SATELLITE LINK DESIGNSATELLITE LINK DESIGN

CHAPTER 3CHAPTER 3

Basic Transmission TheoryBasic Transmission Theory

The fundamental to the understanding of sat The fundamental to the understanding of sat comm syst.comm syst.

These will include all the parameters such as:These will include all the parameters such as: Flux densityFlux density EIRPEIRP Power receivedPower received Power transmitPower transmit System noise temperatureSystem noise temperature Carrier to noise power ratioCarrier to noise power ratio

Flux DensityFlux Density

Transmitting source radiate power Pt uniformly in free Transmitting source radiate power Pt uniformly in free space.space.

At distance R from the source, the flux density crossing the At distance R from the source, the flux density crossing the surface of a sphere with radius R is given by (ideal surface of a sphere with radius R is given by (ideal antenna):antenna):

F = Pt/ (4F = Pt/ (4ππRR22)) W/m2

Isotropic Source

EIRP = Pt Gt

Distance R (m)

Area A (m2)

Flux density F (W/ m2)

Flux Density For Real Flux Density For Real AntennaAntenna

Real antenna are directionalReal antenna are directional It has gain G(It has gain G(θθ) = the ratio of power per unit solid angle radiated in ) = the ratio of power per unit solid angle radiated in

a direction a direction θθ to the average power radiated per unit solid angle. to the average power radiated per unit solid angle. G(G(θθ) = P) = P((θθ)/ (P)/ (P00/4/4ππ) )

G= 4 G= 4 ππ A Aee/ / λλ2 , 2 , G = G = ηη ((ππD/ D/ λλ))22

Where:Where: PP((θθ) = ) = power radiated per unit solid angle by the antennapower radiated per unit solid angle by the antenna PP0 0 = = total power radiated by the antennatotal power radiated by the antenna G(G(θθ) = ) = the gain of the antenna at an angle the gain of the antenna at an angle θθ θθ = = boresight directionboresight direction

ContinuedContinued

Flux density for real antenna in the Flux density for real antenna in the direction of boresight at distance R meter direction of boresight at distance R meter where G(where G(θθ) at angle ) at angle θθ = 0º = 0º

F = PtGt/ F = PtGt/ (4(4ππRR22)) W/m2 Where:Where:

PtGt = Effective isotropic radiated PowerPtGt = Effective isotropic radiated Power The combination of tx power and antenna gain in The combination of tx power and antenna gain in

terms of equivalent isotropic source with power terms of equivalent isotropic source with power radiating uniformly in all directions.radiating uniformly in all directions.

ContinuedContinued

Antenna with physical aperture area of Ar mAntenna with physical aperture area of Ar m22

The energy incident on aperture is reflected away from the The energy incident on aperture is reflected away from the antenna and some is absorbed by lossy componentsantenna and some is absorbed by lossy components

This reduction in efficiency is describe as an effective This reduction in efficiency is describe as an effective aperture Aaperture Aee

Where:Where:

AAee = = ηη Ar m Ar m22

ηη = aperture efficiency = aperture efficiency - all losses between- all losses between the incident wavefronts and the incident wavefronts and the antenna output port. (diffraction effect, the antenna output port. (diffraction effect, feeder feeder loss, blockage)loss, blockage)

Power ReceivedPower Received

For ideal antenna, the power received:For ideal antenna, the power received: Pr = F x APr = F x Ae e wattswatts

Pr = Pt APr = Pt Aee / (4 / (4ππRR22) ) wattswatts

For real antenna, the power received:For real antenna, the power received: Pr = Pt Gt Pr = Pt Gt AAee / / (4(4ππRR22))

Where : Where : AAee = = ηη Ar m Ar m22

Rearrange the equation:Rearrange the equation: Pr = (Pt Gt Pr = (Pt Gt AAee )/ )/ (4(4ππRR22)…………. (i))…………. (i) G= (4 G= (4 ππ A Aee)/ )/ λλ2……………………………………2……………………………………(ii)(ii) Subs (ii) in (i)Subs (ii) in (i)

Pr = (Pt Gt Pr = (Pt Gt GrGr )/ )/ (4(4ππR/ R/ λλ))22

= power received in any radio link= power received in any radio link

Lp =Lp = (4(4ππR/ R/ λλ))22

=path loss / free space loss=path loss / free space loss =the way energy spread out as an emwave =the way energy spread out as an emwave

travels travels away from any transmitting source away from any transmitting source in 3 dimensional in 3 dimensional space. space.

