPean course notes• Dr. Jeremy Allnutt course notes

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System Noise Power

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System Noise Power - 1Performance of system is determined by C/N ratio.Direct relation between C/N and BER for digital systems.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

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Noise Spectral DensityN = K.T.B N/B = N0 is the noise spectral density (density of noise power per hertz):

N0 = noise spectral density is constant up to 300GHz.All bodies with Tp >0K radiate microwave energy.

(dBW/Hz) 0 ss kT

B

BkT

B

NN

8

System Noise Temperature1) System noise power is proportional to

system noise temperature2) Noise from different sources is

uncorrelated (AWGN)Therefore, we can

Add up noise powers from different contributionsWork with noise temperature directly

So:

But, we must:Calculate the effective noise temperature of each contributionReference these noise temperatures to the same location

Additive White Gaussian Noise (AWGN)

RXlinelossLNAantennadtransmittes TTTTTT

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Typical Receiver

(Source: Pratt & Bostian Chapter 4, p115)

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Noise Model


Noise is added and then multiplied by the gain of the device (which is now assumed to be noiseless since the noise was already added prior to the device)

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Equivalent Noise Model of Receiver


Equivalent model: Equivalent noise Ts is added and then multiplied by the equivalent gain of the device, GRFGmGIF

(noiseless).

12

Calculating System Noise Temperature - 1

Receiver noise comes from several sources.We need a method which reduces several sources to a single equivalent noise source at the receiver input.Using model in Fig. 4.5.a gives:

End)-(Front

(Mixer)

(IF)

inRFRFmIF

mmIF

IFIFn

TTkBGGG

BkTGG

BkTGP

(Eqn. 4.15)

13


Divide equation 4.15 by GIFGmGRFkB:

If we replace the model in Fig. 4.5.a by that in Fig. 4.5b

RFm

IF

RF

minRFRFmIFn GG

T

G

TTTkBGGGP

(Eqn. 4.16)

BkTGGGP sRFmIFn (Eqn. 4.17)

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Equate Pn in Eqns 4.16 and 4.17:

Since C is invariably small, N must be minimized.How can we make N as small as possible?

RFm

IF

RF

minRF GG

T

G

TTTT S (Eqn. 4.18)

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Reducing Noise Power

Make B as small as possible – just enough bandwidth to accept all of the signal power (C ).Make TS as small as possible

Lowest TRF

Lowest Tin (How?)

High GRF

If we have a good low noise amplifier (LNA), i.e., low TRF, high GRF, then rest of receiver does not matter that much.

inRFRFm

IF

RF

minRF TT

GG

T

G

TTTT

S

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Reducing Noise Power Low Noise Amplifier

Parametric amplifier (older technology, complex and expensive):Cooled (thermo-electrically or liquid nitrogen or helium):

- 4 GHz : 30 K- 11 GHz: 90 K

Uncooled:- 4 GHz : 40 K- 11 GHz: 100 K

Ga AS FET (Galium Arsenide Field-Effect Transistor): Cooled (thermo-electrically):

- 4 GHz : 50 K- 11 GHz: 125 K

Uncooled:- 4 GHz : 50 K- 11 GHz: 125 K

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Reducing Noise Power Discussion on Tin

Earth Stations: Antennas looking at space which appears cold and produces little thermal noise power (about 50K).Satellites: antennas beaming towards earth (about 300 K):

Making the LNA noise temperature much less gives diminishing returns. Improvements aim reduction of size and weight.

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Antenna Noise Temperature

Contributes for Tin Natural Sources (sky noise):

Cosmic noise (star and inter-stellar matter), decreases with frequency, (negligible above 1GHz). Certain parts of the sky have punctual “hot sources” (hot sky).Sun (T 12000 f-0.75 K): point earth-station antennas away from it.Moon (black body radiator): 200 to 300K if pointed directly to it.Earth (satellite)Propagation medium (e.g. rain, oxygen, water vapor): noise reduced as elevation angle increases.

Man-made sources:Vehicles, industrial machineryOther terrestrial and satellite systems operating at the same frequency of interest.

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Antenna Noise Temperature

Useful approximation for Earth Station antenna temperature on clear sky (no rain): Earth Station Antenna - Noise Temperature

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80 90 100

Elevation Angle (degrees)

Ta

(K)

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Noise from Active Devices

Active devices produce noise from:Dissipative losses in the active deviceDissipative losses in the supporting circuitsElectrical noise caused by the active device

The effective temperature of active devices is specified by the manufacturer

Can be measured by a couple of methodsCan be (somewhat laboriously) calculatedAssumes specific impedance matches

The effective temperature is (almost) always specified at the input of the deviceThe noise is often given as a noise figure (see later)

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Noise from Lossy Elements -1All lossy elements reduce the amount of power transmitted through them

Carrier or signal powerNoise power

The noise temperature contribution of a loss is:

G = 1/Loss

where G is the “gain” (smaller than unit) of the lossy element, also called transmissivity (Pout /Pin) and T0 is the physical temperature of the loss.Note the temperature is at the output of the loss.

[K] G)-(1TT 0N

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Noise from Lossy Elements –2Assume lossy element has gain = GL=1/LNotes: GL <0 dB (because 0 < GL < 1)

T0= physical temperature

G

Noisy, Lossy

S SxG+N

G

Noiseless

S SxG+

N=kTNB+

TN Noise Source at output:

TN=T0(1-G) [K]

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Noise from Lossy Elements –2

G

Noisy, Lossy

S SxG+N

G

Noiseless

S SxG+

N=kTNB+

TN

Noise Source at input:

T’N = TN/G = T0(1/G-1) [K]

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Noise FigureNoise Figure:

Relates the noise temperature to a referenceEasily used in dB scale

Definition:

Convert to Noise Temperature:

T0 = standard noise temperature = 290 K

G = gain of network

)1(0 ne FTT

GBkT

N

NS

NSF

N

out

out

inN

0/

/

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Translating NoiseWe need to have all of the noise referenced to a common pointThe output flange of a lossless antenna is the standard referenceNoise temperature can be moved through components just like power is since the two are linearly related

This is only valid if the system is linearNote that the RX bandwidth must still be wide enough for the signal!

If the temperatures T2 and T3 are referenced to the input (T1 at the output of L1) of the respective component, then:

L1 T3

Tin

G2, T2

Ta Tb Tc

321122122

32111

2

32

11

111

11

1 1

1

TTTTGGTGGTGTG

TTTGTGTT

G

TT

GG

TTTTGT

LG

insysasysbsyscinsysasysb

insysaphys

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Multi-bounce link budgets

If the C/N ratios for each of the linear bent pipe transponder links are available:

so long as the noise is uncorrelated between the linksFor baseband processing links:

111

2

1

1

...

ntotal N

C

N

C

N

C

N

C

ntotal BERBERBERBER ...21

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So many trade-offs !!!

rotherpolrataap

rttr LLLLLLL

GGPP

BKT

P

N

C

s

r

RFm

IF

RF

minRF GG

T

G

TTTT S

2D

G

24

R

LpFLa

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Numerical Examples

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Noise TemperatureExample – 4.2.1

4GHz ReceiverTin =Ta =50 K

TRF =50 K GRF =23 dB (=200)

Tm =500 K Gm =0 dB (=1)

TIF =1000 K GIF =50 dB (=1000)

Tin=50 KGRF=200 Gm=1 GIF=1000

TRF=50 K Tm=500 K TIF=1000 K

System Temperature referred to this point

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K

GG

T

G

TTTT

RFm

IF

RF

minRF

5.10755.25050

1 x 200

1000

200

5005050

S

Solution:

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If mixer had 10 dB lossGm = -10 dB (=0.1)

Comment: GRFGm is too small here, so the IF amplifier contribution is large.