ContinuedContinued

There are other losses need to be There are other losses need to be considered:considered: Losses in atmosphere, rain, water vaporLosses in atmosphere, rain, water vapor Losses in the antenna, miss pointing, Losses in the antenna, miss pointing,

feeder lossfeeder loss Rewrite the equation:Rewrite the equation:

Pr = EIRP + Gr – Lp – Lo dBWPr = EIRP + Gr – Lp – Lo dBW

ContinuedContinued

Example 1Example 1

A sat at a distance of 40000 km from A sat at a distance of 40000 km from a point on the earth’s surface a point on the earth’s surface radiates a power of 10 w from an radiates a power of 10 w from an antenna with a gain of 17 dB in the antenna with a gain of 17 dB in the direction of the observer. Find the direction of the observer. Find the flux density at the receiving point flux density at the receiving point and the power received by an and the power received by an antenna at this point with an antenna at this point with an effective area of 10 meffective area of 10 m22..

Example 2Example 2 A geostationary satellite at a distance of 37000 km A geostationary satellite at a distance of 37000 km

operates at a frequency of 14 GHz. It radiates power operates at a frequency of 14 GHz. It radiates power from an antenna with a gain of 16 dB. The flux density from an antenna with a gain of 16 dB. The flux density at receiving point is 2.86 x 10at receiving point is 2.86 x 10-14-14 W/m W/m22 in the direction in the direction of boresight. The receiving antenna has a physical of boresight. The receiving antenna has a physical aperture of 40 maperture of 40 m22 with efficiency of 55%. with efficiency of 55%.

Calculate:Calculate:

i)i) the power transmit by the transmitter from the the power transmit by the transmitter from the sat to the e/s sat to the e/s in dB.in dB.

ii)ii) the EIRP of the sat in dBthe EIRP of the sat in dBiii)iii) the received gain by e/s in dBthe received gain by e/s in dBiv)iv) the path loss during transmission in dBthe path loss during transmission in dBv)v) the received power at e/s in dBthe received power at e/s in dB

System NoiseSystem Noise Arises from the random thermal motion of Arises from the random thermal motion of

electrons in various resistive and active devices electrons in various resistive and active devices in the receiver.in the receiver.

Thermal noise also generated in the lossy Thermal noise also generated in the lossy components of antenna.components of antenna.

The available noise power from a thermal noise The available noise power from a thermal noise source is given by:source is given by:

Pn = kTBPn = kTB Where:Where:

T = noise tempT = noise temp B = noise bandwidthB = noise bandwidth K = 1.38 x 10K = 1.38 x 10-23-23 J/K = Boltzmann constant J/K = Boltzmann constant

The noise power per unit bandwidth is The noise power per unit bandwidth is termed as the noise power spectral termed as the noise power spectral density, Ndensity, N00..

NN00 = Pn/ B = kT = Pn/ B = kT

The noise temp is directly related to the The noise temp is directly related to the physical temp of the noise source but is physical temp of the noise source but is not always equal to it.not always equal to it.

ContinuedContinued

Example 3Example 3

An antenna has a noise temp of 35 k An antenna has a noise temp of 35 k and is matched into receiver which and is matched into receiver which has a noise temp of 100 k. calculate:has a noise temp of 100 k. calculate:

i)i) the noise power densitythe noise power density

ii)ii) the noise power for a the noise power for a bandwidth bandwidth of 36 MHzof 36 MHz

Antenna NoiseAntenna Noise Antenna operating in the receiving mode Antenna operating in the receiving mode

introduce noise into sat circuit.introduce noise into sat circuit. The antenna noise can be classified into 2 groups:The antenna noise can be classified into 2 groups: Sky noiseSky noise

The microwave radiation which is present throughout The microwave radiation which is present throughout the universe.the universe.