If we made GRF = 50 dB (=105)

KT 5.15220

1000

200

5005050 S

KT 1.100000,10

1000

000,100

5005050 S

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Noise Temperature – Lossy ElementsExample – 4.2.2

In original problem, insert lossy waveguide with 2 dB attenuation between antenna and LNA

Tin=50 KGRF=200 Gm=1 GIF=1000

TRF=50 K Tm=500 K TIF=1000 K

System Temperature referred to this point

GL

TL

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Loss of 2 dB, obtain GL and TL:

K

GT

dBG

LL

L

3.107

)63.01(290

)1(290

63.058.1

12

K 8.138

K 3.0710.63 x 05

TG LLain

TT

•Input noise power is attenuated by 2 dB:New Tin:

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K

GG

T

G

TTTT

RFm

IF

RF

mRFin

3.19655.2508.138

1 x 200

1000

200

500508.138

S

Increased from 107.5 to 196.3 K at the same reference point:

dBT

T

BKT

BKT

N

N

s

s

s

s 6.282.1 1

2

1

2

1

2

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Inserting 2 dB loss in the front end of the received carrier power (C ) by 2 dB and increased noise temperature by 88.8 K, from 107.5 K to 196.3 K (comparing at the same reference point).N has increased by 2.6 dB.C has decreased by 2 dB.Result: C/N has been reduced by 4.6 dB!

Moral:Losses before LNA must be kept very small.

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Antenna Example - 13.7.1 Earth subtends an angle of 17 degrees when

viewed from geostationary orbit. a. What should be the dimensions of a reflector antenna

to provide global coverage at 4 GHz?b. What will be the antenna gain if efficiency =0.55?

a. 3dB = 17 degrees

b. =0.55

mD

D

dB

dB

33.017

075.0x7575

75

3

3

dBGain

EdB

23.2065.10517

7555.0

752

22

3

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Antenna Example - 23.7.1 Continental US subtends a “rectangle” of 6 x 3 degrees.Find gain and dimensions of a reflector antenna to provide global coverage at 11 GHz? a. Using 2 antennas (3 x3 degrees)

b. Using only 1 antenna (3 x 6 degrees)a. 3dB = 3 degrees

b. 3dBA = 6 degrees

3dBE = 3 degrees

mDdB

68.03

0273.0x7575

3

dBGaindB

2.357.33923

7555.0

7522

3

dBGain

EdBAdB

3.323.16963x6

7555.0

75 2

33

2

mD

D

dBA

E

34.06

0273.0x7575

0.68m

3

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Power Budget Example - 14.1.1 Satellite at 40,000 km (range)

Transmits 2WAntenna gain Gt = 17 dB (global beam)

Calculate: a. Flux density on earth’s surface b. Power received by antenna with effective aperture of 10m2

c. Gain of receiving antenna. d. Received C/N assuming Ts =152 K, and Bw =500 MHz

a. Using Eqn. 4.3: (Gt = 17 dB = 50)

2215-

2722

dBW/m 143W/m10 x 4.97

) x(4x104

50 x 2

44

R

GP

R

EIRPF tt

(Solving in dB…)

dBW/m2 1431521120

114

dB[meter] )10x4(log x 2 R

dBW 20173)(27

102

F

dB

GtPtEIRP

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Power Budget Example - 1b. Received Power

dBWW 13310 x 4.97 P

10 x )(4.97x10 A x FP14-

r

-15r

(Solving in dB…)

dBW 133

10)143(

r

r

P

AFP

c. Gain given Ae = 10 m2 and Frequency = 11GHz ( eqn. 4.7)

dBA

G er 3.52

0273.010 x 4π4

2

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Power Budget Example - 1b. System Noise Temperature

dBNC

NCNC

dBWW

dBW

BTKor

KTB

dBdBdB

2.13/

)79.119(133/

13310 x 4.97 PC

97.119

99.8682.21 6.228

10 x 500 x 152x 01 x 38.1PN

14-r

623n

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Power Budget Example - 2Generic DBS-TV:

Received PowerTransponder output power , 160 W 22.0 dBWAntenna beam on-axis gain 34.3 dBPath loss at 12 GHz, 38,500 km path -205.7 dBReceiving antenna gain, on axis 33.5 dBEdge of beam -3.0 dBMiscellaneous losses -0.8 dBReceived power, C -119.7 dBW

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Power Budget Example - 2Noise powerBoltzmann’s constant, k -228.6

dBW/K/HzSystem noise temperature, clear air, 143 K 21.6

dBKReceiver noise bandwidth, 20MHz 73.0

dBHzNoise power, N -134.0 dBW C/N in clear air 14.3 dBLink margin over 8.6 dB threshold 5.7

dBLink availability throughout US Better than

99.7 %

1 satellite link design – part ii joe montana it 488 – fall 2003

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