Originate from matter in any form at finite temp.Originate from matter in any form at finite temp. Rainfall introduce attenuation, therefore it degrades Rainfall introduce attenuation, therefore it degrades

transmission.transmission. Antenna lossAntenna loss

Add to the noise received as radiationAdd to the noise received as radiation The total antenna noise temp is in the sum of The total antenna noise temp is in the sum of

equivalent noise temp of all these sources.equivalent noise temp of all these sources.

Amplifier Noise Amplifier Noise TemperatureTemperature

The input noise energy coming from the antenna is:The input noise energy coming from the antenna is:

The output noise energy:The output noise energy:

The total noise referred to the i/p is simply:The total noise referred to the i/p is simply:

Amplifier

G, T1Tant

N0, inN0, out

Figure 1

N0,in = kTant

N0,out = G k (Tant + T1)

N0,in = k (Tant + T1)

= N0,out / G

The noise energy of amp 2 referred to its own i/p:The noise energy of amp 2 referred to its own i/p:

The noise i/p to ampThe noise i/p to amp 2 from the preceding stages:2 from the preceding stages:

Thus the total noise energy referred to amp2 i/p:Thus the total noise energy referred to amp2 i/p:

Amp 1

G1, T1

Tant

N0, 1 N0, out

Amp 2

G2, T2

N0, 2

Figure 2

ContinuedContinued

N0,2 = kT2

N0,in2 = G1 k (Tant + T1)

N0,in2 = G1 k (Tant + T1) + kT2

The total noise referred to the i/p is :The total noise referred to the i/p is :

System noise temp may defined as Ts by:System noise temp may defined as Ts by:

ContinuedContinued

N0,1 = k [Tant + T1 + (T2/G1)] = N0,2/ G1

N0,1 = kTs

Ts = [Tant + T1 + (T2/G1)]

Ts = [Tant + T1 + (T2/G1) + (T3/G1 G2) ]

Example 4Example 4 Suppose we have 4 GHz receiver with the Suppose we have 4 GHz receiver with the

following gains and noise temp:following gains and noise temp:

Tant = 25 k GRF = 23 dBTant = 25 k GRF = 23 dBTRF = 50 kTRF = 50 k GIF = 30 dBGIF = 30 dBTm = 500 kTm = 500 kTIF = 1000kTIF = 1000k

i)i) Calculate the syst noise temp assuming that Calculate the syst noise temp assuming that the mixer has a gain Gm = 0 dBthe mixer has a gain Gm = 0 dB

ii)ii) Recalculate the syst noise temp when the mixer Recalculate the syst noise temp when the mixer has a 10 dB losshas a 10 dB loss

iii)iii) How can the noise of temp of the receiver be How can the noise of temp of the receiver be minimized when the mixer has a loss of 10 dB?minimized when the mixer has a loss of 10 dB?

Noise FactorNoise Factor

In defining the noise factor of an In defining the noise factor of an amp, the source is taken to be room amp, the source is taken to be room temp, denoted by Ttemp, denoted by T00 (290 k). (290 k).

The i/p noise from such a source is The i/p noise from such a source is kTkT00..

The o/p from the amp is:The o/p from the amp is:N0, out = FGkT0

Relationship between noise temp and noise Relationship between noise temp and noise factor:factor:

Te = noise temp of the ampTe = noise temp of the amp Tant = TTant = T00 = the source at room temp = the source at room temp

Thus:Thus:

The noise figure (f) is simply noise factor (F) The noise figure (f) is simply noise factor (F) expressed in dB.expressed in dB.

GK (T0 + Te) = FGKT0

Te = (F -1)T0

f = 10 log F

ContinuedContinued

1N21

1N

21

3

1

21

G...GGF

..GG1F

G1F

FF

An LNA is connected to a receiver An LNA is connected to a receiver which has a noise figure, f= 12 dB. which has a noise figure, f= 12 dB. The gain of the LNA is 40 dB and its The gain of the LNA is 40 dB and its noise temp is 120 k. calculate the noise temp is 120 k. calculate the overall noise temp referred to the overall noise temp referred to the LNA input.LNA input.

Example 5Example 5

i)i) Calculate the equivalent noise Calculate the equivalent noise temperature for a noise figure of 5 temperature for a noise figure of 5 dB and 5.6 dB. Assume the dB and 5.6 dB. Assume the environmental temperature is 300 environmental temperature is 300 K.K.

ii)ii) For equivalent noise bandwidth of For equivalent noise bandwidth of 15 MHz and total noise power of 15 MHz and total noise power of 0.0357 pW, determine the noise 0.0357 pW, determine the noise density and equivalent noise temp.density and equivalent noise temp.

Example 6Example 6

OCT 2004

Overall System Noise Overall System Noise TemperatureTemperature

Figure above shows a typical rx antenna syst.Figure above shows a typical rx antenna syst. Applying the previous sections yields for the syst noise Applying the previous sections yields for the syst noise

temp referred to the i/p:temp referred to the i/p:

1

0

1

01ants

GT)1F(L

GT)1L(

TTT

LNA

G1, T1

TantReceiver

FLoss L:1

Cable

Figure 3 shows the cable is after the LNA

Thus the equation:Thus the equation:

LNA

G1, T1

TantReceiver

FLoss L:1

Cable

Figure 4 shows the cable is before the LNA

1

010ants

GT)1F(L

LTT)1L(TT

ContinuedContinued

Example 7Example 7

i)i) For the syst shown in fig 3, the For the syst shown in fig 3, the receiver noise figure is 12 dB, the receiver noise figure is 12 dB, the cable loss is 5 dB, the LNA gain is 50 cable loss is 5 dB, the LNA gain is 50 dB and its noise temp is 150k. The dB and its noise temp is 150k. The antenna noise temp is 35 k. antenna noise temp is 35 k. Calculate the noise temp referred to Calculate the noise temp referred to the input. the input.

ii)ii) Repeat the calculation when the Repeat the calculation when the system of fig 3 is arranged as shown system of fig 3 is arranged as shown in fig 4.in fig 4.

Example 8Example 8

A receiving syst consists of an A receiving syst consists of an antenna having a noise temperature antenna having a noise temperature of 60 K, feeding directly into LNA. of 60 K, feeding directly into LNA. The amplifier has a noise The amplifier has a noise temperature of 120K and gain of 45 temperature of 120K and gain of 45 dB. The coaxial feeder between the dB. The coaxial feeder between the LNA and the main receiver has a loss LNA and the main receiver has a loss of 2 dB and the main receiver has a of 2 dB and the main receiver has a noise figure of 9 dB. Calculate the noise figure of 9 dB. Calculate the syst noise temp referred to input.syst noise temp referred to input.

Carrier To Noise RatioCarrier To Noise Ratio A measure of the performance of a sat link.A measure of the performance of a sat link.

Carrier power to noise power Carrier power to noise power Link budget calculationLink budget calculation

Denoted by C/N or C/NDenoted by C/N or C/N00 which equivalent which equivalent to Pto PRR/P/PTT..

RFLkTG

BOANC

kLossesTG

EIRPNC

BwTkLossesGEIRPNC

s

rm

s

r

sr

00

0

Example 8Example 8 In a link calculation of 2 GHz, the free In a link calculation of 2 GHz, the free

space loss is 206 dB, the antenna space loss is 206 dB, the antenna pointing loss is 1 dB and the pointing loss is 1 dB and the atmosphere absorption is 2 dB. The atmosphere absorption is 2 dB. The receiver G/T ratio is 19.5 dB/K and receiver G/T ratio is 19.5 dB/K and the receiver feeder losses are 1 dB. the receiver feeder losses are 1 dB. The EIRP is 48 dBW. Calculate the The EIRP is 48 dBW. Calculate the carrier to noise spectral density ratio.carrier to noise spectral density ratio.

UplinkUplink The uplink of sat cct is the one in which the e/s is transmitting the signal and The uplink of sat cct is the one in which the e/s is transmitting the signal and

the sat is receiving it.the sat is receiving it.

Where:Where:

(C/N0)u = EIRPe/s + (G/T)s – FSL - losses - k

(C/N0)u = Ae +Ψ m+ (G/T)s – RFL - k

Ae +Ψ m = EIRPe/s – FSL - losses + RFL

Example 9Example 9 An uplink operates at 14 GHz and the An uplink operates at 14 GHz and the

flux density required to saturate the flux density required to saturate the transponder is -120 dB (W/Mtransponder is -120 dB (W/M22). The ). The free space loss is 207 dB and the free space loss is 207 dB and the other propagation losses amount to 2 other propagation losses amount to 2 dB. Calculate the e/s EIRP required dB. Calculate the e/s EIRP required for saturation assuming clear sky for saturation assuming clear sky conditions. Assume RFL is negligible.conditions. Assume RFL is negligible.

Input BackoffInput Backoff When a number of carriers increased in When a number of carriers increased in

TWTA, the operating point must be backoff to TWTA, the operating point must be backoff to a linear region of the transfer characteristic a linear region of the transfer characteristic to reduce the effects of IM distortion.to reduce the effects of IM distortion.

Suppose the saturation flux density for a Suppose the saturation flux density for a single carrier operation is known. Input single carrier operation is known. Input backoff will be specified for multiple carrier backoff will be specified for multiple carrier operation referred to the single carrier operation referred to the single carrier saturation level.saturation level.

The e/s EIRP will have to be reduced by the The e/s EIRP will have to be reduced by the specified backoff (BO).specified backoff (BO).

Example 10Example 10

An uplink at 14GHz requires a An uplink at 14GHz requires a saturation flux density of -91.4 saturation flux density of -91.4 dBW/MdBW/M22 and an input backoff of 11 and an input backoff of 11 dB. The sat G/T is -6.7 dB/K and dB. The sat G/T is -6.7 dB/K and receiver feeder loss amount to 0.6 receiver feeder loss amount to 0.6 dB. Calculate the carrier to noise dB. Calculate the carrier to noise density ratio.density ratio.

DownlinkDownlink

The sat transmitting the signal and The sat transmitting the signal and the e/s is receiving it.the e/s is receiving it.

(C/N0)d = EIRPs + (G/T)e/s – FSL - losses - k(C/N)d = EIRPs + (G/T)e/s – FSL - losses – k - Bw

Output BackoffOutput Backoff When i/p BO is employed, a When i/p BO is employed, a

corresponding o/p BO must be corresponding o/p BO must be allowed in the downlink transmission.allowed in the downlink transmission.

The relationship between IBO and The relationship between IBO and OBO in decibels is:OBO in decibels is:

OBO = IBO – 5 dB

Example 11Example 11

A satellite tv signal occupies the full A satellite tv signal occupies the full transponder bandwidth of 36 MHz transponder bandwidth of 36 MHz and it must provide a C/N ratio at the and it must provide a C/N ratio at the destination e/s of 22 dB. Given that destination e/s of 22 dB. Given that the total transmission losses are 200 the total transmission losses are 200 db and te destination e/s (G/T) ratio db and te destination e/s (G/T) ratio is 31 dB/K. calculate the satellite is 31 dB/K. calculate the satellite EIRP required.EIRP required.

Example 12Example 12

The specified parameter for a The specified parameter for a downlink are sat saturation value of downlink are sat saturation value of EIRP 25 dBW. OBO is 6 dB; FSL is 196 EIRP 25 dBW. OBO is 6 dB; FSL is 196 dB; other losses 1.5 dB and e/s (G/T) dB; other losses 1.5 dB and e/s (G/T) 41 dB/K. Calculate the C/N41 dB/K. Calculate the C/N00 at the at the e/s.e/s.

Example 13Example 13 A multiple carrier circuit operates in the 6/4 GHz band A multiple carrier circuit operates in the 6/4 GHz band

with the following characteristic.with the following characteristic. UplinkUplink

Saturation flux density Saturation flux density -67.5-67.5 Ae Ae -37-37 IBOIBO 1111 G/TG/T -11.6-11.6

DownlinkDownlink Satellite EIRPSatellite EIRP 26.626.6 OBOOBO 66 FSLFSL 196.7196.7 G/TG/T 40.740.7 kk -228.6-228.6

Calculate C/N0 for both links and the total C/N0 for the Calculate C/N0 for both links and the total C/N0 for the transmission.transmission.